From cdb4ee20a83034d73b490994c9e3813757db0992 Mon Sep 17 00:00:00 2001 From: Christopher Rackauckas Date: Sat, 28 Jul 2018 07:11:44 -0700 Subject: [PATCH 1/2] Utilize precompilable bigints in their fullest of glory https://github.com/JuliaLang/julia/pull/28296#event-1757754127 --- src/ode_tableaus.jl | 1408 +++++++++++++++++++++---------------------- 1 file changed, 704 insertions(+), 704 deletions(-) diff --git a/src/ode_tableaus.jl b/src/ode_tableaus.jl index 04850eb..29539ac 100644 --- a/src/ode_tableaus.jl +++ b/src/ode_tableaus.jl @@ -1749,17 +1749,17 @@ function constructVernerEfficient6(T::Type = Float64) A[6,3]=246134619571490020064824665//1543816496655405117602368 A[6,4]=-13880495956885686234074067279//113663489566254201783474344 A[6,5]=755005057777788994734129//136485922925633667082436 - A[7,1]=-parse(BigInt,"1663299841566102097180506666498880934230261")//parse(BigInt,"30558424506156170307020957791311384232000") + A[7,1]=-1663299841566102097180506666498880934230261//30558424506156170307020957791311384232000 A[7,2]=0 A[7,3]=130838124195285491799043628811093033//631862949514135618861563657970240 - A[7,4]=-parse(BigInt,"3287100453856023634160618787153901962873")//parse(BigInt,"20724314915376755629135711026851409200") + A[7,4]=-3287100453856023634160618787153901962873//20724314915376755629135711026851409200 A[7,5]=2771826790140332140865242520369241//396438716042723436917079980147600 A[7,6]=-1799166916139193//96743806114007800 - A[8,1]=-parse(BigInt,"832144750039369683895428386437986853923637763")//parse(BigInt,"15222974550069600748763651844667619945204887") + A[8,1]=-832144750039369683895428386437986853923637763//15222974550069600748763651844667619945204887 A[8,2]=0 A[8,3]=818622075710363565982285196611368750//3936576237903728151856072395343129 - A[8,4]=-parse(BigInt,"9818985165491658464841194581385463434793741875")//parse(BigInt,"61642597962658994069869370923196463581866011") - A[8,5]=parse(BigInt,"31796692141848558720425711042548134769375")//parse(BigInt,"4530254033500045975557858016006308628092") + A[8,4]=-9818985165491658464841194581385463434793741875//61642597962658994069869370923196463581866011 + A[8,5]=31796692141848558720425711042548134769375//4530254033500045975557858016006308628092 A[8,6]=-14064542118843830075//766928748264306853644 A[8,7]=-1424670304836288125//2782839104764768088217 A[9,1]=382735282417//11129397249634 @@ -1818,45 +1818,45 @@ function constructVerner7(T::Type = Float64) A[5,1] = 2454451729//3841600000 A[5,3] = -9433712007//3841600000 A[5,4] = 4364554539//1920800000 - A[6,1] = -parse(BigInt,"6187101755456742839167388910402379177523537620")//parse(BigInt,"2324599620333464857202963610201679332423082271") - A[6,3] = parse(BigInt,"27569888999279458303270493567994248533230000")//parse(BigInt,"2551701010245296220859455115479340650299761") - A[6,4] = -parse(BigInt,"37368161901278864592027018689858091583238040000")//parse(BigInt,"4473131870960004275166624817435284159975481033") - A[6,5] = parse(BigInt,"1392547243220807196190880383038194667840000000")//parse(BigInt,"1697219131380493083996999253929006193143549863") + A[6,1] = -6187101755456742839167388910402379177523537620//2324599620333464857202963610201679332423082271 + A[6,3] = 27569888999279458303270493567994248533230000//2551701010245296220859455115479340650299761 + A[6,4] = -37368161901278864592027018689858091583238040000//4473131870960004275166624817435284159975481033 + A[6,5] = 1392547243220807196190880383038194667840000000//1697219131380493083996999253929006193143549863 A[7,1] = 11272026205260557297236918526339//1857697188743815510261537500000 A[7,3] = -48265918242888069//1953194276993750 A[7,4] = 26726983360888651136155661781228//1308381343805114800955157615625 A[7,5] = -2090453318815827627666994432//1096684189897834170412307919 - A[7,6] = parse(BigInt,"1148577938985388929671582486744843844943428041509")//parse(BigInt,"1141532118233823914568777901158338927629837500000") - A[8,1] = parse(BigInt,"1304457204588839386329181466225966641")//parse(BigInt,"108211771565488329642169667802016000") + A[7,6] = 1148577938985388929671582486744843844943428041509//1141532118233823914568777901158338927629837500000 + A[8,1] = 1304457204588839386329181466225966641//108211771565488329642169667802016000 A[8,3] = -1990261989751005//40001418792832 - A[8,4] = parse(BigInt,"2392691599894847687194643439066780106875")//parse(BigInt,"58155654089143548047476915856270826016") - A[8,5] = -parse(BigInt,"1870932273351008733802814881998561250")//parse(BigInt,"419326053051486744762255151208232123") - A[8,6] = parse(BigInt,"1043329047173803328972823866240311074041739158858792987034783181")//parse(BigInt,"510851127745017966999893975119259285040213723744255237522144000") + A[8,4] = 2392691599894847687194643439066780106875//58155654089143548047476915856270826016 + A[8,5] = -1870932273351008733802814881998561250//419326053051486744762255151208232123 + A[8,6] = 1043329047173803328972823866240311074041739158858792987034783181//510851127745017966999893975119259285040213723744255237522144000 A[8,7] = -311918858557595100410788125//3171569057622789618800376448 - A[9,1] = parse(BigInt,"17579784273699839132265404100877911157")//parse(BigInt,"1734023495717116205617154737841023480") + A[9,1] = 17579784273699839132265404100877911157//1734023495717116205617154737841023480 A[9,3] = -18539365951217471064750//434776548575709731377 - A[9,4] = parse(BigInt,"447448655912568142291911830292656995992000")//parse(BigInt,"12511202807447096607487664209063950964109") - A[9,5] = -parse(BigInt,"65907597316483030274308429593905808000000")//parse(BigInt,"15158061430635748897861852383197382130691") - A[9,6] = parse(BigInt,"273847823027445129865693702689010278588244606493753883568739168819449761")//parse(BigInt,"136252034448398939768371761610231099586032870552034688235302796640584360") - A[9,7] = parse(BigInt,"694664732797172504668206847646718750")//parse(BigInt,"1991875650119463976442052358853258111") + A[9,4] = 447448655912568142291911830292656995992000//12511202807447096607487664209063950964109 + A[9,5] = -65907597316483030274308429593905808000000//15158061430635748897861852383197382130691 + A[9,6] = 273847823027445129865693702689010278588244606493753883568739168819449761//136252034448398939768371761610231099586032870552034688235302796640584360 + A[9,7] = 694664732797172504668206847646718750//1991875650119463976442052358853258111 A[9,8] = -19705319055289176355560129234220800//72595753317320295604316217197876507 A[10,1] = -511858190895337044664743508805671//11367030248263048398341724647960 A[10,3] = 2822037469238841750//15064746656776439 - A[10,4] = -parse(BigInt,"23523744880286194122061074624512868000")//parse(BigInt,"152723005449262599342117017051789699") - A[10,5] = parse(BigInt,"10685036369693854448650967542704000000")//parse(BigInt,"575558095977344459903303055137999707") - A[10,6] = -parse(BigInt,"6259648732772142303029374363607629515525848829303541906422993")//parse(BigInt,"876479353814142962817551241844706205620792843316435566420120") + A[10,4] = -23523744880286194122061074624512868000//152723005449262599342117017051789699 + A[10,5] = 10685036369693854448650967542704000000//575558095977344459903303055137999707 + A[10,6] = -6259648732772142303029374363607629515525848829303541906422993//876479353814142962817551241844706205620792843316435566420120 A[10,7] = 17380896627486168667542032602031250//13279937889697320236613879977356033 α[1] = 96762636172307789//2051985304794103980 α[4] = 312188947591288252500000//1212357694274963646019729 α[5] = 13550580884964304000000000000//51686919683339547115937980629 - α[6] = parse(BigInt,"72367769693133178898676076432831566019684378142853445230956642801")//parse(BigInt,"475600216991873963561768100160364792981629064220601844848928537580") + α[6] = 72367769693133178898676076432831566019684378142853445230956642801//475600216991873963561768100160364792981629064220601844848928537580 α[7] = 1619421054120605468750//3278200730370057108183 α[8] = -66898316144057728000//227310933007074849597 α[9] = 181081444637946577//2226845467039736466 αEEst[1] = 117807213929927//2640907728177740 αEEst[4] = 4758744518816629500000//17812069906509312711137 αEEst[5] = 1730775233574080000000000//7863520414322158392809673 - αEEst[6] = parse(BigInt,"2682653613028767167314032381891560552585218935572349997")//parse(BigInt,"12258338284789875762081637252125169126464880985167722660") + αEEst[6] = 2682653613028767167314032381891560552585218935572349997//12258338284789875762081637252125169126464880985167722660 αEEst[7] = 40977117022675781250//178949401077111131341 αEEst[10] = 2152106665253777//106040260335225546 A = map(T,A) @@ -1907,49 +1907,49 @@ function constructVerner8(T::Type = Float64) A[8,5] = -1024030607959889//168929280000000 A[8,6] = 1501408353528689//265697280000000 A[8,7] = 6070139212132283//92502016000000 - A[9,1] = -parse(BigInt,"1472514264486215803881384708877264246346044433307094207829051978044531801133057155")//parse(BigInt,"1246894801620032001157059621643986024803301558393487900440453636168046069686436608") - A[9,4] = -parse(BigInt,"5172294311085668458375175655246981230039025336933699114138315270772319372469280000")//parse(BigInt,"124619381004809145897278630571215298365257079410236252921850936749076487132995191") - A[9,5] = -parse(BigInt,"12070679258469254807978936441733187949484571516120469966534514296406891652614970375")//parse(BigInt,"2722031154761657221710478184531100699497284085048389015085076961673446140398628096") - A[9,6] = parse(BigInt,"780125155843893641323090552530431036567795592568497182701460674803126770111481625")//parse(BigInt,"183110425412731972197889874507158786859226102980861859505241443073629143100805376") - A[9,7] = parse(BigInt,"664113122959911642134782135839106469928140328160577035357155340392950009492511875")//parse(BigInt,"15178465598586248136333023107295349175279765150089078301139943253016877823170816") - A[9,8] = parse(BigInt,"10332848184452015604056836767286656859124007796970668046446015775000000")//parse(BigInt,"1312703550036033648073834248740727914537972028638950165249582733679393783") - A[10,1] = -parse(BigInt,"29055573360337415088538618442231036441314060511")//parse(BigInt,"22674759891089577691327962602370597632000000000") + A[9,1] = -1472514264486215803881384708877264246346044433307094207829051978044531801133057155//1246894801620032001157059621643986024803301558393487900440453636168046069686436608 + A[9,4] = -5172294311085668458375175655246981230039025336933699114138315270772319372469280000//124619381004809145897278630571215298365257079410236252921850936749076487132995191 + A[9,5] = -12070679258469254807978936441733187949484571516120469966534514296406891652614970375//2722031154761657221710478184531100699497284085048389015085076961673446140398628096 + A[9,6] = 780125155843893641323090552530431036567795592568497182701460674803126770111481625//183110425412731972197889874507158786859226102980861859505241443073629143100805376 + A[9,7] = 664113122959911642134782135839106469928140328160577035357155340392950009492511875//15178465598586248136333023107295349175279765150089078301139943253016877823170816 + A[9,8] = 10332848184452015604056836767286656859124007796970668046446015775000000//1312703550036033648073834248740727914537972028638950165249582733679393783 + A[10,1] = -29055573360337415088538618442231036441314060511//22674759891089577691327962602370597632000000000 A[10,4] = -20462749524591049105403365239069//454251913499893469596231268750 A[10,5] = -180269259803172281163724663224981097//38100922558256871086579832832000000 - A[10,6] = parse(BigInt,"21127670214172802870128286992003940810655221489")//parse(BigInt,"4679473877997892906145822697976708633673728000") - A[10,7] = parse(BigInt,"318607235173649312405151265849660869927653414425413")//parse(BigInt,"6714716715558965303132938072935465423910912000000") + A[10,6] = 21127670214172802870128286992003940810655221489//4679473877997892906145822697976708633673728000 + A[10,7] = 318607235173649312405151265849660869927653414425413//6714716715558965303132938072935465423910912000000 A[10,8] = 212083202434519082281842245535894//20022426044775672563822865371173879 - A[10,9] = -parse(BigInt,"2698404929400842518721166485087129798562269848229517793703413951226714583")//parse(BigInt,"469545674913934315077000442080871141884676035902717550325616728175875000000") - A[11,1] = -parse(BigInt,"2342659845814086836951207140065609179073838476242943917")//parse(BigInt,"1358480961351056777022231400139158760857532162795520000") + A[10,9] = -2698404929400842518721166485087129798562269848229517793703413951226714583//469545674913934315077000442080871141884676035902717550325616728175875000000 + A[11,1] = -2342659845814086836951207140065609179073838476242943917//1358480961351056777022231400139158760857532162795520000 A[11,4] = -996286030132538159613930889652//16353068885996164905464325675 A[11,5] = -26053085959256534152588089363841//4377552804565683061011299942400 - A[11,6] = parse(BigInt,"20980822345096760292224086794978105312644533925634933539")//parse(BigInt,"3775889992007550803878727839115494641972212962174156800") - A[11,7] = parse(BigInt,"890722993756379186418929622095833835264322635782294899")//parse(BigInt,"13921242001395112657501941955594013822830119803764736") - A[11,8] = parse(BigInt,"161021426143124178389075121929246710833125")//parse(BigInt,"10997207722131034650667041364346422894371443") - A[11,9] = parse(BigInt,"300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513")//parse(BigInt,"4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000") + A[11,6] = 20980822345096760292224086794978105312644533925634933539//3775889992007550803878727839115494641972212962174156800 + A[11,7] = 890722993756379186418929622095833835264322635782294899//13921242001395112657501941955594013822830119803764736 + A[11,8] = 161021426143124178389075121929246710833125//10997207722131034650667041364346422894371443 + A[11,9] = 300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513//4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000 A[11,10] = -31155237437111730665923206875//392862141594230515010338956291 - A[12,1] = -parse(BigInt,"2866556991825663971778295329101033887534912787724034363")//parse(BigInt,"868226711619262703011213925016143612030669233795338240") - A[12,4] = -parse(BigInt,"16957088714171468676387054358954754000")//parse(BigInt,"143690415119654683326368228101570221") - A[12,5] = -parse(BigInt,"4583493974484572912949314673356033540575")//parse(BigInt,"451957703655250747157313034270335135744") - A[12,6] = parse(BigInt,"2346305388553404258656258473446184419154740172519949575")//parse(BigInt,"256726716407895402892744978301151486254183185289662464") - A[12,7] = parse(BigInt,"1657121559319846802171283690913610698586256573484808662625")//parse(BigInt,"13431480411255146477259155104956093505361644432088109056") - A[12,8] = parse(BigInt,"345685379554677052215495825476969226377187500")//parse(BigInt,"74771167436930077221667203179551347546362089") - A[12,9] = -parse(BigInt,"3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011")//parse(BigInt,"947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120") - A[12,10] = parse(BigInt,"40279545832706233433100438588458933210937500")//parse(BigInt,"8896460842799482846916972126377338947215101") - A[12,11] = -parse(BigInt,"6122933601070769591613093993993358877250")//parse(BigInt,"1050517001510235513198246721302027675953") - A[13,1] = -parse(BigInt,"618675905535482500672800859344538410358660153899637")//parse(BigInt,"203544282118214047100119475340667684874292102389760") - A[13,4] = -parse(BigInt,"4411194916804718600478400319122931000")//parse(BigInt,"40373053902469967450761491269633019") - A[13,5] = -parse(BigInt,"16734711409449292534539422531728520225")//parse(BigInt,"1801243715290088669307203927210237952") - A[13,6] = parse(BigInt,"135137519757054679098042184152749677761254751865630525")//parse(BigInt,"16029587794486289597771326361911895112703716593983488") - A[13,7] = parse(BigInt,"38937568367409876012548551903492196137929710431584875")//parse(BigInt,"340956454090191606099548798001469306974758443147264") - A[13,8] = -parse(BigInt,"6748865855011993037732355335815350667265625")//parse(BigInt,"7002880395717424621213565406715087764770357") - A[13,9] = -parse(BigInt,"1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671")//parse(BigInt,"348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320") - A[13,10] = parse(BigInt,"53381024589235611084013897674181629296875")//parse(BigInt,"8959357584795694524874969598508592944141") + A[12,1] = -2866556991825663971778295329101033887534912787724034363//868226711619262703011213925016143612030669233795338240 + A[12,4] = -16957088714171468676387054358954754000//143690415119654683326368228101570221 + A[12,5] = -4583493974484572912949314673356033540575//451957703655250747157313034270335135744 + A[12,6] = 2346305388553404258656258473446184419154740172519949575//256726716407895402892744978301151486254183185289662464 + A[12,7] = 1657121559319846802171283690913610698586256573484808662625//13431480411255146477259155104956093505361644432088109056 + A[12,8] = 345685379554677052215495825476969226377187500//74771167436930077221667203179551347546362089 + A[12,9] = -3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011//947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120 + A[12,10] = 40279545832706233433100438588458933210937500//8896460842799482846916972126377338947215101 + A[12,11] = -6122933601070769591613093993993358877250//1050517001510235513198246721302027675953 + A[13,1] = -618675905535482500672800859344538410358660153899637//203544282118214047100119475340667684874292102389760 + A[13,4] = -4411194916804718600478400319122931000//40373053902469967450761491269633019 + A[13,5] = -16734711409449292534539422531728520225//1801243715290088669307203927210237952 + A[13,6] = 135137519757054679098042184152749677761254751865630525//16029587794486289597771326361911895112703716593983488 + A[13,7] = 38937568367409876012548551903492196137929710431584875//340956454090191606099548798001469306974758443147264 + A[13,8] = -6748865855011993037732355335815350667265625//7002880395717424621213565406715087764770357 + A[13,9] = -1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671//348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320 + A[13,10] = 53381024589235611084013897674181629296875//8959357584795694524874969598508592944141 α[1] = 44901867737754616851973//1014046409980231013380680 α[6] = 791638675191615279648100000//2235604725089973126411512319 α[7] = 3847749490868980348119500000//15517045062138271618141237517 α[8] = -13734512432397741476562500000//875132892924995907746928783 - α[9] = parse(BigInt,"12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141")//parse(BigInt,"489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040") + α[9] = 12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141//489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040 α[10] = -9798363684577739445312500000//308722986341456031822630699 α[11] = 282035543183190840068750//12295407629873040425991 α[12] = -306814272936976936753//1299331183183744997286 @@ -1958,7 +1958,7 @@ function constructVerner8(T::Type = Float64) αEEst[6] = 13908189778321895491375000//39221135527894265375640567 αEEst[7] = 73487947527027243487625000//296504045773342769773399443 αEEst[8] = 68293140641257649609375000//15353208647806945749946119 - αEEst[9] = parse(BigInt,"22060647948996678611017711379974578860522018208949721559448560203338437626022142776381")//parse(BigInt,"1111542009262325874512959185795727215759010577565736079641376621381577236680929558640") + αEEst[9] = 22060647948996678611017711379974578860522018208949721559448560203338437626022142776381//1111542009262325874512959185795727215759010577565736079641376621381577236680929558640 αEEst[10] = -547971229495642458203125000//23237214025700991642563601 αEEst[13] = -28735456870978964189//79783493704265043693 @@ -2224,7 +2224,7 @@ function constructDormandLockyerMcCorriganPrince6(T::Type = Float64) A[8,2]=0 A[8,3]=19247613365107236707//4836252322132133628 A[8,4]=-3627331815384766429266963559//1852940251413900055822878936 - A[8,5]=-parse(BigInt,"1113629335962635330712822690622675431")//parse(BigInt,"31397585101055611361934971740947112") + A[8,5]=-1113629335962635330712822690622675431//31397585101055611361934971740947112 A[8,6]=7515696221383336//210977455127283 A[8,7]=-2466239729887929744//169565652664150899277 A[9,1]=265211783//3930519060 @@ -2295,30 +2295,30 @@ function constructTanakaKasugaYamashitaYazaki6D(T::Type = Float64) A[5,2]=-5917919395479054157557671728//2612315925376400178578984625 A[5,3]=232280630406488701857197728//1274810171583683287146544497 A[5,4]=5471535080448445690971520//20898527403011201428631877 - A[6,1]=parse(BigInt,"6437510603218083862126582571557692575111484748570978316432703829")//parse(BigInt,"462655382163643505993146289902892129798145865902401535270912000") + A[6,1]=6437510603218083862126582571557692575111484748570978316432703829//462655382163643505993146289902892129798145865902401535270912000 A[6,2]=-25083125032238929237211514053//1741543950250933452385989750 - A[6,3]=parse(BigInt,"191471592827838703414373042295007003190385413366181230722958611")//parse(BigInt,"201998644533947923598793335502244867385083328952030670310246400") - A[6,4]=-parse(BigInt,"723497411149192638041504597211363403675892243966786723532767")//parse(BigInt,"584075332429951001052530262062711448991365353250616692288000") - A[6,5]=parse(BigInt,"20368395873479894700136894919415569811519")//parse(BigInt,"12245317457885350045378058014027636736000") - A[7,1]=-parse(BigInt,"1053235524590544505552847720336831796873415344431325525436387723231012409077771")//parse(BigInt,"151882847900737440255262782278159042659114250070600779935950570906179610869760") + A[6,3]=191471592827838703414373042295007003190385413366181230722958611//201998644533947923598793335502244867385083328952030670310246400 + A[6,4]=-723497411149192638041504597211363403675892243966786723532767//584075332429951001052530262062711448991365353250616692288000 + A[6,5]=20368395873479894700136894919415569811519//12245317457885350045378058014027636736000 + A[7,1]=-1053235524590544505552847720336831796873415344431325525436387723231012409077771//151882847900737440255262782278159042659114250070600779935950570906179610869760 A[7,2]=110556263584594415870053017499108315//15711834237341169934278611772340752 - A[7,3]=parse(BigInt,"27883202411953328597139497795565290131372048742640205053329023156822546337651")//parse(BigInt,"66313136270946971682878125476803367732416846682610519097035561761715919388672") - A[7,4]=-parse(BigInt,"134178686375307065766767719823759096451245561636180411142603830822435042239")//parse(BigInt,"191743203036279335802347994313396039656741862830639889775698722784806666240") - A[7,5]=parse(BigInt,"1192365386732594028658711096219658222748871123673792181")//parse(BigInt,"1339984907884349782764828286663427050229770700990709760") + A[7,3]=27883202411953328597139497795565290131372048742640205053329023156822546337651//66313136270946971682878125476803367732416846682610519097035561761715919388672 + A[7,4]=-134178686375307065766767719823759096451245561636180411142603830822435042239//191743203036279335802347994313396039656741862830639889775698722784806666240 + A[7,5]=1192365386732594028658711096219658222748871123673792181//1339984907884349782764828286663427050229770700990709760 A[7,6]=1//16 - A[8,1]=parse(BigInt,"139472860369418680318405579593202554799958275392817771935632674919979204348213061279")//parse(BigInt,"37743426679794053215512832350173350810071958850079214921681182582585691688393293824") + A[8,1]=139472860369418680318405579593202554799958275392817771935632674919979204348213061279//37743426679794053215512832350173350810071958850079214921681182582585691688393293824 A[8,2]=-764277739442303538051509575419150250//241488900344982122797870353007980909 - A[8,3]=-parse(BigInt,"7371553444464925806572282862981502319484039203525663191183225508630714910425342675")//parse(BigInt,"4846779318912629207559289658412491740053883371241789941360845137312080681624033792") - A[8,4]=parse(BigInt,"8801132642676112554927251590711440081546416618547191842516081677278335900180085")//parse(BigInt,"2071689842640920660980285733506294870283516476694921779219912685665930091210112") - A[8,5]=-parse(BigInt,"298368164571373898500032163301238477118159212135073380804555")//parse(BigInt,"92828694411466377636989261345454987067336292167034303922176") + A[8,3]=-7371553444464925806572282862981502319484039203525663191183225508630714910425342675//4846779318912629207559289658412491740053883371241789941360845137312080681624033792 + A[8,4]=8801132642676112554927251590711440081546416618547191842516081677278335900180085//2071689842640920660980285733506294870283516476694921779219912685665930091210112 + A[8,5]=-298368164571373898500032163301238477118159212135073380804555//92828694411466377636989261345454987067336292167034303922176 A[8,6]=-240786613447142598518650//1482036690339563123748203 A[8,7]=52860332724128242560//47245264125077723987 - A[9,1]=-parse(BigInt,"70335440697678472884389500304621917516220835017456192585613672496070708987720514364185979355621")//parse(BigInt,"5219173052726261361794285880851433852375067076864459834761850509124293962243718819226202095616") - A[9,2]=parse(BigInt,"55057602528492150957512473843952756334951250")//parse(BigInt,"3825542672812430870769605520946554801303339") - A[9,3]=-parse(BigInt,"77980782561050861485751338404689118536953083418300092316918550174770045337324006382574405615")//parse(BigInt,"39424363920896283457695961995433007195554371610645094834381872512385376722954438065398121984") - A[9,4]=parse(BigInt,"2177533338045948502564188609357006384381697842038103984795932632439956259386338338574157919")//parse(BigInt,"387582376874948376545286159615164080595940845312336117877987331598679530792396290947668352") - A[9,5]=-parse(BigInt,"1429465993644112145770349737782620061868013755109155817982734692969685809")//parse(BigInt,"295236772314145005435682097407317274403116518334589230312060489793912832") - A[9,6]=-parse(BigInt,"162882286796273095967517045376244881875035")//parse(BigInt,"1226056358355165076488310595889719561316528") + A[9,1]=-70335440697678472884389500304621917516220835017456192585613672496070708987720514364185979355621//5219173052726261361794285880851433852375067076864459834761850509124293962243718819226202095616 + A[9,2]=55057602528492150957512473843952756334951250//3825542672812430870769605520946554801303339 + A[9,3]=-77980782561050861485751338404689118536953083418300092316918550174770045337324006382574405615//39424363920896283457695961995433007195554371610645094834381872512385376722954438065398121984 + A[9,4]=2177533338045948502564188609357006384381697842038103984795932632439956259386338338574157919//387582376874948376545286159615164080595940845312336117877987331598679530792396290947668352 + A[9,5]=-1429465993644112145770349737782620061868013755109155817982734692969685809//295236772314145005435682097407317274403116518334589230312060489793912832 + A[9,6]=-162882286796273095967517045376244881875035//1226056358355165076488310595889719561316528 A[9,7]=61//43 A[9,8]=0 α[1]=4783097999//163657290888 @@ -2379,29 +2379,29 @@ function constructTanakaKasugaYamashitaYazaki6C(T::Type = Float64) A[5,2]=-2894503641421476941//3306249394253698200 A[5,3]=42536885251557644//181843716683953401 A[5,4]=124767011204926940//545531150051860203 - A[6,1]=parse(BigInt,"2432582077139652291040741961658278931048241123")//parse(BigInt,"1042517831971586211298945274530293397770600000") + A[6,1]=2432582077139652291040741961658278931048241123//1042517831971586211298945274530293397770600000 A[6,2]=-5086533956627126527//2404545014002689600 - A[6,3]=-parse(BigInt,"28233375209799471901757749652001556425049843")//parse(BigInt,"193956805948202085823059585959124353073600000") - A[6,4]=-parse(BigInt,"64143717120482360099075816554051641763250417")//parse(BigInt,"80815335811750869092941494149635147114000000") + A[6,3]=-28233375209799471901757749652001556425049843//193956805948202085823059585959124353073600000 + A[6,4]=-64143717120482360099075816554051641763250417//80815335811750869092941494149635147114000000 A[6,5]=368355687225024998241998861697//229321716687851233749224000000 - A[7,1]=-parse(BigInt,"218146655544801488428299362829574333746140908535614198091")//parse(BigInt,"129671440168534479253493745415914920591854154832474480000") + A[7,1]=-218146655544801488428299362829574333746140908535614198091//129671440168534479253493745415914920591854154832474480000 A[7,2]=3225815231796122073236882//1899026582543293621912725 - A[7,3]=parse(BigInt,"90474621818961969641326264897298400503244755498598833923")//parse(BigInt,"192999352808981550516827900153919881811131765332055040000") - A[7,4]=-parse(BigInt,"1469845402576002022391874744301978646600063888157276277")//parse(BigInt,"1827645386448688925348749054487877668666020505038400000") - A[7,5]=parse(BigInt,"236537380548621166783390004339783981292483")//parse(BigInt,"228189687334919622052120277661453593600000") + A[7,3]=90474621818961969641326264897298400503244755498598833923//192999352808981550516827900153919881811131765332055040000 + A[7,4]=-1469845402576002022391874744301978646600063888157276277//1827645386448688925348749054487877668666020505038400000 + A[7,5]=236537380548621166783390004339783981292483//228189687334919622052120277661453593600000 A[7,6]=1//16 - A[8,1]=parse(BigInt,"20745045233020258374773011834908499926526821480199726607317")//parse(BigInt,"6703021612773885250214340203318686755448684469761576087200") + A[8,1]=20745045233020258374773011834908499926526821480199726607317//6703021612773885250214340203318686755448684469761576087200 A[8,2]=-10062163770239468036471200//3356073465031554356885103 - A[8,3]=-parse(BigInt,"6600722659737487671039676673294259975246135762925896417")//parse(BigInt,"9474444736357442876691573864537554989039417965607475200") - A[8,4]=parse(BigInt,"80225477702329113082476652949959330669319741271791060069")//parse(BigInt,"21801989308095252074205042131464260060005478841312656000") - A[8,5]=-parse(BigInt,"572101553192975384084889663939632620168841743")//parse(BigInt,"192662470105149826757328803363450656933632000") + A[8,3]=-6600722659737487671039676673294259975246135762925896417//9474444736357442876691573864537554989039417965607475200 + A[8,4]=80225477702329113082476652949959330669319741271791060069//21801989308095252074205042131464260060005478841312656000 + A[8,5]=-572101553192975384084889663939632620168841743//192662470105149826757328803363450656933632000 A[8,6]=-223351084874296955//945158103640587564 A[8,7]=3931692514354//3491636633667 - A[9,1]=parse(BigInt,"1042961260483134998083167734826788831236189026066652724982180836527")//parse(BigInt,"166222076505494822625791597828801737913859767695104851064439232400") + A[9,1]=1042961260483134998083167734826788831236189026066652724982180836527//166222076505494822625791597828801737913859767695104851064439232400 A[9,2]=-4754359005740226898713768141325//838855890397374389475867956178 - A[9,3]=-parse(BigInt,"42750676060439966787211838095564987064848978722439603628501619959")//parse(BigInt,"27488922212795009426487499382540855882395413779035427566212172800") - A[9,4]=parse(BigInt,"205686747816311239126907254218859168711623965851131881271189228377")//parse(BigInt,"77312593723485964011996092013396157169237101253537140029971736000") - A[9,5]=-parse(BigInt,"75946282944430327533335124997772458772050053465158929")//parse(BigInt,"62109575359095533697158937720595685916206114892672000") + A[9,3]=-42750676060439966787211838095564987064848978722439603628501619959//27488922212795009426487499382540855882395413779035427566212172800 + A[9,4]=205686747816311239126907254218859168711623965851131881271189228377//77312593723485964011996092013396157169237101253537140029971736000 + A[9,5]=-75946282944430327533335124997772458772050053465158929//62109575359095533697158937720595685916206114892672000 A[9,6]=-264375495891732597330199815785//1220640854393687869579464225198 A[9,7]=8//11 A[9,8]=0 @@ -2549,30 +2549,30 @@ function constructTanakaKasugaYamashitaYazaki6A(T::Type = Float64) A[5,2]=-32049516354411396813791//31633875873558003463200 A[5,3]=415928927703664756394//3202929932197747850649 A[5,4]=4945815476584113561248//16014649660988739253245 - A[6,1]=parse(BigInt,"264364422150553063350374034500534568610052754809099")//parse(BigInt,"76594645373513572971811613560122656201571540854400") + A[6,1]=264364422150553063350374034500534568610052754809099//76594645373513572971811613560122656201571540854400 A[6,2]=-4942738251715985006237//988558621048687608225 - A[6,3]=parse(BigInt,"857070668647981630049588712158864150151776268553")//parse(BigInt,"235675831918503301451728041723454326774066279552") - A[6,4]=-parse(BigInt,"575165070977427883238172569267537197276341339157")//parse(BigInt,"157117221279002200967818694482302884516044186368") + A[6,3]=857070668647981630049588712158864150151776268553//235675831918503301451728041723454326774066279552 + A[6,4]=-575165070977427883238172569267537197276341339157//157117221279002200967818694482302884516044186368 A[6,5]=41539505110086641686706761875//17218030314852652247321445632 - A[7,1]=-parse(BigInt,"7384332843467384251748880311988170834105043085902030057004642579")//parse(BigInt,"1315398593371357506652159044711447383311024734178303038737049600") + A[7,1]=-7384332843467384251748880311988170834105043085902030057004642579//1315398593371357506652159044711447383311024734178303038737049600 A[7,2]=5656750329476775131209405217353//831860122007390417396028410400 - A[7,3]=-parse(BigInt,"333346623364947547771242996577246247659950898456372585977245839")//parse(BigInt,"190226873502934777885081461850578544663440500019631516371204096") - A[7,4]=parse(BigInt,"7100883704616862706920092769411499000150383998766128086388523")//parse(BigInt,"4497089208107205150947552289611785925849657210865993294827520") - A[7,5]=-parse(BigInt,"2179578925723796720158217363641743790096295")//parse(BigInt,"4632538471751007430155293544377007681933312") + A[7,3]=-333346623364947547771242996577246247659950898456372585977245839//190226873502934777885081461850578544663440500019631516371204096 + A[7,4]=7100883704616862706920092769411499000150383998766128086388523//4497089208107205150947552289611785925849657210865993294827520 + A[7,5]=-2179578925723796720158217363641743790096295//4632538471751007430155293544377007681933312 A[7,6]=1//16 - A[8,1]=-parse(BigInt,"2032945134330261992294105795025746391376544519999264654886089003925834569")//parse(BigInt,"370204608795106233716533306294462150635128163745469969879178202980349056") + A[8,1]=-2032945134330261992294105795025746391376544519999264654886089003925834569//370204608795106233716533306294462150635128163745469969879178202980349056 A[8,2]=104400636802444703223540033778325//10372562449415222120508569935887 - A[8,3]=-parse(BigInt,"1282736937871158931724790946085686543914309745805108288599439251128389375")//parse(BigInt,"121675640652937013878860597173704343215741424447811808281967661119415424") - A[8,4]=parse(BigInt,"69591790067148620077849942355176681820069270105493261193720164528698455")//parse(BigInt,"5177686836295192079951514773349120987903890402034545033275219622102784") - A[8,5]=-parse(BigInt,"277247257204675144642737406657510117972977064771225085")//parse(BigInt,"32594437558796549389422402191407749206480247247281408") + A[8,3]=-1282736937871158931724790946085686543914309745805108288599439251128389375//121675640652937013878860597173704343215741424447811808281967661119415424 + A[8,4]=69591790067148620077849942355176681820069270105493261193720164528698455//5177686836295192079951514773349120987903890402034545033275219622102784 + A[8,5]=-277247257204675144642737406657510117972977064771225085//32594437558796549389422402191407749206480247247281408 A[8,6]=206057847729988755370340//362497215363232474360143 A[8,7]=482015452915471040//328927231085842477 - A[9,1]=parse(BigInt,"149325572050522001715919965533803802996087500406626797668220209959218571")//parse(BigInt,"32753013690352528622466162111781793695504165546622151035212132158026496") - A[9,2]=-parse(BigInt,"2802049259729837394660870725638222600")//parse(BigInt,"886389794903952023701108666481909127") - A[9,3]=-parse(BigInt,"247046029472637555138263024224503808349122551711211979490561742618517516481875")//parse(BigInt,"62386925133959095591686249139496495395591773904073928005189977758511970759424") - A[9,4]=parse(BigInt,"17088511387117619026306232328319322341432000611501090216270103426420066685195")//parse(BigInt,"2654762771657833854965372303808361506195394634215911830008084159936679606784") - A[9,5]=-parse(BigInt,"1905127968294488657830239165534292922200553202371049568415")//parse(BigInt,"428517757803501533934438346448102436732262910333700649472") - A[9,6]=parse(BigInt,"348519474109306281943020669241827485")//parse(BigInt,"1086125473870224085200713153977775988") + A[9,1]=149325572050522001715919965533803802996087500406626797668220209959218571//32753013690352528622466162111781793695504165546622151035212132158026496 + A[9,2]=-2802049259729837394660870725638222600//886389794903952023701108666481909127 + A[9,3]=-247046029472637555138263024224503808349122551711211979490561742618517516481875//62386925133959095591686249139496495395591773904073928005189977758511970759424 + A[9,4]=17088511387117619026306232328319322341432000611501090216270103426420066685195//2654762771657833854965372303808361506195394634215911830008084159936679606784 + A[9,5]=-1905127968294488657830239165534292922200553202371049568415//428517757803501533934438346448102436732262910333700649472 + A[9,6]=348519474109306281943020669241827485//1086125473870224085200713153977775988 A[9,7]=5//4 A[9,8]=0 α[1]=703450322//19272872619 @@ -2742,11 +2742,11 @@ function constructChummund62(T::Type = Float64) c[6]=1//2+1//10*5^(1//2) c[7]=1 A[2,1]=750557//18870600 - A[3,1]=-parse(BigInt,"2618524936181374161531835574563010037")//parse(BigInt,"1243120420984397996179713098690223560")+3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) + A[3,1]=-2618524936181374161531835574563010037//1243120420984397996179713098690223560+3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) A[3,2]=79275599164011507825658766043059867//31078010524609949904492827467255589-3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) - A[4,1]=-parse(BigInt,"268026226098849050460940570252841432600176823648465011650077")//parse(BigInt,"5150236239747870879984989921782016384957547807596571966124")+parse(BigInt,"75921270833932035355544618340621749422299940322072982")//parse(BigInt,"1287559059936967719996247480445504096239386951899142991531")*826321815619^(1//2) - A[4,2]=parse(BigInt,"31518353641767830515869136922708314461169361966520350023632789875")//parse(BigInt,"553066166067338591675176701039997652878686435650554094276321374")-parse(BigInt,"35636316203172669679112815645100268396443783685272961209975")//parse(BigInt,"553066166067338591675176701039997652878686435650554094276321374")*826321815619^(1//2) - A[4,3]=-parse(BigInt,"2316654837809440895270062146979974449795559590002488266576771951")//parse(BigInt,"551916642155010749548578353874329493980040828668519599378437454")+parse(BigInt,"3018332469640261586051209426912089268215645947971953376787")//parse(BigInt,"551916642155010749548578353874329493980040828668519599378437454")*826321815619^(1//2) + A[4,1]=-268026226098849050460940570252841432600176823648465011650077//5150236239747870879984989921782016384957547807596571966124+75921270833932035355544618340621749422299940322072982//1287559059936967719996247480445504096239386951899142991531*826321815619^(1//2) + A[4,2]=31518353641767830515869136922708314461169361966520350023632789875//553066166067338591675176701039997652878686435650554094276321374-35636316203172669679112815645100268396443783685272961209975//553066166067338591675176701039997652878686435650554094276321374*826321815619^(1//2) + A[4,3]=-2316654837809440895270062146979974449795559590002488266576771951//551916642155010749548578353874329493980040828668519599378437454+3018332469640261586051209426912089268215645947971953376787//551916642155010749548578353874329493980040828668519599378437454*826321815619^(1//2) A[5,1]=7557928766176693537//21071504819547814620-3808101371666611447//21071504819547814620*5^(1//2)+1830930386299//21071504819547814620*826321815619^(1//2)+2746507673963//21071504819547814620*826321815619^(1//2)*5^(1//2) A[5,2]=-306676166043910279990585069725//1347799564492996272083268634084+281193211701441857849531780175//1347799564492996272083268634084*5^(1//2)-135831974232490143067425//1347799564492996272083268634084*826321815619^(1//2)-203756277349889111562225//1347799564492996272083268634084*826321815619^(1//2)*5^(1//2) A[5,3]=59599519641651017073742851703//154850028368562600922782726012-19070452237413934132405792717//154850028368562600922782726012*5^(1//2)+3249940179998629473139//154850028368562600922782726012*826321815619^(1//2)+4875109240133213731043//154850028368562600922782726012*826321815619^(1//2)*5^(1//2) @@ -2754,12 +2754,12 @@ function constructChummund62(T::Type = Float64) A[6,1]=-6195448976102809771//10535752409773907310-1420753767230413123//10535752409773907310*5^(1//2)+2689284093484//5267876204886953655*826321815619^(1//2)+57223580479//5267876204886953655*826321815619^(1//2)*5^(1//2) A[6,2]=583482891804126952797345387075//673899782246498136041634317042+55992621594804402807018397650//336949891123249068020817158521*5^(1//2)-254249689295131189339575//336949891123249068020817158521*826321815619^(1//2)-49153620024967407924975//673899782246498136041634317042*826321815619^(1//2)*5^(1//2) A[6,3]=19364321623328820251751318839//77425014184281300461391363006+1040656060288496357918934418//38712507092140650230695681503*5^(1//2)-11049041979964718221319//38712507092140650230695681503*826321815619^(1//2)-19382660452189380569035//77425014184281300461391363006*826321815619^(1//2)*5^(1//2) - A[6,4]=parse(BigInt,"115027957037506741565069794992944458832461")//parse(BigInt,"237309179139566721503969545043331027555510")-parse(BigInt,"19371908299625437579435144814464589438224")//parse(BigInt,"118654589569783360751984772521665513777755")*5^(1//2)+parse(BigInt,"64263508455127995016232148201271346")//parse(BigInt,"118654589569783360751984772521665513777755")*826321815619^(1//2)-parse(BigInt,"41163600684913040546114995026601907")//parse(BigInt,"237309179139566721503969545043331027555510")*826321815619^(1//2)*5^(1//2) + A[6,4]=115027957037506741565069794992944458832461//237309179139566721503969545043331027555510-19371908299625437579435144814464589438224//118654589569783360751984772521665513777755*5^(1//2)+64263508455127995016232148201271346//118654589569783360751984772521665513777755*826321815619^(1//2)-41163600684913040546114995026601907//237309179139566721503969545043331027555510*826321815619^(1//2)*5^(1//2) A[6,5]=43435632261//211822050005*5^(1//2)-43432990301//84728820002+205839//423644100010*826321815619^(1//2)*5^(1//2)-514//42364410001*826321815619^(1//2) A[7,1]=9047270149938488929//4214300963909562924+2216536302042479231//1404766987969854308*5^(1//2)-991800665293//1404766987969854308*826321815619^(1//2)*5^(1//2)-12588066760235//4214300963909562924*826321815619^(1//2) A[7,2]=-4301448087821718128020528522125//1347799564492996272083268634084-2525818490403297345388026853875//1347799564492996272083268634084*5^(1//2)+1510317586999119637060875//1347799564492996272083268634084*826321815619^(1//2)*5^(1//2)+5764153657065074502128625//1347799564492996272083268634084*826321815619^(1//2) A[7,3]=-491640814441543287886227446905//154850028368562600922782726012+752920605871714580844952275//1564141700692551524472552788*5^(1//2)+1711626851729573101365//1564141700692551524472552788*826321815619^(1//2)*5^(1//2)+204731138699301217060685//154850028368562600922782726012*826321815619^(1//2) - A[7,4]=-parse(BigInt,"222449163212150849227576515026323419478375")//parse(BigInt,"94923671655826688601587818017332411022204")+parse(BigInt,"805495551976820677052288591080735143509")//parse(BigInt,"958824966220471602036240586033660717396")*5^(1//2)-parse(BigInt,"253684995628220543918448388547756365")//parse(BigInt,"94923671655826688601587818017332411022204")*826321815619^(1//2)+parse(BigInt,"882636009291931420795306294477883")//parse(BigInt,"958824966220471602036240586033660717396")*826321815619^(1//2)*5^(1//2) + A[7,4]=-222449163212150849227576515026323419478375//94923671655826688601587818017332411022204+805495551976820677052288591080735143509//958824966220471602036240586033660717396*5^(1//2)-253684995628220543918448388547756365//94923671655826688601587818017332411022204*826321815619^(1//2)+882636009291931420795306294477883//958824966220471602036240586033660717396*826321815619^(1//2)*5^(1//2) A[7,5]=-44506854521//84728820002*5^(1//2)+214493500755//42364410001-205839//84728820002*826321815619^(1//2)*5^(1//2)+2570//42364410001*826321815619^(1//2) A[7,6]=5//2-1//2*5^(1//2) α[1]=1//12 @@ -3035,20 +3035,20 @@ function constructVernerRobust7(T::Type = Float64) A[7,3]=-9852144759099//2364568872400 A[7,4]=15322550932778398907299//3996134347464283007200 A[7,5]=-18338463121898520004//36506562121215938675 - A[7,6]=parse(BigInt,"23340475544602125119307511373519383499")//parse(BigInt,"34957329425893779598660175543672800000") + A[7,6]=23340475544602125119307511373519383499//34957329425893779598660175543672800000 A[8,1]=81088643022740545033730780169//2975182110231937140152800000 A[8,2]=0 A[8,3]=-2837794586103//67559110640 A[8,4]=-14167575606881316095038341141//1344719188593468553337836000 A[8,5]=2395552232834276839307772//29760062864388068268875 - A[8,6]=-parse(BigInt,"4076715891031001341580357765362043260356514682697")//parse(BigInt,"60535801523558513633981092635987721507186400000") + A[8,6]=-4076715891031001341580357765362043260356514682697//60535801523558513633981092635987721507186400000 A[8,7]=36551527355459957808//2801171464968864455 A[9,1]=-3347747115771808477876752833599//1101327591307901549464211073280 A[9,2]=0 A[9,3]=1214704878477625125//119815105452943264 A[9,4]=-65581118617864038124456452415//10200342297342072539428709672 A[9,5]=-133373082911575479273298406095//84070826916189821955373830704 - A[9,6]=parse(BigInt,"622515683654039386383701463758952267447736841050281950137693")//parse(BigInt,"328994218860140584540186142455568117669077094653332432085760") + A[9,6]=622515683654039386383701463758952267447736841050281950137693//328994218860140584540186142455568117669077094653332432085760 A[9,7]=46169188671551441399013763125//2343692704156841275628930358208 A[9,8]=18880867865877597493091875//3469664148196911643475533504 A[10,1]=-74309815528722196127526037//51427190037752065777334640 @@ -3056,7 +3056,7 @@ function constructVernerRobust7(T::Type = Float64) A[10,3]=913722369253875//113761793498234 A[10,4]=-440658227159292602060396890//58109996881684093545238767 A[10,5]=37290888293935763341814380//10411746696360295961914239 - A[10,6]=-parse(BigInt,"645152888113581065780360392105179310452496326847")//parse(BigInt,"264735425121804814898131042131367320451487910960") + A[10,6]=-645152888113581065780360392105179310452496326847//264735425121804814898131042131367320451487910960 A[10,7]=473757486190086838681892500//556321100802942639360459887 A[10,8]=0 A[10,9]=0 @@ -3065,7 +3065,7 @@ function constructVernerRobust7(T::Type = Float64) α[3]=0 α[4]=18658605936510000//72821569629535727 α[5]=296950875175030000//1101802245630054969 - α[6]=parse(BigInt,"18875276980274212686824835566143151189850553896330009")//parse(BigInt,"148780947139609706104394157596648357994575577036224440") + α[6]=18875276980274212686824835566143151189850553896330009//148780947139609706104394157596648357994575577036224440 α[7]=18663850606812500//74993696164706319 α[8]=179884749312500//58508928482581269 α[9]=349315176247648//7273791403140339 @@ -3075,7 +3075,7 @@ function constructVernerRobust7(T::Type = Float64) αEEst[3]=0 αEEst[4]=7505178129270000//29317774785916981 αEEst[5]=1851744839320000//6843492208882329 - αEEst[6]=parse(BigInt,"750882778189818437512810407839645051128089")//parse(BigInt,"6004363295715536270735789992319176322209240") + αEEst[6]=750882778189818437512810407839645051128089//6004363295715536270735789992319176322209240 αEEst[7]=27902602073000000//110704980052661709 αEEst[8]=0 αEEst[9]=0 @@ -3116,39 +3116,39 @@ A[5,1]=13638791441//21333512000 A[5,2]=0 A[5,3]=-10484391993//4266702400 A[5,4]=1212514581//533337800 -A[6,1]=-parse(BigInt,"10566420537453573046911093467384714791794598586757942301092800")//parse(BigInt,"3945478828013189718441489268080494867217306323934034936408479") +A[6,1]=-10566420537453573046911093467384714791794598586757942301092800//3945478828013189718441489268080494867217306323934034936408479 A[6,2]=0 -A[6,3]=parse(BigInt,"5231021510299954960251585060495720489874110055798400000000")//parse(BigInt,"481214639347870437668189933904195007588401795820714103721") -A[6,4]=-parse(BigInt,"53191822847901986858463766895922715840689391279600297600000000")//parse(BigInt,"6327491292785148384899029440906260154779895213246569749827429") -A[6,5]=parse(BigInt,"1781287527622331824616139968260471142273403953102720000000")//parse(BigInt,"2161611109404685052753814119556349840946763773078759856171") -A[7,1]=parse(BigInt,"40316732614812499600926954604381622079953")//parse(BigInt,"6622027015251398289270845012723400000000") +A[6,3]=5231021510299954960251585060495720489874110055798400000000//481214639347870437668189933904195007588401795820714103721 +A[6,4]=-53191822847901986858463766895922715840689391279600297600000000//6327491292785148384899029440906260154779895213246569749827429 +A[6,5]=1781287527622331824616139968260471142273403953102720000000//2161611109404685052753814119556349840946763773078759856171 +A[7,1]=40316732614812499600926954604381622079953//6622027015251398289270845012723400000000 A[7,2]=0 A[7,3]=-3102627096349187411472//125153701152335532175 -A[7,4]=parse(BigInt,"24512593611811814197027847310011747907776")//parse(BigInt,"1196407956242848578947668299729517712775") +A[7,4]=24512593611811814197027847310011747907776//1196407956242848578947668299729517712775 A[7,5]=-27992220377104300725776520574439264//14697934672024287924310069954740819 -A[7,6]=parse(BigInt,"3894588020195704963647351313475389164102598021642890694420881")//parse(BigInt,"3885780076153082703909872726256212057602657456212198200000000") -A[8,1]=parse(BigInt,"219473830564834473126851658008599711669913643457")//parse(BigInt,"18148581918776897851104105262715070449854720000") +A[7,6]=3894588020195704963647351313475389164102598021642890694420881//3885780076153082703909872726256212057602657456212198200000000 +A[8,1]=219473830564834473126851658008599711669913643457//18148581918776897851104105262715070449854720000 A[8,2]=0 A[8,3]=-10861924990722808125//217658610699713969 -A[8,4]=parse(BigInt,"119480318847905366486490498699126516657779132592500")//parse(BigInt,"2895978969529640099701689414747730700037272591519") -A[8,5]=-parse(BigInt,"1668548580652290279936994936449972411950403625")//parse(BigInt,"374242591559339035424931213674065468041890542") -A[8,6]=parse(BigInt,"38257721102788015064997204763622283132936825913246654962493266309964200473188255317")//parse(BigInt,"18800609083266437975749341539616748050410201552864110184725432140737391745319680000") +A[8,4]=119480318847905366486490498699126516657779132592500//2895978969529640099701689414747730700037272591519 +A[8,5]=-1668548580652290279936994936449972411950403625//374242591559339035424931213674065468041890542 +A[8,6]=38257721102788015064997204763622283132936825913246654962493266309964200473188255317//18800609083266437975749341539616748050410201552864110184725432140737391745319680000 A[8,7]=-500096105036391897537714558203625//5080166748283963062825254164179392 -A[9,1]=parse(BigInt,"73088758866605608581823594159257042017139758291")//parse(BigInt,"7204156842026682625849538837116971615241846400") +A[9,1]=73088758866605608581823594159257042017139758291//7204156842026682625849538837116971615241846400 A[9,2]=0 A[9,3]=-69262713771106609055901000000//1623478443813548051039428229 -A[9,4]=parse(BigInt,"14675490755672909998080009537477454813814604865188000000")//parse(BigInt,"410204279941884058406992680456716961361878302419014157") -A[9,5]=-parse(BigInt,"56001310541527335660935463926718909867728400000")//parse(BigInt,"12914842534226649788973963163793850259828428307") -A[9,6]=parse(BigInt,"1658790111713212343550432782788025386861251060331884987447839679378079088262228191320420318059")//parse(BigInt,"829167683860659102329644660243394316974911850817625934703082071608371922272124378570833366400") -A[9,7]=parse(BigInt,"397383910096482616626611556102242919581343750")//parse(BigInt,"1139945435719262247312274838475128039778393907") -A[9,8]=-parse(BigInt,"15924946453851683996573317555310225254108800")//parse(BigInt,"58718594835565436263767442911746035434825067") -A[10,1]=-parse(BigInt,"14946539621537434020656235571945101642930646111")//parse(BigInt,"332010640625300658857148487489318781645129600") +A[9,4]=14675490755672909998080009537477454813814604865188000000//410204279941884058406992680456716961361878302419014157 +A[9,5]=-56001310541527335660935463926718909867728400000//12914842534226649788973963163793850259828428307 +A[9,6]=1658790111713212343550432782788025386861251060331884987447839679378079088262228191320420318059//829167683860659102329644660243394316974911850817625934703082071608371922272124378570833366400 +A[9,7]=397383910096482616626611556102242919581343750//1139945435719262247312274838475128039778393907 +A[9,8]=-15924946453851683996573317555310225254108800//58718594835565436263767442911746035434825067 +A[10,1]=-14946539621537434020656235571945101642930646111//332010640625300658857148487489318781645129600 A[10,2]=0 A[10,3]=171118989155232139053000000//913940284754207909241943 -A[10,4]=-parse(BigInt,"250906345110237533448815794107434670644623116000000")//parse(BigInt,"1630126656666301353726306757388291345384354510761") -A[10,5]=parse(BigInt,"100053022832376562190601031855550739901200000")//parse(BigInt,"5412177019773639317674437354179369686847329") -A[10,6]=-parse(BigInt,"741124542370420850881498253695230801778840260257881176783159378749906762930019")//parse(BigInt,"104572466684527096537276822312914502674692290031200239724554350786783199401600") -A[10,7]=parse(BigInt,"61868781182570033929134892454042771640656250")//parse(BigInt,"47410089451637179941093334205322110905900061") +A[10,4]=-250906345110237533448815794107434670644623116000000//1630126656666301353726306757388291345384354510761 +A[10,5]=100053022832376562190601031855550739901200000//5412177019773639317674437354179369686847329 +A[10,6]=-741124542370420850881498253695230801778840260257881176783159378749906762930019//104572466684527096537276822312914502674692290031200239724554350786783199401600 +A[10,7]=61868781182570033929134892454042771640656250//47410089451637179941093334205322110905900061 A[10,8]=0 A[10,9]=0 α[1]=23316791871424559928103//494567385514963690893600 @@ -3156,7 +3156,7 @@ A[10,9]=0 α[3]=0 α[4]=167985897310649194506250000000000000//652486332022351662028939973252423307 α[5]=1146393512631783066800000000000//4366210223630112740458758316827 -α[6]=parse(BigInt,"896878436896140749138361006566548336071636396490005664374818159563751598674344336941")//parse(BigInt,"5901910841358241153066354693443102222070394003395707585243672949102475401519736720800") +α[6]=896878436896140749138361006566548336071636396490005664374818159563751598674344336941//5901910841358241153066354693443102222070394003395707585243672949102475401519736720800 α[7]=7313950190577733068066406250//14824175638294700286557272779 α[8]=-16063489150654390383296000//54687057461871573111333849 α[9]=608799317735794481861//7494797304744605111718 @@ -3166,7 +3166,7 @@ A[10,9]=0 αEEst[3]=0 αEEst[4]=3268266429605273275000000000000//12237407528692429753538888074653 αEEst[5]=1613021830993125656000000000//7306908939590938710641463789 -αEEst[6]=parse(BigInt,"791180295543850558970031000997303838661625778390906982427125664631928")//parse(BigInt,"3622667153393802697274794410484953168258089439622231002370760754183025") +αEEst[6]=791180295543850558970031000997303838661625778390906982427125664631928//3622667153393802697274794410484953168258089439622231002370760754183025 αEEst[7]=3939837293445123160156250//17217393308123926000647239 αEEst[8]=0 αEEst[9]=0 @@ -3335,7 +3335,7 @@ function constructSharpSmart7(T::Type = Float64) A[6,5]=132023//106200 A[7,1]=25959766877768976976598957736980//487594514129628295945513157189933 A[7,2]=0 - A[7,3]=parse(BigInt,"347890318302644246405985993187156250")//parse(BigInt,"1321817402067092875750818220388519949") + A[7,3]=347890318302644246405985993187156250//1321817402067092875750818220388519949 A[7,4]=-1717046972617147709491116450178750//7467894926932728111586543618014237 A[7,5]=29780304732725103577764751746216250//258912687002832625147067486467854423 A[7,6]=-302662548054389051180423185000//25662869164717278733974376694207 @@ -3352,7 +3352,7 @@ function constructSharpSmart7(T::Type = Float64) A[9,4]=-50491693720625//29100752640072 A[9,5]=8909776468783164583973193125//6271093223575470807674793192 A[9,6]=-4792324941735635008750//159776107397443897190271 - A[9,7]=-parse(BigInt,"1532806290465891141166096531902118541769245")//parse(BigInt,"1203242011387872547807852011647420329982736") + A[9,7]=-1532806290465891141166096531902118541769245//1203242011387872547807852011647420329982736 A[9,8]=-7500029126894375//132689679447323376 A[10,1]=36393032615434450612//324390586094889663425 A[10,2]=0 @@ -3360,7 +3360,7 @@ function constructSharpSmart7(T::Type = Float64) A[10,4]=4135780451822750//874504037187843 A[10,5]=-2349378733647002895234008950//1090914599757106529355865311 A[10,6]=-78686605908422443750//52446632451499515953 - A[10,7]=parse(BigInt,"2315079813491204524435067899365885119542372444358703")//parse(BigInt,"316169042039527157595235231573788308031260760584200") + A[10,7]=2315079813491204524435067899365885119542372444358703//316169042039527157595235231573788308031260760584200 A[10,8]=-33473047374792524975//32907430028856870472 A[10,9]=5594658687556280397846//1893189870520997940175 A[11,1]=2508607706701842363083//197875357745688550590720 @@ -3369,7 +3369,7 @@ function constructSharpSmart7(T::Type = Float64) A[11,4]=13293920580875//2874148408896 A[11,5]=-599188464780493707137440161875//277270064173229869784600732736 A[11,6]=-3601465055348923762849875//2146128454918752594358208 - A[11,7]=parse(BigInt,"606030238246181777051198920509497430523044409408159")//parse(BigInt,"74752050141640998967813674460513197348653288024576") + A[11,7]=606030238246181777051198920509497430523044409408159//74752050141640998967813674460513197348653288024576 A[11,8]=-1922750201834125//1941504226023936 A[11,9]=12539348439579//3975412795840 A[11,10]=0 @@ -3379,7 +3379,7 @@ function constructSharpSmart7(T::Type = Float64) α[4]=0 α[5]=28304779228000000//53707434325074117 α[6]=-296881060859375//515060733835389 - α[7]=parse(BigInt,"744858303758379680905615939985761920312207508379")//parse(BigInt,"2487223884477764590764433396524922145673887618400") + α[7]=744858303758379680905615939985761920312207508379//2487223884477764590764433396524922145673887618400 α[8]=-5118512171875//11763620626464 α[9]=136801854099//127885521925 α[10]=103626500437//1717635089268 @@ -3390,7 +3390,7 @@ function constructSharpSmart7(T::Type = Float64) αEEst[4]=0 αEEst[5]=7786773134600000//14452831163890377 αEEst[6]=-408698637296875//567617951573694 - αEEst[7]=parse(BigInt,"4426705150369152638325381078278067803359")//parse(BigInt,"14828075230102658203818343670586143438076") + αEEst[7]=4426705150369152638325381078278067803359//14828075230102658203818343670586143438076 αEEst[8]=-5004542378125//10330679593521 αEEst[9]=154806770859//124231649870 αEEst[10]=0 @@ -3432,59 +3432,59 @@ function constructTanakaYamashitaEfficient7(T::Type = Float64) A[5,2]=0 A[5,3]=-68331192803887602162951//24112920357813127230992 A[5,4]=7825717455900471140481//3014115044726640903874 - A[6,1]=-parse(BigInt,"2425518501234340256175806929031336393991001205323654593685210322030691047097621496102266496")//parse(BigInt,"201073929944556265242953373967503382318096046559546854970564286270157897072030532387737241") + A[6,1]=-2425518501234340256175806929031336393991001205323654593685210322030691047097621496102266496//201073929944556265242953373967503382318096046559546854970564286270157897072030532387737241 A[6,2]=0 - A[6,3]=parse(BigInt,"126875939114499086848675646731069753055308007638565564293214808307459627250976287910912")//parse(BigInt,"2631823273838775215546306644775636213113650954300949659959480717139276934490785884841") - A[6,4]=-parse(BigInt,"18238165682427587123600563411903599919711680222699338744428834349094610403849667513626245575680")//parse(BigInt,"479212348415302218688412787744011607018072627155280851781784515530195350673833210517995172867") - A[6,5]=parse(BigInt,"74777425357290689294313120787550134201356775453356604582280658347816977407509825814840320")//parse(BigInt,"27848089034948481594251542168496834020714916243735255636715495143105044359669539013058107") - A[7,1]=parse(BigInt,"42210784012026021620512889337138957588173072058924928398799062235")//parse(BigInt,"401168555464694196502745570125544252560955194769351196028554688") + A[6,3]=126875939114499086848675646731069753055308007638565564293214808307459627250976287910912//2631823273838775215546306644775636213113650954300949659959480717139276934490785884841 + A[6,4]=-18238165682427587123600563411903599919711680222699338744428834349094610403849667513626245575680//479212348415302218688412787744011607018072627155280851781784515530195350673833210517995172867 + A[6,5]=74777425357290689294313120787550134201356775453356604582280658347816977407509825814840320//27848089034948481594251542168496834020714916243735255636715495143105044359669539013058107 + A[7,1]=42210784012026021620512889337138957588173072058924928398799062235//401168555464694196502745570125544252560955194769351196028554688 A[7,2]=0 - A[7,3]=-parse(BigInt,"53537582181289418572806048482253962781541488")//parse(BigInt,"128102133978061070595749084326726258918069") - A[7,4]=parse(BigInt,"6373437319382536771018620806214785516542915567996760353063349991182871200304")//parse(BigInt,"19178871740288180724887392022898914045213833131528843480576173243533301485") - A[7,5]=-parse(BigInt,"836513109281956728811652083904588515347012294160401579661057793958992")//parse(BigInt,"42189346226535262916910956145917457264775063492307360825161811325023") - A[7,6]=parse(BigInt,"10038768138260655813133796321688310283082351149893792474426644227234755871856831386997923013888351")//parse(BigInt,"8279123943002224665888560854425725483235895533066047643118716510648226939201056966728652698557760") - A[8,1]=parse(BigInt,"1454976871505621321312348899226731229297985195430097820532172928754404221419640982320963761")//parse(BigInt,"12687546780768188413911065021432924447284583965992535848754097389537051103097048673168256") + A[7,3]=-53537582181289418572806048482253962781541488//128102133978061070595749084326726258918069 + A[7,4]=6373437319382536771018620806214785516542915567996760353063349991182871200304//19178871740288180724887392022898914045213833131528843480576173243533301485 + A[7,5]=-836513109281956728811652083904588515347012294160401579661057793958992//42189346226535262916910956145917457264775063492307360825161811325023 + A[7,6]=10038768138260655813133796321688310283082351149893792474426644227234755871856831386997923013888351//8279123943002224665888560854425725483235895533066047643118716510648226939201056966728652698557760 + A[8,1]=1454976871505621321312348899226731229297985195430097820532172928754404221419640982320963761//12687546780768188413911065021432924447284583965992535848754097389537051103097048673168256 A[8,2]=0 - A[8,3]=-parse(BigInt,"1452249436938195913836212549773886207822959770792")//parse(BigInt,"3187825000852340545619892931005470986913487349") - A[8,4]=parse(BigInt,"3193785703967379485471835519262043520640585789136428552340853315619929163223926155626278646291801931779256")//parse(BigInt,"8816743814108800069900425523882492176796603795861854625575345408990649746129323017714575203134405597571") - A[8,5]=-parse(BigInt,"314398569508916946629277462588835135011587938712337655816458752800894863689255534896547161759213480")//parse(BigInt,"14507196201560052990013371105817112064769849230048646555812475120383456376679192045076337148816813") - A[8,6]=parse(BigInt,"5021633516852870452803558794670341128133410978274753232000155240629688617274518068065484524425884625107263111090060721584249881611265924113")//parse(BigInt,"3807402575192378287101053794016079417728266285278436439472658972755893033722804748992796724254152818232996309281540415603729279478920107136") - A[8,7]=-parse(BigInt,"894451839895008223904010765658125850176064186717638397881061173697811879745")//parse(BigInt,"186244934020117483847289332768639722211239803963523669807238114327710091115676") - A[9,1]=parse(BigInt,"152015786770038627019906826956584678402371493198250158080970494807155603994339")//parse(BigInt,"1319428594672311986480108760138089275639618425553698631283119461253421932416") + A[8,3]=-1452249436938195913836212549773886207822959770792//3187825000852340545619892931005470986913487349 + A[8,4]=3193785703967379485471835519262043520640585789136428552340853315619929163223926155626278646291801931779256//8816743814108800069900425523882492176796603795861854625575345408990649746129323017714575203134405597571 + A[8,5]=-314398569508916946629277462588835135011587938712337655816458752800894863689255534896547161759213480//14507196201560052990013371105817112064769849230048646555812475120383456376679192045076337148816813 + A[8,6]=5021633516852870452803558794670341128133410978274753232000155240629688617274518068065484524425884625107263111090060721584249881611265924113//3807402575192378287101053794016079417728266285278436439472658972755893033722804748992796724254152818232996309281540415603729279478920107136 + A[8,7]=-894451839895008223904010765658125850176064186717638397881061173697811879745//186244934020117483847289332768639722211239803963523669807238114327710091115676 + A[9,1]=152015786770038627019906826956584678402371493198250158080970494807155603994339//1319428594672311986480108760138089275639618425553698631283119461253421932416 A[9,2]=0 - A[9,3]=-parse(BigInt,"19887569115365707672105043997835466942389220328")//parse(BigInt,"43451712251082409470704235239058276887205131") - A[9,4]=parse(BigInt,"6298831527954572673520838478029639446424615570453903300371170696118960335541193275024146681623960")//parse(BigInt,"17307483347318198085207889427954666589398911583434527253470846782562794571553580157056644256313") - A[9,5]=-parse(BigInt,"16267621644623777942279856217571823792451732234540266142050307930357537283432611648312520")//parse(BigInt,"747020211145282116967827947968990352912884924402891384654470989583659988117513448655559") - A[9,6]=parse(BigInt,"491920517345271821393960134665582163547632868347911487496995665146055538579545277983570189994492481977206720065882583432234119698425636137169515")//parse(BigInt,"371241970695441505578374965290296000309261530083026613438333515399198575394818137422626328203755084156959422247928840402063855870066548878130304") - A[9,7]=-parse(BigInt,"17535891839112183607157943692398769696531153719141528498448224128785868799210475")//parse(BigInt,"3881175428498724209649715816699297677268154716152409333146177577349474565697791732") - A[9,8]=-parse(BigInt,"31140449219386755112730831706895080247696102690585728771850210691242594436100540310")//parse(BigInt,"58531715707220748822628340615174217489020037018063169180406742622693159384762890406389") - A[10,1]=parse(BigInt,"24861126512935523838485032295435745281790804119672244200744512677831357181363")//parse(BigInt,"215828469302253893975010055544246846578750854407392771457340001283636121600") + A[9,3]=-19887569115365707672105043997835466942389220328//43451712251082409470704235239058276887205131 + A[9,4]=6298831527954572673520838478029639446424615570453903300371170696118960335541193275024146681623960//17307483347318198085207889427954666589398911583434527253470846782562794571553580157056644256313 + A[9,5]=-16267621644623777942279856217571823792451732234540266142050307930357537283432611648312520//747020211145282116967827947968990352912884924402891384654470989583659988117513448655559 + A[9,6]=491920517345271821393960134665582163547632868347911487496995665146055538579545277983570189994492481977206720065882583432234119698425636137169515//371241970695441505578374965290296000309261530083026613438333515399198575394818137422626328203755084156959422247928840402063855870066548878130304 + A[9,7]=-17535891839112183607157943692398769696531153719141528498448224128785868799210475//3881175428498724209649715816699297677268154716152409333146177577349474565697791732 + A[9,8]=-31140449219386755112730831706895080247696102690585728771850210691242594436100540310//58531715707220748822628340615174217489020037018063169180406742622693159384762890406389 + A[10,1]=24861126512935523838485032295435745281790804119672244200744512677831357181363//215828469302253893975010055544246846578750854407392771457340001283636121600 A[10,2]=0 A[10,3]=-76626859319946149305867456329803//167454524692981091214376557800 - A[10,4]=parse(BigInt,"257532657386915224604779230484778835596042580268896440943054087972106955277512448850995064336363")//parse(BigInt,"707777528357579864776572552477247532276956780876653359042572831013312547307465249178438602200") - A[10,5]=-parse(BigInt,"103092665221253777021612043042409780416654274677686197534469014507504059634284484983141143")//parse(BigInt,"4735075386204034224907103653335170134874540866215348781137359896717512695961598377363000") - A[10,6]=parse(BigInt,"1318945254307068672853031172410281620677291556423152759282406612372948205789241763483098989903852936890735513699395545618802215742952753372919")//parse(BigInt,"995520191927224509158660659519643916330847017611189618002256023928790665495276022949114110343406997764203331763292012060684160018593393766400") - A[10,7]=-parse(BigInt,"2175691361381933486174620849991740173349017185199505364607841")//parse(BigInt,"482872625303278742130341621563226511344221688759361797916327450") - A[10,8]=-parse(BigInt,"11327601987184122343710458559595782081610122892585097")//parse(BigInt,"21251874884678431935286330856983429378055579208005268000") + A[10,4]=257532657386915224604779230484778835596042580268896440943054087972106955277512448850995064336363//707777528357579864776572552477247532276956780876653359042572831013312547307465249178438602200 + A[10,5]=-103092665221253777021612043042409780416654274677686197534469014507504059634284484983141143//4735075386204034224907103653335170134874540866215348781137359896717512695961598377363000 + A[10,6]=1318945254307068672853031172410281620677291556423152759282406612372948205789241763483098989903852936890735513699395545618802215742952753372919//995520191927224509158660659519643916330847017611189618002256023928790665495276022949114110343406997764203331763292012060684160018593393766400 + A[10,7]=-2175691361381933486174620849991740173349017185199505364607841//482872625303278742130341621563226511344221688759361797916327450 + A[10,8]=-11327601987184122343710458559595782081610122892585097//21251874884678431935286330856983429378055579208005268000 A[10,9]=0 - α[1]=parse(BigInt,"677260699094873524061210073954310211")//parse(BigInt,"13212228177645157882237395248920447488") + α[1]=677260699094873524061210073954310211//13212228177645157882237395248920447488 α[2]=0 α[3]=0 - α[4]=parse(BigInt,"5627843976805934592544586970647029617399366281651959837492864")//parse(BigInt,"20448796992082885248862284273169726631726393791864145954479875") - α[5]=parse(BigInt,"1359735671458057021603668186882234273947181034928034734244224")//parse(BigInt,"4035225037829041960922838374222759264846456609494840689395475") - α[6]=parse(BigInt,"3575764371063841994042920363615768888383369782579963896064642431626191680598750790399139608006651160426580137040859330533720256407")//parse(BigInt,"18833618269956378326078572170759846509476617594300797062242096554507068838086062412372695473217373611870290738365243380652826304000") - α[7]=parse(BigInt,"14322850798205614664394883796805489119964080948503151")//parse(BigInt,"1692788382425178679633337406927131793062126418747780") - α[8]=-parse(BigInt,"16735096417960349589058935251250023138290806176584545269411")//parse(BigInt,"128573843052304513208482301684749747737236254208431871400") + α[4]=5627843976805934592544586970647029617399366281651959837492864//20448796992082885248862284273169726631726393791864145954479875 + α[5]=1359735671458057021603668186882234273947181034928034734244224//4035225037829041960922838374222759264846456609494840689395475 + α[6]=3575764371063841994042920363615768888383369782579963896064642431626191680598750790399139608006651160426580137040859330533720256407//18833618269956378326078572170759846509476617594300797062242096554507068838086062412372695473217373611870290738365243380652826304000 + α[7]=14322850798205614664394883796805489119964080948503151//1692788382425178679633337406927131793062126418747780 + α[8]=-16735096417960349589058935251250023138290806176584545269411//128573843052304513208482301684749747737236254208431871400 α[9]=33050288141543277444692395096256051//271248590133163812341791503489000 α[10]=0 - αEEst[1]=parse(BigInt,"962650826879437817605721930727384851")//parse(BigInt,"18874611682350225546053421784172067840") + αEEst[1]=962650826879437817605721930727384851//18874611682350225546053421784172067840 αEEst[2]=0 αEEst[3]=0 - αEEst[4]=parse(BigInt,"99703652969826806275610089806158069716600653757297413344")//parse(BigInt,"361062893830367886445877712954352019629670588714825566425") - αEEst[5]=parse(BigInt,"17540887447270394964911517553576959050951784592644178144")//parse(BigInt,"52550888012671962193116521992300249584518949945887203425") - αEEst[6]=parse(BigInt,"101855668513773837712956593596043266148479443244790887636953159551191054134940671472736229702711787350735239179")//parse(BigInt,"504322587935299170723833764883183242017770187561624249681119708768991642691172146267201689787026963930014131200") - αEEst[7]=parse(BigInt,"179578338747395946570172802104016572846366090083599")//parse(BigInt,"31203472487100067827342625012481692038011546889360") - αEEst[8]=-parse(BigInt,"500374162579884236288722085953024481890963958534161489781")//parse(BigInt,"5844265593286568782203740985670443078965284282201448700") + αEEst[4]=99703652969826806275610089806158069716600653757297413344//361062893830367886445877712954352019629670588714825566425 + αEEst[5]=17540887447270394964911517553576959050951784592644178144//52550888012671962193116521992300249584518949945887203425 + αEEst[6]=101855668513773837712956593596043266148479443244790887636953159551191054134940671472736229702711787350735239179//504322587935299170723833764883183242017770187561624249681119708768991642691172146267201689787026963930014131200 + αEEst[7]=179578338747395946570172802104016572846366090083599//31203472487100067827342625012481692038011546889360 + αEEst[8]=-500374162579884236288722085953024481890963958534161489781//5844265593286568782203740985670443078965284282201448700 αEEst[9]=0 αEEst[10]=80 @@ -3525,38 +3525,38 @@ function constructTanakaYamashitaStable7(T::Type = Float64) A[5,2]=0 A[5,3]=134004261625//1187078945472 A[5,4]=149425089125//1780618418208 - A[6,1]=parse(BigInt,"874723327324627172137139789673935509613630495")//parse(BigInt,"56881344496107103495850556251109088355454531158") + A[6,1]=874723327324627172137139789673935509613630495//56881344496107103495850556251109088355454531158 A[6,2]=0 - A[6,3]=parse(BigInt,"140089490273660861720564275306545765967660125")//parse(BigInt,"4375488038162084884296196634700699104265733166") - A[6,4]=-parse(BigInt,"2038049847879400647989164901369906650290192935250")//parse(BigInt,"47909406273855748440601205051655304842157645301117") - A[6,5]=parse(BigInt,"2992403630086592541124850354372857004595944160")//parse(BigInt,"168193972876080132251638040959092347542006316207") + A[6,3]=140089490273660861720564275306545765967660125//4375488038162084884296196634700699104265733166 + A[6,4]=-2038049847879400647989164901369906650290192935250//47909406273855748440601205051655304842157645301117 + A[6,5]=2992403630086592541124850354372857004595944160//168193972876080132251638040959092347542006316207 A[7,1]=-2001378790961964301303250341598299//131178829335937360185206084581250 A[7,2]=0 A[7,3]=-1366679891168526950613//3342867750190010177170 - A[7,4]=-parse(BigInt,"197077954039191584877658472075693196650")//parse(BigInt,"14482289235786224954374999272581521053") - A[7,5]=parse(BigInt,"2928205733652489758138852423071126752")//parse(BigInt,"289494157432907631631314224968221875") - A[7,6]=parse(BigInt,"32572843800597493853254181634376441943013874856495312")//parse(BigInt,"1642002429836009758962688168840520197029337863346875") - A[8,1]=parse(BigInt,"226949925367094612475083609619198193642397605")//parse(BigInt,"120406368918742115270494114142742317844627456") + A[7,4]=-197077954039191584877658472075693196650//14482289235786224954374999272581521053 + A[7,5]=2928205733652489758138852423071126752//289494157432907631631314224968221875 + A[7,6]=32572843800597493853254181634376441943013874856495312//1642002429836009758962688168840520197029337863346875 + A[8,1]=226949925367094612475083609619198193642397605//120406368918742115270494114142742317844627456 A[8,2]=0 A[8,3]=83451940525721530822125//1129677771714575730562048 - A[8,4]=parse(BigInt,"7035716180093388934005544535766324331669337496890597125")//parse(BigInt,"8744668672303692797949525789789288711635037496457428992") - A[8,5]=parse(BigInt,"1783910495800307104322539337559667105512922125")//parse(BigInt,"384741540181237650862158213355907627413029681664") - A[8,6]=-parse(BigInt,"84153602056538973791098303633128803165153465256807063611390103929570560775")//parse(BigInt,"37282901435832588263568764858094381410386083732352113498074163165795975168") - A[8,7]=parse(BigInt,"529655154424978769932790603243342890625")//parse(BigInt,"2074272966571578715335103162383459680256") - A[9,1]=-parse(BigInt,"2220302447236283385210081868020072818509")//parse(BigInt,"374126802552343922668161638021420098000") + A[8,4]=7035716180093388934005544535766324331669337496890597125//8744668672303692797949525789789288711635037496457428992 + A[8,5]=1783910495800307104322539337559667105512922125//384741540181237650862158213355907627413029681664 + A[8,6]=-84153602056538973791098303633128803165153465256807063611390103929570560775//37282901435832588263568764858094381410386083732352113498074163165795975168 + A[8,7]=529655154424978769932790603243342890625//2074272966571578715335103162383459680256 + A[9,1]=-2220302447236283385210081868020072818509//374126802552343922668161638021420098000 A[9,2]=0 A[9,3]=-580875348986851918117575//7422906155739208262352728 - A[9,4]=-parse(BigInt,"10152884092399228192381460837845336141124812794348025")//parse(BigInt,"1298474693887469810743537803700532058113206856602944") - A[9,5]=parse(BigInt,"57628597675871150072147324302138021982593246488")//parse(BigInt,"8694208064927983865022808524707850651868593125") - A[9,6]=parse(BigInt,"25006323928409346448859146781582297955220041834414805003311931721685248934905197")//parse(BigInt,"3116797087097920659891402066923116953398124957660879445267880838924530153376000") - A[9,7]=-parse(BigInt,"991935992163983524020354479671037652370649875")//parse(BigInt,"1096924827756227471690652450958041839154828032") - A[9,8]=parse(BigInt,"11028636941861502413824025771962099757599945728")//parse(BigInt,"10166706010345110864067934052134974581343819375") - A[10,1]=parse(BigInt,"2847557162233802909802913419338134005277")//parse(BigInt,"175580852316165047798631596921711256000") + A[9,4]=-10152884092399228192381460837845336141124812794348025//1298474693887469810743537803700532058113206856602944 + A[9,5]=57628597675871150072147324302138021982593246488//8694208064927983865022808524707850651868593125 + A[9,6]=25006323928409346448859146781582297955220041834414805003311931721685248934905197//3116797087097920659891402066923116953398124957660879445267880838924530153376000 + A[9,7]=-991935992163983524020354479671037652370649875//1096924827756227471690652450958041839154828032 + A[9,8]=11028636941861502413824025771962099757599945728//10166706010345110864067934052134974581343819375 + A[10,1]=2847557162233802909802913419338134005277//175580852316165047798631596921711256000 A[10,2]=0 A[10,3]=1552914837310075//7167358071597822 - A[10,4]=parse(BigInt,"7813795507395804332400817811705117266280297151179075")//parse(BigInt,"609385085239477995902119898391644620983028518989568") - A[10,5]=-parse(BigInt,"306358654025510315315806741256227901425369583")//parse(BigInt,"37780230596405542839291492772111971777338125") - A[10,6]=-parse(BigInt,"30230616135053261889365940573714713926595600173797519397657905897494488117634591")//parse(BigInt,"1462739064177653822206630548583223553011887775071057363338006334613651993472000") + A[10,4]=7813795507395804332400817811705117266280297151179075//609385085239477995902119898391644620983028518989568 + A[10,5]=-306358654025510315315806741256227901425369583//37780230596405542839291492772111971777338125 + A[10,6]=-30230616135053261889365940573714713926595600173797519397657905897494488117634591//1462739064177653822206630548583223553011887775071057363338006334613651993472000 A[10,7]=-3556025825918703192187464108779875//11170666795578957880984290260063232 A[10,8]=2140578935503723938488131712//2556174768949326564363043125 A[10,9]=0 @@ -3565,7 +3565,7 @@ function constructTanakaYamashitaStable7(T::Type = Float64) α[3]=0 α[4]=-5319231056637407390089058139231875//4078513870347642725257280732562048 α[5]=2430832495624902882205404599808//1640677233246140147577399278125 - α[6]=parse(BigInt,"58846832125102891510730576086257275195560457005949780449038492433452787")//parse(BigInt,"55051022626529988904867724618756855605285697694381512902783594390080000") + α[6]=58846832125102891510730576086257275195560457005949780449038492433452787//55051022626529988904867724618756855605285697694381512902783594390080000 α[7]=8765694250492187515737289375//142862058843931893355781359104 α[8]=282726763309436004945812396032//864839130161188820942829590625 α[9]=35795813026789129771//507885604115513709330 @@ -3575,7 +3575,7 @@ function constructTanakaYamashitaStable7(T::Type = Float64) αEEst[3]=0 αEEst[4]=-2188638181830974432849378205625//2703688346269567600435718085888 αEEst[5]=1313681506776569792299836438//1214416900996402773928496875 - αEEst[6]=parse(BigInt,"3205635250634133320066291736997892470430172563677735127041069")//parse(BigInt,"5224293273794925935053617011014728265925425567271645535360000") + αEEst[6]=3205635250634133320066291736997892470430172563677735127041069//5224293273794925935053617011014728265925425567271645535360000 αEEst[7]=153260086062341088187716875//1103181921574763655256998912 αEEst[8]=1144102534493369691260897984//4260291281582210940605071875 αEEst[9]=0 @@ -3915,54 +3915,54 @@ function constructEnrightVerner8(T::Type = Float64) A[8,5]=-29670244019740727//6363654238520000 A[8,6]=503350581600824913//125990342179812500 A[8,7]=9 - A[9,1]=-parse(BigInt,"16045918035544526531085666708200976799092954349059102554439418058855237034803138076235914485211856830024864166368323768200")//parse(BigInt,"9829483157728664844198544034921655975378257830080951893693520116322068439377446708493269493633244146421522730587295739613") + A[9,1]=-16045918035544526531085666708200976799092954349059102554439418058855237034803138076235914485211856830024864166368323768200//9829483157728664844198544034921655975378257830080951893693520116322068439377446708493269493633244146421522730587295739613 A[9,2]=0 A[9,3]=0 - A[9,4]=-parse(BigInt,"2358539147881877873039445811751103289867403691705393271280994482043263320271984518766662589229245453919623760032009543680000000")//parse(BigInt,"217835526181955565558022800341429464086385172122906608031349543583863022015887117168566338470163090032498196064101837445053273") - A[9,5]=-parse(BigInt,"991136638972626168678903371416456100093900405535164924683058122802429707354033382826947398158683765324439618282500000000")//parse(BigInt,"79848142008846002789298925227605775190331269194726743910364273272231784282184770467794155269096224513726772081370189773") - A[9,6]=parse(BigInt,"99411279821210413387149352497211785829547149358696952646781033905129048593757052549024957474512389085654050445280000000")//parse(BigInt,"10219750071154355529199360565479179548497227516418867455143546824991883616697162903707552409044338358355837306818391433") - A[9,7]=parse(BigInt,"194327599672380134095898291719912961363678073793023525007081328425098431574448809779310732532821200046895000000000")//parse(BigInt,"11996011488227722649656673931136490891256463292620473601841875115170259043531987881275965965525693289412424400177") - A[9,8]=-parse(BigInt,"4738143867684122189593816244199450540483384372163549951990525387550768038015218275414120082248510000000000")//parse(BigInt,"45627381556119209828916528385326434273376137158228892503158792567081801761628344925618992749059885819540261") - A[10,1]=parse(BigInt,"100509763879264306824096153463041174636629364248095333923106653001873")//parse(BigInt,"229490324007644628042361756217436155832461488260089524115475000000000") + A[9,4]=-2358539147881877873039445811751103289867403691705393271280994482043263320271984518766662589229245453919623760032009543680000000//217835526181955565558022800341429464086385172122906608031349543583863022015887117168566338470163090032498196064101837445053273 + A[9,5]=-991136638972626168678903371416456100093900405535164924683058122802429707354033382826947398158683765324439618282500000000//79848142008846002789298925227605775190331269194726743910364273272231784282184770467794155269096224513726772081370189773 + A[9,6]=99411279821210413387149352497211785829547149358696952646781033905129048593757052549024957474512389085654050445280000000//10219750071154355529199360565479179548497227516418867455143546824991883616697162903707552409044338358355837306818391433 + A[9,7]=194327599672380134095898291719912961363678073793023525007081328425098431574448809779310732532821200046895000000000//11996011488227722649656673931136490891256463292620473601841875115170259043531987881275965965525693289412424400177 + A[9,8]=-4738143867684122189593816244199450540483384372163549951990525387550768038015218275414120082248510000000000//45627381556119209828916528385326434273376137158228892503158792567081801761628344925618992749059885819540261 + A[10,1]=100509763879264306824096153463041174636629364248095333923106653001873//229490324007644628042361756217436155832461488260089524115475000000000 A[10,2]=0 A[10,3]=0 - A[10,4]=parse(BigInt,"35076261889213578261995286390053983221937920015616")//parse(BigInt,"8903662403052468890234321680409039895089390971875") - A[10,5]=parse(BigInt,"29877053472248545227782869189767925950557009")//parse(BigInt,"10443709158645362958089905740134206606110000") - A[10,6]=-parse(BigInt,"72602025182798889442893966553844286012776770019588838776297031451")//parse(BigInt,"40918439380405007926071673834718276106178863851548244800289187500") - A[10,7]=-parse(BigInt,"15322912063864370512130145988492098605486502994107816190")//parse(BigInt,"3130069400645604876183669549605539076333579290524919889") - A[10,8]=parse(BigInt,"66085154677219418645471125072555541174985695924")//parse(BigInt,"310222736648235062495097951962638800384203417327") - A[10,9]=-parse(BigInt,"33475654618965607625490266678231230366345830527265525310030016230875755239420324728600957368877132012320553021")//parse(BigInt,"563607181486505082775419237614873016043169125130359330269370345097328575740250457475506596993780051575000000000") - A[11,1]=-parse(BigInt,"5101097760197841615137571256611109219669965728737004453654940399435749927779")//parse(BigInt,"3460254790065218498025394912113654440547987641021174968985010753183759952128") + A[10,4]=35076261889213578261995286390053983221937920015616//8903662403052468890234321680409039895089390971875 + A[10,5]=29877053472248545227782869189767925950557009//10443709158645362958089905740134206606110000 + A[10,6]=-72602025182798889442893966553844286012776770019588838776297031451//40918439380405007926071673834718276106178863851548244800289187500 + A[10,7]=-15322912063864370512130145988492098605486502994107816190//3130069400645604876183669549605539076333579290524919889 + A[10,8]=66085154677219418645471125072555541174985695924//310222736648235062495097951962638800384203417327 + A[10,9]=-33475654618965607625490266678231230366345830527265525310030016230875755239420324728600957368877132012320553021//563607181486505082775419237614873016043169125130359330269370345097328575740250457475506596993780051575000000000 + A[11,1]=-5101097760197841615137571256611109219669965728737004453654940399435749927779//3460254790065218498025394912113654440547987641021174968985010753183759952128 A[11,2]=0 A[11,3]=0 - A[11,4]=-parse(BigInt,"739282853758412257967453242147288028248514875000")//parse(BigInt,"67244182875654829098323943713374207709631980757") - A[11,5]=-parse(BigInt,"304301954438407952266341438991435702455078125")//parse(BigInt,"26817588459995310678515661957421952038871616") - A[11,6]=parse(BigInt,"7944893992399893116476631697520363855501654462308622798446100145004371780765625")//parse(BigInt,"887005161602928659252827604035768657298435884939489754462273147402132735951354") - A[11,7]=parse(BigInt,"271466662889835128614810796916069488062485834784939879774912795880859375")//parse(BigInt,"17080057868208807584911919572395871967414618088449127584294090356526117") - A[11,8]=-parse(BigInt,"547671639173493535187249719091874257724281347519101322819710937500")//parse(BigInt,"5545897345777551056363997101744668576293320106258184122878184564689") - A[11,9]=parse(BigInt,"278805054229456473051914785770130401056277521071386274820253852826023602554035252878888463451556710568650135086751734733498388408614837563")//parse(BigInt,"57032789758993842471673989706725819315996341861372243823982103984407642346136141015055914541200747733442561186185728215790313661884647470336") - A[11,10]=-parse(BigInt,"7641031089620713267943821483116886435546875")//parse(BigInt,"1865115549729059107236140767953375513727732867") - A[12,1]=-parse(BigInt,"2173296165244568434534168496725754283210370856714048295955495704392191998074219")//parse(BigInt,"826329709817197468253912814996276721297719271873047121496939265708086637102000") + A[11,4]=-739282853758412257967453242147288028248514875000//67244182875654829098323943713374207709631980757 + A[11,5]=-304301954438407952266341438991435702455078125//26817588459995310678515661957421952038871616 + A[11,6]=7944893992399893116476631697520363855501654462308622798446100145004371780765625//887005161602928659252827604035768657298435884939489754462273147402132735951354 + A[11,7]=271466662889835128614810796916069488062485834784939879774912795880859375//17080057868208807584911919572395871967414618088449127584294090356526117 + A[11,8]=-547671639173493535187249719091874257724281347519101322819710937500//5545897345777551056363997101744668576293320106258184122878184564689 + A[11,9]=278805054229456473051914785770130401056277521071386274820253852826023602554035252878888463451556710568650135086751734733498388408614837563//57032789758993842471673989706725819315996341861372243823982103984407642346136141015055914541200747733442561186185728215790313661884647470336 + A[11,10]=-7641031089620713267943821483116886435546875//1865115549729059107236140767953375513727732867 + A[12,1]=-2173296165244568434534168496725754283210370856714048295955495704392191998074219//826329709817197468253912814996276721297719271873047121496939265708086637102000 A[12,2]=0 A[12,3]=0 - A[12,4]=-parse(BigInt,"1176485889334472345397948024769479865991267657667189808793600000")//parse(BigInt,"128238274125745784857395023683055391720808636521055761250085619") - A[12,5]=-parse(BigInt,"901641526273088667293677983960434306145731566007759375000")//parse(BigInt,"47006051321531726477650870675115597779536141098588395119") - A[12,6]=parse(BigInt,"44619197709345843038609995810290222092713734357503573021289399188441075277893825000")//parse(BigInt,"3047226829867759667805678237083584916028456629069014496162891378892137605913688013") - A[12,7]=parse(BigInt,"948339742665210716931560767459705347432692833888702670755668800833857753125000")//parse(BigInt,"54100203068523816523920547203712158257383235486719126879290708372319555115953") - A[12,8]=-parse(BigInt,"469359986530784242367841163967997985280992052062479522694037718750000")//parse(BigInt,"1262000068797740029604893636717124646814536106030908513651797310900389") - A[12,9]=-parse(BigInt,"664127481006260866245417353167879111725438608160134129788715555378465573117813001757238260693051901812594341608922016461968723754067215934799054852630446938063")//parse(BigInt,"947405313675779327886462044861834846879473861539583479995101168291116168844040438751584392785913224239894029843821464363224405440877235651675827150051218506000") - A[12,10]=parse(BigInt,"124594688949431236718278718078688571245967961641584151713065625000")//parse(BigInt,"2442266119995123914599926487344630873565880304003136401896150897137") - A[12,11]=parse(BigInt,"561064742310110985699639624014768981793940948761680464947352")//parse(BigInt,"671379391526329055316725343694451428305592235340194400714475") - A[13,1]=parse(BigInt,"2112537365439605317842214400294939600845864356126794907105288476157299972777")//parse(BigInt,"9791129992576348954381966935712572673760150144277222568673000574989723295600") + A[12,4]=-1176485889334472345397948024769479865991267657667189808793600000//128238274125745784857395023683055391720808636521055761250085619 + A[12,5]=-901641526273088667293677983960434306145731566007759375000//47006051321531726477650870675115597779536141098588395119 + A[12,6]=44619197709345843038609995810290222092713734357503573021289399188441075277893825000//3047226829867759667805678237083584916028456629069014496162891378892137605913688013 + A[12,7]=948339742665210716931560767459705347432692833888702670755668800833857753125000//54100203068523816523920547203712158257383235486719126879290708372319555115953 + A[12,8]=-469359986530784242367841163967997985280992052062479522694037718750000//1262000068797740029604893636717124646814536106030908513651797310900389 + A[12,9]=-664127481006260866245417353167879111725438608160134129788715555378465573117813001757238260693051901812594341608922016461968723754067215934799054852630446938063//947405313675779327886462044861834846879473861539583479995101168291116168844040438751584392785913224239894029843821464363224405440877235651675827150051218506000 + A[12,10]=124594688949431236718278718078688571245967961641584151713065625000//2442266119995123914599926487344630873565880304003136401896150897137 + A[12,11]=561064742310110985699639624014768981793940948761680464947352//671379391526329055316725343694451428305592235340194400714475 + A[13,1]=2112537365439605317842214400294939600845864356126794907105288476157299972777//9791129992576348954381966935712572673760150144277222568673000574989723295600 A[13,2]=0 A[13,3]=0 - A[13,4]=parse(BigInt,"63401732568650174882469655273037557867024014649473659852800000")//parse(BigInt,"7597437179564699900056826682790095876501867794005624909986891") - A[13,5]=parse(BigInt,"6086761737797404637560639819223305802258863489403125000")//parse(BigInt,"2784859079002788542258846760345051095481316496802932391") - A[13,6]=-parse(BigInt,"2559665601805637409198888850698428172565517218973577146475607855715703433900000")//parse(BigInt,"1517075781450111169555356439342115045941218379260955323225394329122945220575603") - A[13,7]=-parse(BigInt,"3562962724414944757891560164749973139486260772587248231213362868690625000")//parse(BigInt,"408976639178968899516222045518619849445955714595234573207901740578867341") - A[13,8]=parse(BigInt,"27274774093948890572327172846505411328624378015249298079900000000")//parse(BigInt,"1115922486918625141794316350997246426030217325603407120793811703663") - A[13,9]=parse(BigInt,"1517649980273287794810711480928689762969941359446589355244683243470868873980537462717945530891242892188019850453060256773054273287757818339")//parse(BigInt,"17931096351403549517324822951619492690590259109554169692111771494162805088297821242848492102923447532215742446890559805801281057084758250800") - A[13,10]=parse(BigInt,"36524642706569597276845612368244490741747970924877885921875000")//parse(BigInt,"67204508345515429491838411146746729660269255184823759889942481") + A[13,4]=63401732568650174882469655273037557867024014649473659852800000//7597437179564699900056826682790095876501867794005624909986891 + A[13,5]=6086761737797404637560639819223305802258863489403125000//2784859079002788542258846760345051095481316496802932391 + A[13,6]=-2559665601805637409198888850698428172565517218973577146475607855715703433900000//1517075781450111169555356439342115045941218379260955323225394329122945220575603 + A[13,7]=-3562962724414944757891560164749973139486260772587248231213362868690625000//408976639178968899516222045518619849445955714595234573207901740578867341 + A[13,8]=27274774093948890572327172846505411328624378015249298079900000000//1115922486918625141794316350997246426030217325603407120793811703663 + A[13,9]=1517649980273287794810711480928689762969941359446589355244683243470868873980537462717945530891242892188019850453060256773054273287757818339//17931096351403549517324822951619492690590259109554169692111771494162805088297821242848492102923447532215742446890559805801281057084758250800 + A[13,10]=36524642706569597276845612368244490741747970924877885921875000//67204508345515429491838411146746729660269255184823759889942481 A[13,11]=0 A[13,12]=0 α[1]=55284231195707975647126708111723//1258814250475014554517603612114000 @@ -3970,11 +3970,11 @@ function constructEnrightVerner8(T::Type = Float64) α[3]=0 α[4]=0 α[5]=0 - α[6]=parse(BigInt,"101652048214282205518610445783893750000000")//parse(BigInt,"289586658278060310247144250081091360673509") - α[7]=parse(BigInt,"6219731958882093270433753490048828125000000")//parse(BigInt,"25268792314562899182186819800834272764054341") - α[8]=parse(BigInt,"471525882014932587321673707929687500000000")//parse(BigInt,"523728817391198795728810839649314044495553") - α[9]=parse(BigInt,"63998419659074502960979467027044380533513499562179716145788153981258354882170183557294261050806789914954901252698438375102943237148428019253408419")//parse(BigInt,"14067383878224159980676935999500324267727723947516309536464061683130063437616452951326819824531063499969576146304645311203502485409773697867038000") - α[10]=parse(BigInt,"594562755257530592552224345703125000000")//parse(BigInt,"123802720910327682301431417435953442122031") + α[6]=101652048214282205518610445783893750000000//289586658278060310247144250081091360673509 + α[7]=6219731958882093270433753490048828125000000//25268792314562899182186819800834272764054341 + α[8]=471525882014932587321673707929687500000000//523728817391198795728810839649314044495553 + α[9]=63998419659074502960979467027044380533513499562179716145788153981258354882170183557294261050806789914954901252698438375102943237148428019253408419//14067383878224159980676935999500324267727723947516309536464061683130063437616452951326819824531063499969576146304645311203502485409773697867038000 + α[10]=594562755257530592552224345703125000000//123802720910327682301431417435953442122031 α[11]=-1886691133979705639959153870454656//397947585885835383951563312487675 α[12]=-50061468875139778913910254637881//141186641936036184819986782313781 α[13]=0 @@ -3983,11 +3983,11 @@ function constructEnrightVerner8(T::Type = Float64) αEEst[3]=0 αEEst[4]=0 αEEst[5]=0 - αEEst[6]=parse(BigInt,"91472553308336221233020750122000000000")//parse(BigInt,"270389036674192633283981559366098375979") - αEEst[7]=parse(BigInt,"31245710879106859500854236329453125000000")//parse(BigInt,"125747467177230198813995913261775760852127") - αEEst[8]=parse(BigInt,"7580382785455138868782239796250000000000")//parse(BigInt,"33873008089978031564549954803189465564389") - αEEst[9]=-parse(BigInt,"1264668207534772000389416909088295806823076185957298091511366356638145411319432807599860924173256812108555319505561297378438513")//parse(BigInt,"31458133682363879376359837328611310990099259233936346807079836410100132902013789877583819562913435723874810037875576750158649200") - αEEst[10]=parse(BigInt,"2363202400377740499662213515625000000")//parse(BigInt,"19167474982246118950523520271861502109") + αEEst[6]=91472553308336221233020750122000000000//270389036674192633283981559366098375979 + αEEst[7]=31245710879106859500854236329453125000000//125747467177230198813995913261775760852127 + αEEst[8]=7580382785455138868782239796250000000000//33873008089978031564549954803189465564389 + αEEst[9]=-1264668207534772000389416909088295806823076185957298091511366356638145411319432807599860924173256812108555319505561297378438513//31458133682363879376359837328611310990099259233936346807079836410100132902013789877583819562913435723874810037875576750158649200 + αEEst[10]=2363202400377740499662213515625000000//19167474982246118950523520271861502109 αEEst[11]=0 αEEst[12]=0 αEEst[13]=2965876353908674111604434604609//47062213978678728273328927437927 @@ -4049,14 +4049,14 @@ function constructdverk78(T::Type = Float64) A[8,5]=-8339128164608//939060038475 A[8,6]=341936800488//47951126225 A[8,7]=1993321838240//380523459069 - A[9,1]=-parse(BigInt,"1840911252282376584438157336464708426954728061551")//parse(BigInt,"2991923615171151921596253813483118262195533733898") + A[9,1]=-1840911252282376584438157336464708426954728061551//2991923615171151921596253813483118262195533733898 A[9,2]=0 A[9,3]=0 - A[9,4]=-parse(BigInt,"14764960804048657303638372252908780219281424435")//parse(BigInt,"2981692102565021975611711269209606363661854518") - A[9,5]=-parse(BigInt,"875325048502130441118613421785266742862694404520560000")//parse(BigInt,"170212030428894418395571677575961339495435011888324169") - A[9,6]=parse(BigInt,"7632051964154290925661849798370645637589377834346780")//parse(BigInt,"1734087257418811583049800347581865260479233950396659") - A[9,7]=parse(BigInt,"7519834791971137517048532179652347729899303513750000")//parse(BigInt,"1045677303502317596597890707812349832637339039997351") - A[9,8]=parse(BigInt,"1366042683489166351293315549358278750")//parse(BigInt,"144631418224267718165055326464180836641") + A[9,4]=-14764960804048657303638372252908780219281424435//2981692102565021975611711269209606363661854518 + A[9,5]=-875325048502130441118613421785266742862694404520560000//170212030428894418395571677575961339495435011888324169 + A[9,6]=7632051964154290925661849798370645637589377834346780//1734087257418811583049800347581865260479233950396659 + A[9,7]=7519834791971137517048532179652347729899303513750000//1045677303502317596597890707812349832637339039997351 + A[9,8]=1366042683489166351293315549358278750//144631418224267718165055326464180836641 A[10,1]=-63077736705254280154824845013881//78369357853786633855112190394368 A[10,2]=0 A[10,3]=0 @@ -4065,26 +4065,26 @@ function constructdverk78(T::Type = Float64) A[10,6]=1001587844183325981198091450220795//184232684207722503701669953872896 A[10,7]=187023075231349900768014890274453125//25224698849808178010752575653374848 A[10,8]=1908158550070998850625//117087067039189929394176 - A[10,9]=-parse(BigInt,"52956818288156668227044990077324877908565")//parse(BigInt,"2912779959477433986349822224412353951940608") - A[11,1]=-parse(BigInt,"10116106591826909534781157993685116703")//parse(BigInt,"9562819945036894030442231411871744000") + A[10,9]=-52956818288156668227044990077324877908565//2912779959477433986349822224412353951940608 + A[11,1]=-10116106591826909534781157993685116703//9562819945036894030442231411871744000 A[11,2]=0 A[11,3]=0 A[11,4]=-9623541317323077848129//3864449564977792573440 A[11,5]=-4823348333146829406881375//576413233634141239944816 - A[11,6]=parse(BigInt,"6566119246514996884067001154977284529")//parse(BigInt,"970305487021846325473990863582315520") - A[11,7]=parse(BigInt,"2226455130519213549256016892506730559375")//parse(BigInt,"364880443159675255577435648380047355776") + A[11,6]=6566119246514996884067001154977284529//970305487021846325473990863582315520 + A[11,7]=2226455130519213549256016892506730559375//364880443159675255577435648380047355776 A[11,8]=39747262782380466933662225//1756032802431424164410720256 - A[11,9]=parse(BigInt,"48175771419260955335244683805171548038966866545122229")//parse(BigInt,"1989786420513815146528880165952064118903852843612160000") + A[11,9]=48175771419260955335244683805171548038966866545122229//1989786420513815146528880165952064118903852843612160000 A[11,10]=-2378292068163246//47768728487211875 A[12,1]=-3218022174758599831659045535578571//1453396753634469525663775847094384 A[12,2]=0 A[12,3]=0 A[12,4]=26290092604284231996745//5760876126062860430544 A[12,5]=-697069297560926452045586710000//41107967755245430594036502319 - A[12,6]=parse(BigInt,"1827357820434213461438077550902273440")//parse(BigInt,"139381013914245317709567680839641697") - A[12,7]=parse(BigInt,"643504802814241550941949227194107500000")//parse(BigInt,"242124609118836550860494007545333945331") + A[12,6]=1827357820434213461438077550902273440//139381013914245317709567680839641697 + A[12,7]=643504802814241550941949227194107500000//242124609118836550860494007545333945331 A[12,8]=162259938151380266113750//59091082835244183497007 - A[12,9]=-parse(BigInt,"23028251632873523818545414856857015616678575554130463402")//parse(BigInt,"20013169183191444503443905240405603349978424504151629055") + A[12,9]=-23028251632873523818545414856857015616678575554130463402//20013169183191444503443905240405603349978424504151629055 A[12,10]=7958341351371843889152//3284467988443203581305 A[12,11]=-507974327957860843878400//121555654819179042718967 A[13,1]=-549080624436801105208519835138333//353987109028707139687100885600400 @@ -4093,9 +4093,9 @@ function constructdverk78(T::Type = Float64) A[13,4]=29116675312186033956481//5331818957833865866320 A[13,5]=-91153092961177216058210567600//7609267653017028089793994539 A[13,6]=1540775569495234383390307262972464//164751248733597841985831445059895 - A[13,7]=-parse(BigInt,"2027488254536386321212021357622300000")//parse(BigInt,"7563800784313191306927092359781550321") + A[13,7]=-2027488254536386321212021357622300000//7563800784313191306927092359781550321 A[13,8]=-707592954577756600025//2430671607007101253926 - A[13,9]=-parse(BigInt,"315869406877370103440389763510384832076674110731")//parse(BigInt,"550845901016714794114516357859531754926300500125") + A[13,9]=-315869406877370103440389763510384832076674110731//550845901016714794114516357859531754926300500125 A[13,10]=4305840920849725632512//5066413598663346018375 A[13,11]=0 A[13,12]=0 @@ -4107,7 +4107,7 @@ function constructdverk78(T::Type = Float64) α[6]=14327219974204125//40489566827933216 α[7]=2720762324010009765625000//10917367480696813922225349 α[8]=-498533005859375//95352091037424 - α[9]=parse(BigInt,"405932030463777247926705030596175437402459637909765779")//parse(BigInt,"78803919436321841083201886041201537229769115088303952") + α[9]=405932030463777247926705030596175437402459637909765779//78803919436321841083201886041201537229769115088303952 α[10]=-10290327637248//1082076946951 α[11]=863264105888000//85814662253313 α[12]=-29746300739//247142463456 @@ -4120,7 +4120,7 @@ function constructdverk78(T::Type = Float64) αEEst[6]=495437430316125//1396191959583904 αEEst[7]=760741072216796875000//3055518466469861159313 αEEst[8]=1186143278515625//444976424841312 - αEEst[9]=parse(BigInt,"13791579353894559147128282108092181066885426809")//parse(BigInt,"3515333032435874239702147176443897942760320040") + αEEst[9]=13791579353894559147128282108092181066885426809//3515333032435874239702147176443897942760320040 αEEst[10]=-30733299644928//5410384734755 αEEst[11]=0 αEEst[12]=0 @@ -4184,53 +4184,53 @@ function constructTsitourasPapakostas8(T::Type = Float64) A[8,5]=-318556182235222634647116091//27172411532484037214054400 A[8,6]=1205563885850790193966807//132365727505912221222912 A[8,7]=254//39 - A[9,1]=-parse(BigInt,"20629396399716689122801179264428539394462855874226604463554767070845753369")//parse(BigInt,"42881759662770155956657513470012114488076017981128105307375594963152353200") + A[9,1]=-20629396399716689122801179264428539394462855874226604463554767070845753369//42881759662770155956657513470012114488076017981128105307375594963152353200 A[9,2]=0 A[9,3]=0 - A[9,4]=-parse(BigInt,"3315443074343659404779422149387397712986453181141168247590906370819301077749322753")//parse(BigInt,"498517112641608872807821838566847987729514312398278633788185835348997643218553476") - A[9,5]=-parse(BigInt,"273749409411654060286948141164828452109898379203526945684314474186724062841643")//parse(BigInt,"60427583951377552503967840653825589117167443021628367691773162913607984889600") - A[9,6]=parse(BigInt,"16656372518874512738268060504309924900437672263609245028809229865738327731797537")//parse(BigInt,"4276990138533930522782076385771016009097627930550149628282203007913538394549504") - A[9,7]=parse(BigInt,"42008080033354305590804322944084805264441066760038302359736803632")//parse(BigInt,"4865302423216534910074823287811605599629170295030631799935804001") - A[9,8]=parse(BigInt,"668459780930716338000066627236927417191947396177093524377824")//parse(BigInt,"71100452948884643779799087713322002499799983434685642170251833") - A[10,1]=-parse(BigInt,"1793603946322260900828212460706877142477132870159527")//parse(BigInt,"2313097568511990753781649719556084665131024900300800") + A[9,4]=-3315443074343659404779422149387397712986453181141168247590906370819301077749322753//498517112641608872807821838566847987729514312398278633788185835348997643218553476 + A[9,5]=-273749409411654060286948141164828452109898379203526945684314474186724062841643//60427583951377552503967840653825589117167443021628367691773162913607984889600 + A[9,6]=16656372518874512738268060504309924900437672263609245028809229865738327731797537//4276990138533930522782076385771016009097627930550149628282203007913538394549504 + A[9,7]=42008080033354305590804322944084805264441066760038302359736803632//4865302423216534910074823287811605599629170295030631799935804001 + A[9,8]=668459780930716338000066627236927417191947396177093524377824//71100452948884643779799087713322002499799983434685642170251833 + A[10,1]=-1793603946322260900828212460706877142477132870159527//2313097568511990753781649719556084665131024900300800 A[10,2]=0 A[10,3]=0 - A[10,4]=-parse(BigInt,"14776874123722838192315406145167687512425345723701")//parse(BigInt,"1847893530366076701102014146927696206329050105856") - A[10,5]=-parse(BigInt,"19587020919884661714856757105130246995757906603")//parse(BigInt,"2911893296942532038566182868170393629789388800") - A[10,6]=parse(BigInt,"6364380863259071677112259236455506477417699780613300364807")//parse(BigInt,"1150428174584942133406579091549443438814988349188394057728") - A[10,7]=parse(BigInt,"27725164402569748756040320433848245155581006369")//parse(BigInt,"2544159473655547770881695354241256106302348256") - A[10,8]=parse(BigInt,"10744247163960019876833255044784609639")//parse(BigInt,"534761804739901348825491947768304503296") - A[10,9]=-parse(BigInt,"50977737930792808232204417497248979399878217280011103197862899")//parse(BigInt,"1300915694564913675613280314081837358644964393191337994183389184") - A[11,1]=-parse(BigInt,"3587625717068952487214493441966897048737050755812600710793")//parse(BigInt,"3015733164033229624772006086429467685046639983706974412800") + A[10,4]=-14776874123722838192315406145167687512425345723701//1847893530366076701102014146927696206329050105856 + A[10,5]=-19587020919884661714856757105130246995757906603//2911893296942532038566182868170393629789388800 + A[10,6]=6364380863259071677112259236455506477417699780613300364807//1150428174584942133406579091549443438814988349188394057728 + A[10,7]=27725164402569748756040320433848245155581006369//2544159473655547770881695354241256106302348256 + A[10,8]=10744247163960019876833255044784609639//534761804739901348825491947768304503296 + A[10,9]=-50977737930792808232204417497248979399878217280011103197862899//1300915694564913675613280314081837358644964393191337994183389184 + A[11,1]=-3587625717068952487214493441966897048737050755812600710793//3015733164033229624772006086429467685046639983706974412800 A[11,2]=0 A[11,3]=0 - A[11,4]=-parse(BigInt,"5453011711267804731211501837262816944661201619903")//parse(BigInt,"764973320899716397072448644710733101329290196992") - A[11,5]=-parse(BigInt,"884348836774584715070440485633026464653487653")//parse(BigInt,"92725983515963799584249219499787659014963200") - A[11,6]=parse(BigInt,"26823469063654084387375587616552322383082061411417182757389742951")//parse(BigInt,"3541299744763681675473620647087123057228744296123642301654630400") - A[11,7]=parse(BigInt,"142363419491686507162007051071007722765323162710521029")//parse(BigInt,"12634887202368261565807449771335728082273587905775840") - A[11,8]=parse(BigInt,"64747617454909275289531520412519442831235890581")//parse(BigInt,"1269317188117975960996670628974453443777854830080") - A[11,9]=parse(BigInt,"112633808253272720979874303367503891597499261046700689572459050065039333987335667")//parse(BigInt,"1404514291245034532812181377119034501014039830518218465064579291611563374608650240") - A[11,10]=-parse(BigInt,"10612202518573994431153697720606405883")//parse(BigInt,"67082546658259846778754594976831647575") - A[12,1]=-parse(BigInt,"7534081165544982478296202335922049210803875045423")//parse(BigInt,"19219575665440848756074598051658416387002479820800") + A[11,4]=-5453011711267804731211501837262816944661201619903//764973320899716397072448644710733101329290196992 + A[11,5]=-884348836774584715070440485633026464653487653//92725983515963799584249219499787659014963200 + A[11,6]=26823469063654084387375587616552322383082061411417182757389742951//3541299744763681675473620647087123057228744296123642301654630400 + A[11,7]=142363419491686507162007051071007722765323162710521029//12634887202368261565807449771335728082273587905775840 + A[11,8]=64747617454909275289531520412519442831235890581//1269317188117975960996670628974453443777854830080 + A[11,9]=112633808253272720979874303367503891597499261046700689572459050065039333987335667//1404514291245034532812181377119034501014039830518218465064579291611563374608650240 + A[11,10]=-10612202518573994431153697720606405883//67082546658259846778754594976831647575 + A[12,1]=-7534081165544982478296202335922049210803875045423//19219575665440848756074598051658416387002479820800 A[12,2]=0 A[12,3]=0 - A[12,4]=parse(BigInt,"237696087452786717802270375283034262859273455")//parse(BigInt,"60688480889936839261131818793519097177034752") - A[12,5]=-parse(BigInt,"20610578209826329263318986584876108069323")//parse(BigInt,"7356333776438834884293014575840932659200") - A[12,6]=parse(BigInt,"51260471529841028040709654458903254781320136131844164563")//parse(BigInt,"20998023776318546907382302106788168158765514131585630208") - A[12,7]=-parse(BigInt,"3077214437173472971196810795615384000211457151011")//parse(BigInt,"1272435592582280820597059432060116893200684680384") - A[12,8]=-parse(BigInt,"1539218116260541896259682954580256454049")//parse(BigInt,"4534670830750360983422999946409310393344") - A[12,9]=parse(BigInt,"241886539350268429372116296787271276553970618941104594460614948326132797451456131")//parse(BigInt,"1240669632662465892528916120041123051054026283188324780101555345343662316090597376") + A[12,4]=237696087452786717802270375283034262859273455//60688480889936839261131818793519097177034752 + A[12,5]=-20610578209826329263318986584876108069323//7356333776438834884293014575840932659200 + A[12,6]=51260471529841028040709654458903254781320136131844164563//20998023776318546907382302106788168158765514131585630208 + A[12,7]=-3077214437173472971196810795615384000211457151011//1272435592582280820597059432060116893200684680384 + A[12,8]=-1539218116260541896259682954580256454049//4534670830750360983422999946409310393344 + A[12,9]=241886539350268429372116296787271276553970618941104594460614948326132797451456131//1240669632662465892528916120041123051054026283188324780101555345343662316090597376 A[12,10]=-80556486832245966191717452425924975//414445409518676597565032008051106461 - A[12,11]=parse(BigInt,"2944781680874500347594142792814463350")//parse(BigInt,"4965161383073676983610218096030654529") - A[13,1]=-parse(BigInt,"7757739937862944832927743694336116203639371542761")//parse(BigInt,"5225100678421794325654850845451340473577260032000") + A[12,11]=2944781680874500347594142792814463350//4965161383073676983610218096030654529 + A[13,1]=-7757739937862944832927743694336116203639371542761//5225100678421794325654850845451340473577260032000 A[13,2]=0 A[13,3]=0 - A[13,4]=-parse(BigInt,"433889546009521405913741133329446636837810749")//parse(BigInt,"181488796115643001621310691169322233346938880") - A[13,5]=-parse(BigInt,"246044720162308748108107126829066792329071")//parse(BigInt,"21999103311417807170100413255475150848000") - A[13,6]=parse(BigInt,"2140331235425829844389060818616719848637810765257179167")//parse(BigInt,"245428182036011897638028252815369258646052549878743040") - A[13,7]=parse(BigInt,"1573990926219809229258666534611598771063240529")//parse(BigInt,"214535514317495538101650508596881057760818080") - A[13,8]=parse(BigInt,"62408280667309375445301959066100433563")//parse(BigInt,"4838320046251983849512355559327451645440") - A[13,9]=parse(BigInt,"1145609822249493677618113725359506642998153205603226883141207089968379")//parse(BigInt,"26902802166822768476367427840835743139559294105398677975568538466119680") + A[13,4]=-433889546009521405913741133329446636837810749//181488796115643001621310691169322233346938880 + A[13,5]=-246044720162308748108107126829066792329071//21999103311417807170100413255475150848000 + A[13,6]=2140331235425829844389060818616719848637810765257179167//245428182036011897638028252815369258646052549878743040 + A[13,7]=1573990926219809229258666534611598771063240529//214535514317495538101650508596881057760818080 + A[13,8]=62408280667309375445301959066100433563//4838320046251983849512355559327451645440 + A[13,9]=1145609822249493677618113725359506642998153205603226883141207089968379//26902802166822768476367427840835743139559294105398677975568538466119680 A[13,10]=-408950356875874683139089678053832//7674292714443204070455739595109785 A[13,11]=0 A[13,12]=0 @@ -4242,7 +4242,7 @@ function constructTsitourasPapakostas8(T::Type = Float64) α[6]=2335496795323782464411846394611//6598368783294020109895379936256 α[7]=7636073376527143565375240869888//30725949199261296642046754748645 α[8]=-4237087214169934312729607487//12735791394214625116604076160 - α[9]=parse(BigInt,"408505291291133241760995514121984335914363927884426780078325258228227984174126699")//parse(BigInt,"212624874612193697466655159405635202123821166475348052734199905546455860773575680") + α[9]=408505291291133241760995514121984335914363927884426780078325258228227984174126699//212624874612193697466655159405635202123821166475348052734199905546455860773575680 α[10]=-1108225296327029096435947//405679075893979729103310 α[11]=2460988291206213825688467985//1756342789520947764222671739 α[12]=4808707937311//50545545388065 @@ -4255,7 +4255,7 @@ function constructTsitourasPapakostas8(T::Type = Float64) αEEst[6]=62284335162928966987066121//175437206755843240272669696 αEEst[7]=184309146777472302831695872//742417767522160213324368465 αEEst[8]=-509771598215811385123057257//210282269969085698264101760 - αEEst[9]=parse(BigInt,"2701602489646143640362891402924962500766379885231830470264478480621389")//parse(BigInt,"1688575269294196295712420798364925687791337062814161130291144634516480") + αEEst[9]=2701602489646143640362891402924962500766379885231830470264478480621389//1688575269294196295712420798364925687791337062814161130291144634516480 αEEst[10]=-7218534073012286740367561//3986456306153224954098780 αEEst[11]=0 αEEst[12]=0 @@ -4278,11 +4278,11 @@ function constructVernerRobust9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//25 - c[3]=parse(BigInt,"48")//parse(BigInt,"335")-parse(BigInt,"32")//parse(BigInt,"1675")*6^(1//2) - c[4]=parse(BigInt,"72")//parse(BigInt,"335")-parse(BigInt,"48")//parse(BigInt,"1675")*6^(1//2) + c[3]=48//335-32//1675*6^(1//2) + c[4]=72//335-48//1675*6^(1//2) c[5]=72//125 - c[6]=parse(BigInt,"48")//parse(BigInt,"125")-parse(BigInt,"8")//parse(BigInt,"125")*6^(1//2) - c[7]=parse(BigInt,"48")//parse(BigInt,"125")+parse(BigInt,"8")//parse(BigInt,"125")*6^(1//2) + c[6]=48//125-8//125*6^(1//2) + c[7]=48//125+8//125*6^(1//2) c[8]=16//25 c[9]=12//25 c[10]=3377//50000 @@ -4293,123 +4293,123 @@ function constructVernerRobust9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//25 - A[3,1]=-parse(BigInt,"15792")//parse(BigInt,"112225")+parse(BigInt,"5536")//parse(BigInt,"112225")*6^(1//2) - A[3,2]=parse(BigInt,"31872")//parse(BigInt,"112225")-parse(BigInt,"1536")//parse(BigInt,"22445")*6^(1//2) - A[4,1]=parse(BigInt,"18")//parse(BigInt,"335")-parse(BigInt,"12")//parse(BigInt,"1675")*6^(1//2) + A[3,1]=-15792//112225+5536//112225*6^(1//2) + A[3,2]=31872//112225-1536//22445*6^(1//2) + A[4,1]=18//335-12//1675*6^(1//2) A[4,2]=0 - A[4,3]=parse(BigInt,"54")//parse(BigInt,"335")-parse(BigInt,"36")//parse(BigInt,"1675")*6^(1//2) - A[5,1]=parse(BigInt,"4014")//parse(BigInt,"3125")+parse(BigInt,"252")//parse(BigInt,"625")*6^(1//2) + A[4,3]=54//335-36//1675*6^(1//2) + A[5,1]=4014//3125+252//625*6^(1//2) A[5,2]=0 - A[5,3]=-parse(BigInt,"14742")//parse(BigInt,"3125")-parse(BigInt,"972")//parse(BigInt,"625")*6^(1//2) - A[5,4]=parse(BigInt,"12528")//parse(BigInt,"3125")+parse(BigInt,"144")//parse(BigInt,"125")*6^(1//2) - A[6,1]=parse(BigInt,"1232")//parse(BigInt,"16875")-parse(BigInt,"152")//parse(BigInt,"16875")*6^(1//2) + A[5,3]=-14742//3125-972//625*6^(1//2) + A[5,4]=12528//3125+144//125*6^(1//2) + A[6,1]=1232//16875-152//16875*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=parse(BigInt,"29684")//parse(BigInt,"106875")-parse(BigInt,"13372")//parse(BigInt,"320625")*6^(1//2) - A[6,5]=parse(BigInt,"2132")//parse(BigInt,"64125")-parse(BigInt,"284")//parse(BigInt,"21375")*6^(1//2) - A[7,1]=parse(BigInt,"2032")//parse(BigInt,"16875")+parse(BigInt,"152")//parse(BigInt,"16875")*6^(1//2) + A[6,4]=29684//106875-13372//320625*6^(1//2) + A[6,5]=2132//64125-284//21375*6^(1//2) + A[7,1]=2032//16875+152//16875*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=-parse(BigInt,"7348")//parse(BigInt,"98325")-parse(BigInt,"33652")//parse(BigInt,"294975")*6^(1//2) - A[7,5]=parse(BigInt,"10132")//parse(BigInt,"64125")-parse(BigInt,"716")//parse(BigInt,"21375")*6^(1//2) - A[7,6]=parse(BigInt,"2592")//parse(BigInt,"14375")+parse(BigInt,"2912")//parse(BigInt,"14375")*6^(1//2) + A[7,4]=-7348//98325-33652//294975*6^(1//2) + A[7,5]=10132//64125-716//21375*6^(1//2) + A[7,6]=2592//14375+2912//14375*6^(1//2) A[8,1]=16//225 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=parse(BigInt,"64")//parse(BigInt,"225")+parse(BigInt,"4")//parse(BigInt,"225")*6^(1//2) - A[8,7]=parse(BigInt,"64")//parse(BigInt,"225")-parse(BigInt,"4")//parse(BigInt,"225")*6^(1//2) + A[8,6]=64//225+4//225*6^(1//2) + A[8,7]=64//225-4//225*6^(1//2) A[9,1]=57//800 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=parse(BigInt,"177")//parse(BigInt,"800")+parse(BigInt,"69")//parse(BigInt,"1600")*6^(1//2) - A[9,7]=parse(BigInt,"177")//parse(BigInt,"800")-parse(BigInt,"69")//parse(BigInt,"1600")*6^(1//2) + A[9,6]=177//800+69//1600*6^(1//2) + A[9,7]=177//800-69//1600*6^(1//2) A[9,8]=-27//800 A[10,1]=2844530829046074022657//58982400000000000000000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=parse(BigInt,"4287156859652598464203")//parse(BigInt,"58982400000000000000000")-parse(BigInt,"1598864762333658025459")//parse(BigInt,"117964800000000000000000")*6^(1//2) - A[10,7]=parse(BigInt,"4287156859652598464203")//parse(BigInt,"58982400000000000000000")+parse(BigInt,"1598864762333658025459")//parse(BigInt,"117964800000000000000000")*6^(1//2) + A[10,6]=4287156859652598464203//58982400000000000000000-1598864762333658025459//117964800000000000000000*6^(1//2) + A[10,7]=4287156859652598464203//58982400000000000000000+1598864762333658025459//117964800000000000000000*6^(1//2) A[10,8]=-141033886218604337343//6553600000000000000000 A[10,9]=-21409264848554971927//204800000000000000000 - A[11,1]=-parse(BigInt,"72189389771")//parse(BigInt,"9959178240000")-parse(BigInt,"459663572789")//parse(BigInt,"59755069440000")*6^(1//2) + A[11,1]=-72189389771//9959178240000-459663572789//59755069440000*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-parse(BigInt,"14201240926266911")//parse(BigInt,"557169364500480000")-parse(BigInt,"31790792357660029")//parse(BigInt,"557169364500480000")*6^(1//2) - A[11,8]=parse(BigInt,"22414436941")//parse(BigInt,"1563197440000")+parse(BigInt,"459663572789")//parse(BigInt,"56275107840000")*6^(1//2) - A[11,9]=parse(BigInt,"154180604903")//parse(BigInt,"2534154240000")+parse(BigInt,"459663572789")//parse(BigInt,"11403694080000")*6^(1//2) - A[11,10]=parse(BigInt,"21871487332435000000")//parse(BigInt,"125536952879579583419")+parse(BigInt,"18386542911560000000")//parse(BigInt,"1129832575916216250771")*6^(1//2) - A[12,1]=-parse(BigInt,"178144571353393080183496267158614821877982611914666395752937745405391408707734804982447062502773")//parse(BigInt,"1247718010112994054746145516410425353598134947600568397156373491324203879120405304413829778240000")+parse(BigInt,"352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357")//parse(BigInt,"8110167065734461355849945856667764798387877159403694581516427693607325214282634478689893558560000")*6^(1//2) + A[11,7]=-14201240926266911//557169364500480000-31790792357660029//557169364500480000*6^(1//2) + A[11,8]=22414436941//1563197440000+459663572789//56275107840000*6^(1//2) + A[11,9]=154180604903//2534154240000+459663572789//11403694080000*6^(1//2) + A[11,10]=21871487332435000000//125536952879579583419+18386542911560000000//1129832575916216250771*6^(1//2) + A[12,1]=-178144571353393080183496267158614821877982611914666395752937745405391408707734804982447062502773//1247718010112994054746145516410425353598134947600568397156373491324203879120405304413829778240000+352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357//8110167065734461355849945856667764798387877159403694581516427693607325214282634478689893558560000*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-parse(BigInt,"39115022545645779688585831988975140882502245161831122703201435591036520210945751850583137867")//parse(BigInt,"38425428798268102367071108589483043166777031255688218331140907046999467997785653437677908480")-parse(BigInt,"490826700396287454540598331961129757400186839154291202145347161815801053957874498846640625")//parse(BigInt,"15370171519307240946828443435793217266710812502275287332456362818799787199114261375071163392")*6^(1//2) - A[12,7]=-parse(BigInt,"622064296680932516193525865473060264652463486635595667447855699920023546211607797417635623004817316459")//parse(BigInt,"907451703567059050763665262359998604536360756710836393258911136378360869155327677312519401429106240000")+parse(BigInt,"643210041535328932923955834959360270277930780334485030265105750796567439186095378077346484617022694073")//parse(BigInt,"1814903407134118101527330524719997209072721513421672786517822272756721738310655354625038802858212480000")*6^(1//2) - A[12,8]=parse(BigInt,"1203943546728385294644268186854769106596033156989737459970836017592684437096940490927391123081521")//parse(BigInt,"6546732431504927940789740125933173479539636700187880198168132038132534360122730704444373657280000")-parse(BigInt,"151110511960958278763850506139095613011386663021919350564690684891134877118069370443383945077153")//parse(BigInt,"3273366215752463970394870062966586739769818350093940099084066019066267180061365352222186828640000")*6^(1//2) - A[12,9]=parse(BigInt,"63681466156701378449525903160928961790100434377497936201427140303316098275608362465676059840449")//parse(BigInt,"119057634931893490852780569777780769114850167606078444507680127107913165342297705956314829715000")-parse(BigInt,"352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357")//parse(BigInt,"1547749254114615381086147407111149998493052178879019778599841652402871149449870177432092786295000")*6^(1//2) - A[12,10]=parse(BigInt,"10278934048763239705668635930656276438279802537812076691952406255660602976082835598179622579836784640000000")//parse(BigInt,"20706607333558650004563853916074751077994608347553087587301432465002027701979512351053114927376343490460197")-parse(BigInt,"24757946279683404392669266925829425235785590869511266396518921812563538267024485653444025561440747520000000")//parse(BigInt,"269185895336262450059330100908971764013929908518190138634918622045026360125733660563690494055892465375982561")*6^(1//2) - A[12,11]=parse(BigInt,"19635000096509466380843956455829094932847113883632439882926745444809822658280742880787456")//parse(BigInt,"15009933124323477487137151792766813737022277834253210285601916815234167186635020874092933") - A[13,1]=-parse(BigInt,"25488511950948766602163761842966272037005387677568247")//parse(BigInt,"25343364340644945281003771622773961523200000000000000")+parse(BigInt,"2525608241949563386308964624438617443527")//parse(BigInt,"12416017897756354830807859200000000000000")*6^(1//2) + A[12,6]=-39115022545645779688585831988975140882502245161831122703201435591036520210945751850583137867//38425428798268102367071108589483043166777031255688218331140907046999467997785653437677908480-490826700396287454540598331961129757400186839154291202145347161815801053957874498846640625//15370171519307240946828443435793217266710812502275287332456362818799787199114261375071163392*6^(1//2) + A[12,7]=-622064296680932516193525865473060264652463486635595667447855699920023546211607797417635623004817316459//907451703567059050763665262359998604536360756710836393258911136378360869155327677312519401429106240000+643210041535328932923955834959360270277930780334485030265105750796567439186095378077346484617022694073//1814903407134118101527330524719997209072721513421672786517822272756721738310655354625038802858212480000*6^(1//2) + A[12,8]=1203943546728385294644268186854769106596033156989737459970836017592684437096940490927391123081521//6546732431504927940789740125933173479539636700187880198168132038132534360122730704444373657280000-151110511960958278763850506139095613011386663021919350564690684891134877118069370443383945077153//3273366215752463970394870062966586739769818350093940099084066019066267180061365352222186828640000*6^(1//2) + A[12,9]=63681466156701378449525903160928961790100434377497936201427140303316098275608362465676059840449//119057634931893490852780569777780769114850167606078444507680127107913165342297705956314829715000-352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357//1547749254114615381086147407111149998493052178879019778599841652402871149449870177432092786295000*6^(1//2) + A[12,10]=10278934048763239705668635930656276438279802537812076691952406255660602976082835598179622579836784640000000//20706607333558650004563853916074751077994608347553087587301432465002027701979512351053114927376343490460197-24757946279683404392669266925829425235785590869511266396518921812563538267024485653444025561440747520000000//269185895336262450059330100908971764013929908518190138634918622045026360125733660563690494055892465375982561*6^(1//2) + A[12,11]=19635000096509466380843956455829094932847113883632439882926745444809822658280742880787456//15009933124323477487137151792766813737022277834253210285601916815234167186635020874092933 + A[13,1]=-25488511950948766602163761842966272037005387677568247//25343364340644945281003771622773961523200000000000000+2525608241949563386308964624438617443527//12416017897756354830807859200000000000000*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-parse(BigInt,"2617546081675469247418718340204655213")//parse(BigInt,"431392587109884206933606400000000000")-552470350996365859393640759989//2400793528263703412500070400000*6^(1//2) - A[13,7]=-parse(BigInt,"45969294618407232267578352626581642155421231201")//parse(BigInt,"10187731154133781589406192186163200000000000000")+parse(BigInt,"1540493536582818303738906021531546510663696889")//parse(BigInt,"885889665576850572991842798796800000000000000")*6^(1//2) - A[13,8]=parse(BigInt,"203013873418014401588800777489550153682185921397719")//parse(BigInt,"6003783517480134311881093736968119910400000000000000")-parse(BigInt,"3968812951635028178485515838403541696971")//parse(BigInt,"18374628007211630439078297600000000000000")*6^(1//2) - A[13,9]=parse(BigInt,"57340072791914637839492204156400815228449519011392389")//parse(BigInt,"19744238839693126186283635091213610188800000000000000")-parse(BigInt,"677602211254760908521917338264019314117")//parse(BigInt,"635714271434389910412902400000000000000")*6^(1//2) - A[13,10]=parse(BigInt,"24100788715039192225758197856261740786803059875758180717")//parse(BigInt,"9662717001210818114953908042643919942065136939286292000")-parse(BigInt,"8800028717594297513271653743688562521")//parse(BigInt,"20449362746897197076153911415852248500")*6^(1//2) - A[13,11]=parse(BigInt,"124358916033523439225154730110040589545064737")//parse(BigInt,"19935912449945669485002510178704400000000000") - A[13,12]=parse(BigInt,"594716139297486674475082356103592029886330739685357945223223985387172161751824241784555387316314439")//parse(BigInt,"818019847119678359631725769101238313386585208743795596694052943582031156000597320370585600000000000") - A[14,1]=parse(BigInt,"184592679361470753674594239208189459317466722387929369596771")//parse(BigInt,"127891217091830656233364014205731655064571321600000000000000")-parse(BigInt,"293880952873230803935166416296767553377")//parse(BigInt,"866938749696854853908947200000000000000")*6^(1//2) + A[13,6]=-2617546081675469247418718340204655213//431392587109884206933606400000000000-552470350996365859393640759989//2400793528263703412500070400000*6^(1//2) + A[13,7]=-45969294618407232267578352626581642155421231201//10187731154133781589406192186163200000000000000+1540493536582818303738906021531546510663696889//885889665576850572991842798796800000000000000*6^(1//2) + A[13,8]=203013873418014401588800777489550153682185921397719//6003783517480134311881093736968119910400000000000000-3968812951635028178485515838403541696971//18374628007211630439078297600000000000000*6^(1//2) + A[13,9]=57340072791914637839492204156400815228449519011392389//19744238839693126186283635091213610188800000000000000-677602211254760908521917338264019314117//635714271434389910412902400000000000000*6^(1//2) + A[13,10]=24100788715039192225758197856261740786803059875758180717//9662717001210818114953908042643919942065136939286292000-8800028717594297513271653743688562521//20449362746897197076153911415852248500*6^(1//2) + A[13,11]=124358916033523439225154730110040589545064737//19935912449945669485002510178704400000000000 + A[13,12]=594716139297486674475082356103592029886330739685357945223223985387172161751824241784555387316314439//818019847119678359631725769101238313386585208743795596694052943582031156000597320370585600000000000 + A[14,1]=184592679361470753674594239208189459317466722387929369596771//127891217091830656233364014205731655064571321600000000000000-293880952873230803935166416296767553377//866938749696854853908947200000000000000*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=parse(BigInt,"5966995986367380181027852718263477")//parse(BigInt,"684582962942931480729600000000000")+parse(BigInt,"2897291244884828193281565089")//parse(BigInt,"19049265055803310768128000000")*6^(1//2) - A[14,7]=parse(BigInt,"99009240614446727611594225452277068906413179")//parse(BigInt,"16167053833464253010532287404800000000000000")-parse(BigInt,"3748619435624523040662096435375495632409181")//parse(BigInt,"1405830768127326348741938035200000000000000")*6^(1//2) - A[14,8]=parse(BigInt,"4632645823113234486269357844283603936661991916850927460433")//parse(BigInt,"5096189922215990577140952099757378096638035200000000000000")+parse(BigInt,"41982993267604400562166630899538221911")//parse(BigInt,"116635822311401951029305600000000000000")*6^(1//2) - A[14,9]=-parse(BigInt,"12135475677184688070559819501757154968443992507349800863475059")//parse(BigInt,"3337534088557268857775113382843672473526974754800000000000000")+parse(BigInt,"293880952873230803935166416296767553377")//parse(BigInt,"165447122399672764770545400000000000000")*6^(1//2) - A[14,10]=-parse(BigInt,"8031428603597180964147750321204281053557209400385686643427859804352")//parse(BigInt,"2513586440178391306900178164909088113749933981949109368563389778875")+parse(BigInt,"21495292553013453087829315020563569618432")//parse(BigInt,"29973653446264566614372595657785433238875")*6^(1//2) - A[14,11]=-parse(BigInt,"44866632128961269158599595825347949153517725172080973")//parse(BigInt,"5429607175821308141232283339099249860726338769531250") - A[14,12]=-parse(BigInt,"359988533934752543813368225945058137961504440675167771570563740579175484411998973149563531328527853237660249760109643")//parse(BigInt,"234128137445668240736067711662442379892483470931740696615716602345729933343308008758732590194294958617150200000000000") + A[14,6]=5966995986367380181027852718263477//684582962942931480729600000000000+2897291244884828193281565089//19049265055803310768128000000*6^(1//2) + A[14,7]=99009240614446727611594225452277068906413179//16167053833464253010532287404800000000000000-3748619435624523040662096435375495632409181//1405830768127326348741938035200000000000000*6^(1//2) + A[14,8]=4632645823113234486269357844283603936661991916850927460433//5096189922215990577140952099757378096638035200000000000000+41982993267604400562166630899538221911//116635822311401951029305600000000000000*6^(1//2) + A[14,9]=-12135475677184688070559819501757154968443992507349800863475059//3337534088557268857775113382843672473526974754800000000000000+293880952873230803935166416296767553377//165447122399672764770545400000000000000*6^(1//2) + A[14,10]=-8031428603597180964147750321204281053557209400385686643427859804352//2513586440178391306900178164909088113749933981949109368563389778875+21495292553013453087829315020563569618432//29973653446264566614372595657785433238875*6^(1//2) + A[14,11]=-44866632128961269158599595825347949153517725172080973//5429607175821308141232283339099249860726338769531250 + A[14,12]=-359988533934752543813368225945058137961504440675167771570563740579175484411998973149563531328527853237660249760109643//234128137445668240736067711662442379892483470931740696615716602345729933343308008758732590194294958617150200000000000 A[14,13]=1011136807359189181222571916914688//2927578889427871359661497484969729 - A[15,1]=-parse(BigInt,"43117938494612449223384237106139955697243762787772847383")//parse(BigInt,"14030104862294690648579566521727488445420965260989440000")+parse(BigInt,"4220334940168717525563719481764309232553")//parse(BigInt,"5553268895030690235789996003491120640000")*6^(1//2) + A[15,1]=-43117938494612449223384237106139955697243762787772847383//14030104862294690648579566521727488445420965260989440000+4220334940168717525563719481764309232553//5553268895030690235789996003491120640000*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-parse(BigInt,"492170504431044248358505817476691843")//parse(BigInt,"26311016381549020957251979880325120")-parse(BigInt,"65372649360291914372644744384375")//parse(BigInt,"457582893592156886213077910962176")*6^(1//2) - A[15,7]=-parse(BigInt,"60242025722206083647640080390153021797730167")//parse(BigInt,"4671870346091448695506240355969515576320000")+parse(BigInt,"312292306982904450161582808948983992497619279")//parse(BigInt,"54031196176535884913246084116864832317440000")*6^(1//2) - A[15,8]=-parse(BigInt,"10128486019754425336362855829794634260766582925227304979")//parse(BigInt,"2051440458733049774272501566471676463052668060718080000")-parse(BigInt,"4220334940168717525563719481764309232553")//parse(BigInt,"5229862652007483519857107084128791040000")*6^(1//2) - A[15,9]=parse(BigInt,"90164396775224825317874747969895939573106537263617688583")//parse(BigInt,"9932194582195572820411492715910530662743409752296080000")-parse(BigInt,"4220334940168717525563719481764309232553")//parse(BigInt,"1059789239915401287502749181781142480000")*6^(1//2) - A[15,10]=parse(BigInt,"822220421784353922416106346105112190310210366765138782108892460117760000000")//parse(BigInt,"112539961436930436130682455392076582934435837857314380718907401253008522853")-parse(BigInt,"43216229787327667461772487493266526541342720000000")//parse(BigInt,"26879922067906624005297106621487120800647611685231")*6^(1//2) - A[15,11]=parse(BigInt,"209814213871916216679569640811090009729840605120")//parse(BigInt,"11651974660960738096987230622554824075229159217") - A[15,12]=parse(BigInt,"3941550892863952281184122715485813150214519858148244578543766661999079625453432169420046111603168071904019820197053706993310801913")//parse(BigInt,"576348806945747835561749398160966945390916610765210182493857593996732757363976976471505530337022074730630638475548489174498085584") - A[15,13]=-parse(BigInt,"4759443892077050695292772766912275498897121280000000000")//parse(BigInt,"4614026158486489304426198097242323507384603506591241137") - A[15,14]=parse(BigInt,"38733614144315448443538220691259283298308750000000")//parse(BigInt,"93806291160324220065540465392781147766752569954001") - A[16,1]=parse(BigInt,"18092408213832965447840389945226814727838921316097789")//parse(BigInt,"4568260908663202892681034746459555501706277524480000")-parse(BigInt,"156317653995567850184921063401246768027")//parse(BigInt,"212359240683067701291661898043594240000")*6^(1//2) + A[15,6]=-492170504431044248358505817476691843//26311016381549020957251979880325120-65372649360291914372644744384375//457582893592156886213077910962176*6^(1//2) + A[15,7]=-60242025722206083647640080390153021797730167//4671870346091448695506240355969515576320000+312292306982904450161582808948983992497619279//54031196176535884913246084116864832317440000*6^(1//2) + A[15,8]=-10128486019754425336362855829794634260766582925227304979//2051440458733049774272501566471676463052668060718080000-4220334940168717525563719481764309232553//5229862652007483519857107084128791040000*6^(1//2) + A[15,9]=90164396775224825317874747969895939573106537263617688583//9932194582195572820411492715910530662743409752296080000-4220334940168717525563719481764309232553//1059789239915401287502749181781142480000*6^(1//2) + A[15,10]=822220421784353922416106346105112190310210366765138782108892460117760000000//112539961436930436130682455392076582934435837857314380718907401253008522853-43216229787327667461772487493266526541342720000000//26879922067906624005297106621487120800647611685231*6^(1//2) + A[15,11]=209814213871916216679569640811090009729840605120//11651974660960738096987230622554824075229159217 + A[15,12]=3941550892863952281184122715485813150214519858148244578543766661999079625453432169420046111603168071904019820197053706993310801913//576348806945747835561749398160966945390916610765210182493857593996732757363976976471505530337022074730630638475548489174498085584 + A[15,13]=-4759443892077050695292772766912275498897121280000000000//4614026158486489304426198097242323507384603506591241137 + A[15,14]=38733614144315448443538220691259283298308750000000//93806291160324220065540465392781147766752569954001 + A[16,1]=18092408213832965447840389945226814727838921316097789//4568260908663202892681034746459555501706277524480000-156317653995567850184921063401246768027//212359240683067701291661898043594240000*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=parse(BigInt,"65946837846509057750066287355594411")//parse(BigInt,"3018431611722608724311451319541760")+parse(BigInt,"41984484090942118562371132909375")//parse(BigInt,"52494462812567108248894805557248")*6^(1//2) - A[16,7]=parse(BigInt,"8692965898134239206513518248119006769975359")//parse(BigInt,"535962614823230784958890847664050959360000")-parse(BigInt,"38800907634871851557429961190168666395776983")//parse(BigInt,"6198524154042582121698476759940763269120000")*6^(1//2) - A[16,8]=parse(BigInt,"2641630262222426284468500071736583566105608571199325883")//parse(BigInt,"235343729805469979809271071241826755571130067491840000")+parse(BigInt,"156317653995567850184921063401246768027")//parse(BigInt,"199992055607259790546219146109360640000")*6^(1//2) - A[16,9]=-parse(BigInt,"193422103474923353694542105476136625982637168991506421")//parse(BigInt,"16048357343710211432072833749116213173856151273040000")+parse(BigInt,"156317653995567850184921063401246768027")//parse(BigInt,"40526767661819895652001992553977680000")*6^(1//2) - A[16,10]=-parse(BigInt,"19419587503350096681694941672242361995243037384025897671049255680000000")//parse(BigInt,"2155738929233095407456284002740551925607350553898010429805538450410571")+parse(BigInt,"1600692776914614785893591689228766904596480000000")//parse(BigInt,"1027899053306897212338272667278244239283200723671")*6^(1//2) - A[16,11]=-parse(BigInt,"27285760059113968837908932750404506400064658240")//parse(BigInt,"1336728621411169422812695849204871581103756891") - A[16,12]=-parse(BigInt,"194853016061874333335484555436551917329750324944158872786342511110263341294405932910123138589192221578993200454377")//parse(BigInt,"15840605894584140753571150900860666508000461134947537749588341642048479030548925808450142813874420689113167632464") - A[16,13]=parse(BigInt,"89488735256675489275877211680603518179732480000000000")//parse(BigInt,"58814073298029244653337926984054935524805348324518339") + A[16,6]=65946837846509057750066287355594411//3018431611722608724311451319541760+41984484090942118562371132909375//52494462812567108248894805557248*6^(1//2) + A[16,7]=8692965898134239206513518248119006769975359//535962614823230784958890847664050959360000-38800907634871851557429961190168666395776983//6198524154042582121698476759940763269120000*6^(1//2) + A[16,8]=2641630262222426284468500071736583566105608571199325883//235343729805469979809271071241826755571130067491840000+156317653995567850184921063401246768027//199992055607259790546219146109360640000*6^(1//2) + A[16,9]=-193422103474923353694542105476136625982637168991506421//16048357343710211432072833749116213173856151273040000+156317653995567850184921063401246768027//40526767661819895652001992553977680000*6^(1//2) + A[16,10]=-19419587503350096681694941672242361995243037384025897671049255680000000//2155738929233095407456284002740551925607350553898010429805538450410571+1600692776914614785893591689228766904596480000000//1027899053306897212338272667278244239283200723671*6^(1//2) + A[16,11]=-27285760059113968837908932750404506400064658240//1336728621411169422812695849204871581103756891 + A[16,12]=-194853016061874333335484555436551917329750324944158872786342511110263341294405932910123138589192221578993200454377//15840605894584140753571150900860666508000461134947537749588341642048479030548925808450142813874420689113167632464 + A[16,13]=89488735256675489275877211680603518179732480000000000//58814073298029244653337926984054935524805348324518339 A[16,14]=0 A[16,15]=0 α[1]=100976787617015984669475787//6921502952403262310437464576 @@ -4421,10 +4421,10 @@ function constructVernerRobust9(T::Type = Float64) α[7]=0 α[8]=8877148253451235588984375//4385514038208782482187638272 α[9]=961916572949681511747758515625//4416417715504587515036809762176 - α[10]=parse(BigInt,"1967337516701564001434375000000000000000000000000")//parse(BigInt,"15431364863119854943071851131903908575429289017877") + α[10]=1967337516701564001434375000000000000000000000000//15431364863119854943071851131903908575429289017877 α[11]=2323713252076974806855457536//10352378514220126928031114081 - α[12]=parse(BigInt,"28308600293241456954311939117138937391141264054325158121088859798090056999504636993802634122671806566061266984631226363619")//parse(BigInt,"158391546540670080968065757007173890885877631132509858232987982213169380898029758612356596464561682203552186100842929847264") - α[13]=parse(BigInt,"296136352341197653422080000000000000")//parse(BigInt,"3899432561650270968394778037550931439") + α[12]=28308600293241456954311939117138937391141264054325158121088859798090056999504636993802634122671806566061266984631226363619//158391546540670080968065757007173890885877631132509858232987982213169380898029758612356596464561682203552186100842929847264 + α[13]=296136352341197653422080000000000000//3899432561650270968394778037550931439 α[14]=117048651891177050452812500000000//903958175807874008864483503817601 α[15]=145778296653275182685983//4945417885871057962703934 α[16]=0 @@ -4437,9 +4437,9 @@ function constructVernerRobust9(T::Type = Float64) αEEst[7]=0 αEEst[8]=11089416604965799654140625//10367645480399012960254464 αEEst[9]=19661377435148646805703125//255979697183364488207083392 - αEEst[10]=parse(BigInt,"688790393936688343750000000000000000000000")//parse(BigInt,"6091295374506475008386869675533556427693991") + αEEst[10]=688790393936688343750000000000000000000000//6091295374506475008386869675533556427693991 αEEst[11]=2387113868151976968347648//9351742108599933990994683 - αEEst[12]=-parse(BigInt,"12428699133337309103655890990808226652772000718643045082918121983471100560973332724469319414156511978021429")//parse(BigInt,"12648919237095643063555422745116719205173888728920704277722434371356124846214898200346632677347950735102176") + αEEst[12]=-12428699133337309103655890990808226652772000718643045082918121983471100560973332724469319414156511978021429//12648919237095643063555422745116719205173888728920704277722434371356124846214898200346632677347950735102176 αEEst[13]=185286960316915979617280000000000000//465364379785423284294027008596613217 αEEst[14]=0 αEEst[15]=0 @@ -4463,11 +4463,11 @@ function constructVernerEfficient9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1731//50000 - c[3]=parse(BigInt,"7630049")//parse(BigInt,"53810000")-parse(BigInt,"983539")//parse(BigInt,"53810000")*6^(1//2) - c[4]=parse(BigInt,"22890147")//parse(BigInt,"107620000")-parse(BigInt,"2950617")//parse(BigInt,"107620000")*6^(1//2) + c[3]=7630049//53810000-983539//53810000*6^(1//2) + c[4]=22890147//107620000-2950617//107620000*6^(1//2) c[5]=561//1000 - c[6]=parse(BigInt,"387")//parse(BigInt,"1000")-parse(BigInt,"129")//parse(BigInt,"2000")*6^(1//2) - c[7]=parse(BigInt,"387")//parse(BigInt,"1000")+parse(BigInt,"129")//parse(BigInt,"2000")*6^(1//2) + c[6]=387//1000-129//2000*6^(1//2) + c[7]=387//1000+129//2000*6^(1//2) c[8]=129//200 c[9]=387//800 c[10]=6757//100000 @@ -4478,123 +4478,123 @@ function constructVernerEfficient9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1731//50000 - A[3,1]=-parse(BigInt,"177968356965557")//parse(BigInt,"1002427673820000")+parse(BigInt,"14180534491313")//parse(BigInt,"250606918455000")*6^(1//2) - A[3,2]=parse(BigInt,"64021741529527")//parse(BigInt,"200485534764000")-parse(BigInt,"7504450763411")//parse(BigInt,"100242767382000")*6^(1//2) - A[4,1]=parse(BigInt,"22890147")//parse(BigInt,"430480000")-parse(BigInt,"2950617")//parse(BigInt,"430480000")*6^(1//2) + A[3,1]=-177968356965557//1002427673820000+14180534491313//250606918455000*6^(1//2) + A[3,2]=64021741529527//200485534764000-7504450763411//100242767382000*6^(1//2) + A[4,1]=22890147//430480000-2950617//430480000*6^(1//2) A[4,2]=0 - A[4,3]=parse(BigInt,"68670441")//parse(BigInt,"430480000")-parse(BigInt,"8851851")//parse(BigInt,"430480000")*6^(1//2) - A[5,1]=parse(BigInt,"592203994261020339")//parse(BigInt,"513126355505556250")+parse(BigInt,"730386990293623641")//parse(BigInt,"2052505422022225000")*6^(1//2) + A[4,3]=68670441//430480000-8851851//430480000*6^(1//2) + A[5,1]=592203994261020339//513126355505556250+730386990293623641//2052505422022225000*6^(1//2) A[5,2]=0 - A[5,3]=-parse(BigInt,"8712153884182794903")//parse(BigInt,"2052505422022225000")-parse(BigInt,"2843421359195851533")//parse(BigInt,"2052505422022225000")*6^(1//2) - A[5,4]=parse(BigInt,"1873698362223295443")//parse(BigInt,"513126355505556250")+parse(BigInt,"528258592225556973")//parse(BigInt,"513126355505556250")*6^(1//2) - A[6,1]=parse(BigInt,"11380823631")//parse(BigInt,"157617812000")-parse(BigInt,"339148869")//parse(BigInt,"39404453000")*6^(1//2) + A[5,3]=-8712153884182794903//2052505422022225000-2843421359195851533//2052505422022225000*6^(1//2) + A[5,4]=1873698362223295443//513126355505556250+528258592225556973//513126355505556250*6^(1//2) + A[6,1]=11380823631//157617812000-339148869//39404453000*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=parse(BigInt,"16193232887091831")//parse(BigInt,"58864341808507450")-parse(BigInt,"2355345717024309")//parse(BigInt,"58864341808507450")*6^(1//2) - A[6,5]=parse(BigInt,"165912282616977")//parse(BigInt,"4179075230308000")-parse(BigInt,"33181894472511")//parse(BigInt,"2089537615154000")*6^(1//2) - A[7,1]=parse(BigInt,"26523528363")//parse(BigInt,"231790900000")+parse(BigInt,"863255358")//parse(BigInt,"123138915625")*6^(1//2) + A[6,4]=16193232887091831//58864341808507450-2355345717024309//58864341808507450*6^(1//2) + A[6,5]=165912282616977//4179075230308000-33181894472511//2089537615154000*6^(1//2) + A[7,1]=26523528363//231790900000+863255358//123138915625*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=-parse(BigInt,"38208748178016484817787")//parse(BigInt,"842517966262441068418750")-parse(BigInt,"86118788556282369822807")//parse(BigInt,"842517966262441068418750")*6^(1//2) - A[7,5]=parse(BigInt,"92362336407446913")//parse(BigInt,"290322814529044000")-parse(BigInt,"232039320950012997")//parse(BigInt,"2467743923496874000")*6^(1//2) - A[7,6]=-parse(BigInt,"362925891")//parse(BigInt,"1690350537500")+parse(BigInt,"857800423623")//parse(BigInt,"3380701075000")*6^(1//2) + A[7,4]=-38208748178016484817787//842517966262441068418750-86118788556282369822807//842517966262441068418750*6^(1//2) + A[7,5]=92362336407446913//290322814529044000-232039320950012997//2467743923496874000*6^(1//2) + A[7,6]=-362925891//1690350537500+857800423623//3380701075000*6^(1//2) A[8,1]=43//600 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=parse(BigInt,"43")//parse(BigInt,"150")+parse(BigInt,"43")//parse(BigInt,"2400")*6^(1//2) - A[8,7]=parse(BigInt,"43")//parse(BigInt,"150")-parse(BigInt,"43")//parse(BigInt,"2400")*6^(1//2) + A[8,6]=43//150+43//2400*6^(1//2) + A[8,7]=43//150-43//2400*6^(1//2) A[9,1]=7353//102400 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=parse(BigInt,"22833")//parse(BigInt,"102400")+parse(BigInt,"8901")//parse(BigInt,"204800")*6^(1//2) - A[9,7]=parse(BigInt,"22833")//parse(BigInt,"102400")-parse(BigInt,"8901")//parse(BigInt,"204800")*6^(1//2) + A[9,6]=22833//102400+8901//204800*6^(1//2) + A[9,7]=22833//102400-8901//204800*6^(1//2) A[9,8]=-3483//102400 A[10,1]=376708742472214988700853//7788456028125000000000000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=parse(BigInt,"187914666753956840195279")//parse(BigInt,"2596152009375000000000000")-parse(BigInt,"210440846556290693268911")//parse(BigInt,"15576912056250000000000000")*6^(1//2) - A[10,7]=parse(BigInt,"187914666753956840195279")//parse(BigInt,"2596152009375000000000000")+parse(BigInt,"210440846556290693268911")//parse(BigInt,"15576912056250000000000000")*6^(1//2) + A[10,6]=187914666753956840195279//2596152009375000000000000-210440846556290693268911//15576912056250000000000000*6^(1//2) + A[10,7]=187914666753956840195279//2596152009375000000000000+210440846556290693268911//15576912056250000000000000*6^(1//2) A[10,8]=-18552667221896744226647//865384003125000000000000 A[10,9]=-3167799860072183913409//30423656359863281250000 - A[11,1]=-parse(BigInt,"426968570497")//parse(BigInt,"54394415898750")-parse(BigInt,"92754382349")//parse(BigInt,"12087647977500")*6^(1//2) + A[11,1]=-426968570497//54394415898750-92754382349//12087647977500*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-parse(BigInt,"2865012129681958")//parse(BigInt,"114898584332330625")-parse(BigInt,"12962517687655099")//parse(BigInt,"229797168664661250")*6^(1//2) - A[11,8]=parse(BigInt,"4389715333607")//parse(BigInt,"309890657317500")+parse(BigInt,"92754382349")//parse(BigInt,"11477431752500")*6^(1//2) - A[11,9]=parse(BigInt,"4990058173976")//parse(BigInt,"83757096376875")+parse(BigInt,"371017529396")//parse(BigInt,"9306344041875")*6^(1//2) - A[11,10]=parse(BigInt,"1099523524595993125000")//parse(BigInt,"6257667909869756018891")+parse(BigInt,"100957348037989687500")//parse(BigInt,"6257667909869756018891")*6^(1//2) - A[12,1]=parse(BigInt,"18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756")//parse(BigInt,"13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375")+parse(BigInt,"407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536")//parse(BigInt,"28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875")*6^(1//2) + A[11,7]=-2865012129681958//114898584332330625-12962517687655099//229797168664661250*6^(1//2) + A[11,8]=4389715333607//309890657317500+92754382349//11477431752500*6^(1//2) + A[11,9]=4990058173976//83757096376875+371017529396//9306344041875*6^(1//2) + A[11,10]=1099523524595993125000//6257667909869756018891+100957348037989687500//6257667909869756018891*6^(1//2) + A[12,1]=18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756//13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375+407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536//28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-parse(BigInt,"333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904")//parse(BigInt,"2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635")+parse(BigInt,"4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000")//parse(BigInt,"23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877")*6^(1//2) - A[12,7]=-parse(BigInt,"136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416")//parse(BigInt,"3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375")+parse(BigInt,"169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904")//parse(BigInt,"1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875")*6^(1//2) - A[12,8]=parse(BigInt,"5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208")//parse(BigInt,"92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875")-parse(BigInt,"5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432")//parse(BigInt,"365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625")*6^(1//2) - A[12,9]=parse(BigInt,"54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328")//parse(BigInt,"301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125")-parse(BigInt,"6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576")//parse(BigInt,"86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375")*6^(1//2) - A[12,10]=parse(BigInt,"9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000")//parse(BigInt,"58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783")-parse(BigInt,"8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000")//parse(BigInt,"265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757")*6^(1//2) - A[12,11]=parse(BigInt,"123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952")//parse(BigInt,"281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461") - A[13,1]=-parse(BigInt,"56042772675322042139227629978042586330633622706053363946766144416933631")//parse(BigInt,"58808540772323190525590122613223430507352118534557342666015625000000000")+parse(BigInt,"281404579734699232141455524604487724159024972527")//parse(BigInt,"1478009944832743180452316204077188415527343750000")*6^(1//2) + A[12,6]=-333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904//2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635+4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000//23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877*6^(1//2) + A[12,7]=-136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416//3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375+169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904//1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875*6^(1//2) + A[12,8]=5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208//92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875-5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432//365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625*6^(1//2) + A[12,9]=54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328//301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125-6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576//86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375*6^(1//2) + A[12,10]=9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000//58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783-8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000//265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757*6^(1//2) + A[12,11]=123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952//281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461 + A[13,1]=-56042772675322042139227629978042586330633622706053363946766144416933631//58808540772323190525590122613223430507352118534557342666015625000000000+281404579734699232141455524604487724159024972527//1478009944832743180452316204077188415527343750000*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-parse(BigInt,"1027163900229750356561238237947225332675621517")//parse(BigInt,"179261894431132664078747698292867431640625000")-parse(BigInt,"2745292391641202525373103979336813513372321")//parse(BigInt,"11702216468464340311060649744558385937500000")*6^(1//2) - A[13,7]=-parse(BigInt,"157229999853748227305165773364426925282378072238332930121")//parse(BigInt,"36699907367985458573273204094330716033963413238525390625")+parse(BigInt,"5757606442802795095318986067317837904184278650664590252101")//parse(BigInt,"3523191107326604023034227593055748739260487670898437500000")*6^(1//2) - A[13,8]=-parse(BigInt,"9311448168593934146015965019904013602133802943325818346622781285907057")//parse(BigInt,"4255970849010124217193135449668739985401313363005576159362792968750000")-parse(BigInt,"844213739204097696424366573813463172477074917581")//parse(BigInt,"4210188359946578336976868164966163024902343750000")*6^(1//2) - A[13,9]=parse(BigInt,"885774233856672590222951867695327816457340130391639153070521335485617578")//parse(BigInt,"301098541380295011015469248465465290112505656143757799934635162353515625")-parse(BigInt,"281404579734699232141455524604487724159024972527")//parse(BigInt,"284481916364737983221402322504830303192138671875")*6^(1//2) - A[13,10]=parse(BigInt,"315479116729780153956412124052199685097744239386639023787359107959254802182")//parse(BigInt,"134481850506505848012587842215515574380212543200894932329128471154748828125")-parse(BigInt,"2940396453647872276646068776592292229737651937934623")//parse(BigInt,"7345465058781983710795837429530784777245286520703125")*6^(1//2) - A[13,11]=parse(BigInt,"2250996163406545378616532039018846586217631599453822541")//parse(BigInt,"382491303797095993563304148204275636433504028320312500") - A[13,12]=parse(BigInt,"2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493")//parse(BigInt,"959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000") - A[14,1]=parse(BigInt,"47342003848024391498707976847688893013083074441159779465719863625051668939887702630319")//parse(BigInt,"44802546873926050730401222636656855760802419993852060264615320801485392456054687500000")-parse(BigInt,"866369530987077991125562402829092187100493209601")//parse(BigInt,"3325522375873672156017711459173673934936523437500")*6^(1//2) + A[13,6]=-1027163900229750356561238237947225332675621517//179261894431132664078747698292867431640625000-2745292391641202525373103979336813513372321//11702216468464340311060649744558385937500000*6^(1//2) + A[13,7]=-157229999853748227305165773364426925282378072238332930121//36699907367985458573273204094330716033963413238525390625+5757606442802795095318986067317837904184278650664590252101//3523191107326604023034227593055748739260487670898437500000*6^(1//2) + A[13,8]=-9311448168593934146015965019904013602133802943325818346622781285907057//4255970849010124217193135449668739985401313363005576159362792968750000-844213739204097696424366573813463172477074917581//4210188359946578336976868164966163024902343750000*6^(1//2) + A[13,9]=885774233856672590222951867695327816457340130391639153070521335485617578//301098541380295011015469248465465290112505656143757799934635162353515625-281404579734699232141455524604487724159024972527//284481916364737983221402322504830303192138671875*6^(1//2) + A[13,10]=315479116729780153956412124052199685097744239386639023787359107959254802182//134481850506505848012587842215515574380212543200894932329128471154748828125-2940396453647872276646068776592292229737651937934623//7345465058781983710795837429530784777245286520703125*6^(1//2) + A[13,11]=2250996163406545378616532039018846586217631599453822541//382491303797095993563304148204275636433504028320312500 + A[13,12]=2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493//959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000 + A[14,1]=47342003848024391498707976847688893013083074441159779465719863625051668939887702630319//44802546873926050730401222636656855760802419993852060264615320801485392456054687500000-866369530987077991125562402829092187100493209601//3325522375873672156017711459173673934936523437500*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=parse(BigInt,"871779321807802447463310035318238762878527157")//parse(BigInt,"134446420823349498059060773719650573730468750")+parse(BigInt,"107641268480999396081848975271849857994818")//parse(BigInt,"1097082793918531904161935913552348681640625")*6^(1//2) - A[14,7]=parse(BigInt,"496103786351862292800034805114190705484800743513354117014")//parse(BigInt,"110099722103956375719819612282992148101890239715576171875")-parse(BigInt,"1329938412606197485769312599390307351191540891599374831099")//parse(BigInt,"660598332623738254318917673697952888611341438293457031250")*6^(1//2) - A[14,8]=parse(BigInt,"40774077277747636354598451708891165494123131383777235229538611989392175193285994266471")//parse(BigInt,"15264290546248162101058985941588079518256741255377031736357946125713524703979492187500")+parse(BigInt,"123767075855296855875080343261298883871499029943")//parse(BigInt,"451091609994276250390378731960660324096679687500")*6^(1//2) - A[14,9]=-parse(BigInt,"10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664")//parse(BigInt,"3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375")+parse(BigInt,"3465478123948311964502249611316368748401972838404")//parse(BigInt,"2560337247282641848992620902543472728729248046875")*6^(1//2) - A[14,10]=-parse(BigInt,"27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984")//parse(BigInt,"12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375")+parse(BigInt,"574774300271998598683873114105472016699241495055292")//parse(BigInt,"1049352151254569101542262489932969253892183788671875")*6^(1//2) - A[14,11]=-parse(BigInt,"34241134351848245624232809437676889009431930503529853032576417589898516")//parse(BigInt,"5613347824358651981100985009024281007603230062439942682713165283203125") - A[14,12]=-parse(BigInt,"3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609")//parse(BigInt,"1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000") - A[14,13]=parse(BigInt,"4746930876023919335079451612726717649218264199984")//parse(BigInt,"18592065538407049755200144388134089346432755594877") - A[15,1]=-parse(BigInt,"25188329249258825443748527038142409879923012133738985313265430932280250855708601")//parse(BigInt,"11370641325574469312056961874077298550827642308774647316995717036347558064286250")+parse(BigInt,"1234273058981860170179592598535508631343082535549881956")//parse(BigInt,"2105633771469628744518390642968552144069898845895808125")*6^(1//2) + A[14,6]=871779321807802447463310035318238762878527157//134446420823349498059060773719650573730468750+107641268480999396081848975271849857994818//1097082793918531904161935913552348681640625*6^(1//2) + A[14,7]=496103786351862292800034805114190705484800743513354117014//110099722103956375719819612282992148101890239715576171875-1329938412606197485769312599390307351191540891599374831099//660598332623738254318917673697952888611341438293457031250*6^(1//2) + A[14,8]=40774077277747636354598451708891165494123131383777235229538611989392175193285994266471//15264290546248162101058985941588079518256741255377031736357946125713524703979492187500+123767075855296855875080343261298883871499029943//451091609994276250390378731960660324096679687500*6^(1//2) + A[14,9]=-10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664//3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375+3465478123948311964502249611316368748401972838404//2560337247282641848992620902543472728729248046875*6^(1//2) + A[14,10]=-27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984//12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375+574774300271998598683873114105472016699241495055292//1049352151254569101542262489932969253892183788671875*6^(1//2) + A[14,11]=-34241134351848245624232809437676889009431930503529853032576417589898516//5613347824358651981100985009024281007603230062439942682713165283203125 + A[14,12]=-3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609//1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000 + A[14,13]=4746930876023919335079451612726717649218264199984//18592065538407049755200144388134089346432755594877 + A[15,1]=-25188329249258825443748527038142409879923012133738985313265430932280250855708601//11370641325574469312056961874077298550827642308774647316995717036347558064286250+1234273058981860170179592598535508631343082535549881956//2105633771469628744518390642968552144069898845895808125*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-parse(BigInt,"54821142119685055562477216205428613949905430396088")//parse(BigInt,"3959439837009461289085587746748097947393101278095")-parse(BigInt,"1511276753825982856072891469504471256664975925000")//parse(BigInt,"40386286337496505148672995016830599063409633036569")*6^(1//2) - A[15,7]=-parse(BigInt,"60922424274061599918603524049390657305431262635197540405697952")//parse(BigInt,"6484861747489032169774584624759953148531564032417461909516875")+parse(BigInt,"84558575751635978733109961893984238786929550462615375699341616")//parse(BigInt,"19454585242467096509323753874279859445594692097252385728550625")*6^(1//2) - A[15,8]=-parse(BigInt,"116118147575045169733222875835719955334334798191459879782123534889390467935109772")//parse(BigInt,"8810626901954835245672275131295870892503713957512170681453300814988417642493125")-parse(BigInt,"176324722711694310025656085505072661620440362221411708")//parse(BigInt,"285619406719829107485771207042040133465420149964555625")*6^(1//2) - A[15,9]=parse(BigInt,"17769448722513898342276837490665097286927607247073335618566987143467294900183033216")//parse(BigInt,"2551217008137889615056342146084561867122485163596619283719957742418751029506356875")-parse(BigInt,"19748368943709762722873481576568138101489320568798111296")//parse(BigInt,"6484554262322259071286545935997129135111813687175650625")*6^(1//2) - A[15,10]=parse(BigInt,"97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000")//parse(BigInt,"18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599")-parse(BigInt,"85297084611782122474911131363078900058888025224607913745000000")//parse(BigInt,"69210659450201393843166746722954036326338355649915383851733911")*6^(1//2) - A[15,11]=parse(BigInt,"473389749049752963256114649231353822492912259509649519870869750525")//parse(BigInt,"35412440882360341799798842428365422941216508121322622479260846291") - A[15,12]=parse(BigInt,"33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637")//parse(BigInt,"2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966") - A[15,13]=-parse(BigInt,"38714992656958413389743252726016897599283911682945255636643554687500000")//parse(BigInt,"48540494926971587499294589382572212036169135429877901702347521300421767") - A[15,14]=parse(BigInt,"14800250200940323717124616175641261235119295795768814717803955078125")//parse(BigInt,"33565577125141877760287380588632421223433194078156948298488471160489") - A[16,1]=parse(BigInt,"2305785696086397561080858186939897173645641331085041313944389849986584101287")//parse(BigInt,"617508244345282265819087370078275122671246164669900462139876057008239440000")-parse(BigInt,"85404623305589712632165905233974183137607899140719")//parse(BigInt,"124822287169084833758410283469525117460541643292500")*6^(1//2) + A[15,6]=-54821142119685055562477216205428613949905430396088//3959439837009461289085587746748097947393101278095-1511276753825982856072891469504471256664975925000//40386286337496505148672995016830599063409633036569*6^(1//2) + A[15,7]=-60922424274061599918603524049390657305431262635197540405697952//6484861747489032169774584624759953148531564032417461909516875+84558575751635978733109961893984238786929550462615375699341616//19454585242467096509323753874279859445594692097252385728550625*6^(1//2) + A[15,8]=-116118147575045169733222875835719955334334798191459879782123534889390467935109772//8810626901954835245672275131295870892503713957512170681453300814988417642493125-176324722711694310025656085505072661620440362221411708//285619406719829107485771207042040133465420149964555625*6^(1//2) + A[15,9]=17769448722513898342276837490665097286927607247073335618566987143467294900183033216//2551217008137889615056342146084561867122485163596619283719957742418751029506356875-19748368943709762722873481576568138101489320568798111296//6484554262322259071286545935997129135111813687175650625*6^(1//2) + A[15,10]=97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000//18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599-85297084611782122474911131363078900058888025224607913745000000//69210659450201393843166746722954036326338355649915383851733911*6^(1//2) + A[15,11]=473389749049752963256114649231353822492912259509649519870869750525//35412440882360341799798842428365422941216508121322622479260846291 + A[15,12]=33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637//2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966 + A[15,13]=-38714992656958413389743252726016897599283911682945255636643554687500000//48540494926971587499294589382572212036169135429877901702347521300421767 + A[15,14]=14800250200940323717124616175641261235119295795768814717803955078125//33565577125141877760287380588632421223433194078156948298488471160489 + A[16,1]=2305785696086397561080858186939897173645641331085041313944389849986584101287//617508244345282265819087370078275122671246164669900462139876057008239440000-85404623305589712632165905233974183137607899140719//124822287169084833758410283469525117460541643292500*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=parse(BigInt,"102903996961580448264190625267026062654799259083")//parse(BigInt,"5046398084890004857481629999673320438819484730")+parse(BigInt,"41320925487304219313300272052128374567081128125")//parse(BigInt,"51473260465878049546312625996667868475958744246")*6^(1//2) - A[16,7]=parse(BigInt,"62798443349876457506718920843975661399949564598018488144466")//parse(BigInt,"4132553498782573324058263582553715220777051359780141380625")-parse(BigInt,"72308807081932961554425711089716771013571419950657300729103")//parse(BigInt,"12397660496347719972174790747661145662331154079340424141875")*6^(1//2) - A[16,8]=parse(BigInt,"1794909142126482564390848522924225553221469019751470544959297614654661293377")//parse(BigInt,"52596481193994264435601626109752988674679691644275456716633975785978672500")+parse(BigInt,"12200660472227101804595129319139169019658271305817")//parse(BigInt,"16931561456559959115207709344056578263397760602500")*6^(1//2) - A[16,9]=-parse(BigInt,"2775244732780109667342845612394739319115662636371477300455747022423270475907256")//parse(BigInt,"228417153675584029725018045422706955827996328208181619436454383447149337555625")+parse(BigInt,"341618493222358850528663620935896732550431596562876")//parse(BigInt,"96101338378773357469245211954911505447551097205625")*6^(1//2) - A[16,10]=-parse(BigInt,"27680554659769016623530979176727448251292244310769996015342190819068970556083063125000")//parse(BigInt,"3299557777429648960576561382256606844677258438797072955341581354051375036522231471437")+parse(BigInt,"4426552127579895373479670356100179759944766558141730312500")//parse(BigInt,"3077113738667320707748877199804636746494977000658967987677")*6^(1//2) - A[16,11]=-parse(BigInt,"292603171929706291053929402159930330736639136252680853622275")//parse(BigInt,"15473622826279161150227076887290262443510550964275858143964") - A[16,12]=-parse(BigInt,"9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431")//parse(BigInt,"286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992") - A[16,13]=parse(BigInt,"2729491144709837905799148766650782532906050298971406518524169921875")//parse(BigInt,"2158115888622139473142775812109447802920656149243127309253686951469") + A[16,6]=102903996961580448264190625267026062654799259083//5046398084890004857481629999673320438819484730+41320925487304219313300272052128374567081128125//51473260465878049546312625996667868475958744246*6^(1//2) + A[16,7]=62798443349876457506718920843975661399949564598018488144466//4132553498782573324058263582553715220777051359780141380625-72308807081932961554425711089716771013571419950657300729103//12397660496347719972174790747661145662331154079340424141875*6^(1//2) + A[16,8]=1794909142126482564390848522924225553221469019751470544959297614654661293377//52596481193994264435601626109752988674679691644275456716633975785978672500+12200660472227101804595129319139169019658271305817//16931561456559959115207709344056578263397760602500*6^(1//2) + A[16,9]=-2775244732780109667342845612394739319115662636371477300455747022423270475907256//228417153675584029725018045422706955827996328208181619436454383447149337555625+341618493222358850528663620935896732550431596562876//96101338378773357469245211954911505447551097205625*6^(1//2) + A[16,10]=-27680554659769016623530979176727448251292244310769996015342190819068970556083063125000//3299557777429648960576561382256606844677258438797072955341581354051375036522231471437+4426552127579895373479670356100179759944766558141730312500//3077113738667320707748877199804636746494977000658967987677*6^(1//2) + A[16,11]=-292603171929706291053929402159930330736639136252680853622275//15473622826279161150227076887290262443510550964275858143964 + A[16,12]=-9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431//286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992 + A[16,13]=2729491144709837905799148766650782532906050298971406518524169921875//2158115888622139473142775812109447802920656149243127309253686951469 A[16,14]=0 A[16,15]=0 α[1]=8198160366203173411119943711500331//561057579384085860167277847128765528 @@ -4604,13 +4604,13 @@ function constructVernerEfficient9(T::Type = Float64) α[5]=0 α[6]=0 α[7]=0 - α[8]=-parse(BigInt,"455655493073428838813281446213740000000")//parse(BigInt,"1163808011150910561240464225837312497869") - α[9]=parse(BigInt,"19965163648706008081135075746915614720000000")//parse(BigInt,"86394404190537086868394686205782432516544599") - α[10]=parse(BigInt,"89231107919981418705566970804343750000000000000000000000")//parse(BigInt,"699979870988335674445594679856445060562597693583175985391") + α[8]=-455655493073428838813281446213740000000//1163808011150910561240464225837312497869 + α[9]=19965163648706008081135075746915614720000000//86394404190537086868394686205782432516544599 + α[10]=89231107919981418705566970804343750000000000000000000000//699979870988335674445594679856445060562597693583175985391 α[11]=47104273954945906713184913871143492//209684639122339601934631113492763467 - α[12]=parse(BigInt,"20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083")//parse(BigInt,"36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608") - α[13]=parse(BigInt,"6053037282142306509795911286909179687500000000")//parse(BigInt,"103899257350518063455290077573775162739725126989") - α[14]=parse(BigInt,"917401104920993498360358406096725463867187500")//parse(BigInt,"6724249815911346653315790737453607382989551463") + α[12]=20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083//36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608 + α[13]=6053037282142306509795911286909179687500000000//103899257350518063455290077573775162739725126989 + α[14]=917401104920993498360358406096725463867187500//6724249815911346653315790737453607382989551463 α[15]=2585449557665268951371699596493957//84574345160764140163208606048427531 α[16]=0 αEEst[1]=552562031208180939317806684253//27669654257734667858523344041464 @@ -4621,11 +4621,11 @@ function constructVernerEfficient9(T::Type = Float64) αEEst[6]=0 αEEst[7]=0 αEEst[8]=221223388631423597589898601690000000//100946136798587090054685074667127461 - αEEst[9]=parse(BigInt,"101835408791305297984657812561920000000")//parse(BigInt,"1149763833200743759976506650241312100139") - αEEst[10]=parse(BigInt,"1313720309077630014453239843750000000000000000000")//parse(BigInt,"11518201923215510989126466531107437037395719117133") + αEEst[9]=101835408791305297984657812561920000000//1149763833200743759976506650241312100139 + αEEst[10]=1313720309077630014453239843750000000000000000000//11518201923215510989126466531107437037395719117133 αEEst[11]=4833611232701440504508086151728//19081321241454145230196661524503 - αEEst[12]=-parse(BigInt,"2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957")//parse(BigInt,"1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568") - αEEst[13]=parse(BigInt,"1084761591753640855844358063964843750000000")//parse(BigInt,"3182895486031249071938549691320502488733423") + αEEst[12]=-2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957//1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568 + αEEst[13]=1084761591753640855844358063964843750000000//3182895486031249071938549691320502488733423 αEEst[14]=0 αEEst[15]=0 αEEst[16]=1839190071060649887127895100784//38045139523510634351420875415397 @@ -4649,11 +4649,11 @@ function constructSharp9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//50 - c[3]=parse(BigInt,"3837236")//parse(BigInt,"48429375")+parse(BigInt,"1031368")//parse(BigInt,"145288125")*6^(1//2) - c[4]=parse(BigInt,"1918618")//parse(BigInt,"16143125")+parse(BigInt,"515684")//parse(BigInt,"48429375")*6^(1//2) + c[3]=3837236//48429375+1031368//145288125*6^(1//2) + c[4]=1918618//16143125+515684//48429375*6^(1//2) c[5]=14//45 - c[6]=parse(BigInt,"156")//parse(BigInt,"625")+parse(BigInt,"26")//parse(BigInt,"625")*6^(1//2) - c[7]=parse(BigInt,"156")//parse(BigInt,"625")-parse(BigInt,"26")//parse(BigInt,"625")*6^(1//2) + c[6]=156//625+26//625*6^(1//2) + c[7]=156//625-26//625*6^(1//2) c[8]=52//125 c[9]=39//125 c[10]=21//200 @@ -4664,48 +4664,48 @@ function constructSharp9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//50 - A[3,1]=-parse(BigInt,"24000387317036")//parse(BigInt,"281448523546875")-parse(BigInt,"5917264532296")//parse(BigInt,"281448523546875")*6^(1//2) - A[3,2]=parse(BigInt,"46300580261936")//parse(BigInt,"281448523546875")+parse(BigInt,"7915204837696")//parse(BigInt,"281448523546875")*6^(1//2) - A[4,1]=parse(BigInt,"959309")//parse(BigInt,"32286250")+parse(BigInt,"128921")//parse(BigInt,"48429375")*6^(1//2) + A[3,1]=-24000387317036//281448523546875-5917264532296//281448523546875*6^(1//2) + A[3,2]=46300580261936//281448523546875+7915204837696//281448523546875*6^(1//2) + A[4,1]=959309//32286250+128921//48429375*6^(1//2) A[4,2]=0 - A[4,3]=parse(BigInt,"2877927")//parse(BigInt,"32286250")+parse(BigInt,"128921")//parse(BigInt,"16143125")*6^(1//2) - A[5,1]=parse(BigInt,"2826523628723851")//parse(BigInt,"5953434698904030")-parse(BigInt,"68459492317475")//parse(BigInt,"595343469890403")*6^(1//2) + A[4,3]=2877927//32286250+128921//16143125*6^(1//2) + A[5,1]=2826523628723851//5953434698904030-68459492317475//595343469890403*6^(1//2) A[5,2]=0 - A[5,3]=-parse(BigInt,"704240024458145")//parse(BigInt,"396895646593602")+parse(BigInt,"91277530807085")//parse(BigInt,"198447823296801")*6^(1//2) - A[5,4]=parse(BigInt,"958925642225180")//parse(BigInt,"595343469890403")-parse(BigInt,"205373100103780")//parse(BigInt,"595343469890403")*6^(1//2) - A[6,1]=parse(BigInt,"376341108")//parse(BigInt,"9406484375")+parse(BigInt,"207933466")//parse(BigInt,"65845390625")*6^(1//2) + A[5,3]=-704240024458145//396895646593602+91277530807085//198447823296801*6^(1//2) + A[5,4]=958925642225180//595343469890403-205373100103780//595343469890403*6^(1//2) + A[6,1]=376341108//9406484375+207933466//65845390625*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=parse(BigInt,"4343545768844529")//parse(BigInt,"27892881885795625")+parse(BigInt,"469265141246109")//parse(BigInt,"27892881885795625")*6^(1//2) - A[6,5]=parse(BigInt,"1559927818449")//parse(BigInt,"28957835234375")+parse(BigInt,"4382126882523")//parse(BigInt,"202704846640625")*6^(1//2) - A[7,1]=parse(BigInt,"11781705468")//parse(BigInt,"235162109375")+parse(BigInt,"2328587014")//parse(BigInt,"1646134765625")*6^(1//2) + A[6,4]=4343545768844529//27892881885795625+469265141246109//27892881885795625*6^(1//2) + A[6,5]=1559927818449//28957835234375+4382126882523//202704846640625*6^(1//2) + A[7,1]=11781705468//235162109375+2328587014//1646134765625*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=parse(BigInt,"23459106068523828440829")//parse(BigInt,"354298872323611753203125")+parse(BigInt,"7870375504052283205581")//parse(BigInt,"354298872323611753203125")*6^(1//2) - A[7,5]=parse(BigInt,"146263465360621089")//parse(BigInt,"7558718942052734375")-parse(BigInt,"1881455818308499953")//parse(BigInt,"52911032594369140625")*6^(1//2) - A[7,6]=parse(BigInt,"9444124356888")//parse(BigInt,"82889304453125")-parse(BigInt,"2459298027368")//parse(BigInt,"82889304453125")*6^(1//2) + A[7,4]=23459106068523828440829//354298872323611753203125+7870375504052283205581//354298872323611753203125*6^(1//2) + A[7,5]=146263465360621089//7558718942052734375-1881455818308499953//52911032594369140625*6^(1//2) + A[7,6]=9444124356888//82889304453125-2459298027368//82889304453125*6^(1//2) A[8,1]=52//1125 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=parse(BigInt,"208")//parse(BigInt,"1125")-parse(BigInt,"13")//parse(BigInt,"1125")*6^(1//2) - A[8,7]=parse(BigInt,"208")//parse(BigInt,"1125")+parse(BigInt,"13")//parse(BigInt,"1125")*6^(1//2) + A[8,6]=208//1125-13//1125*6^(1//2) + A[8,7]=208//1125+13//1125*6^(1//2) A[9,1]=741//16000 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=parse(BigInt,"2301")//parse(BigInt,"16000")-parse(BigInt,"897")//parse(BigInt,"32000")*6^(1//2) - A[9,7]=parse(BigInt,"2301")//parse(BigInt,"16000")+parse(BigInt,"897")//parse(BigInt,"32000")*6^(1//2) + A[9,6]=2301//16000-897//32000*6^(1//2) + A[9,7]=2301//16000+897//32000*6^(1//2) A[9,8]=-351//16000 A[10,1]=35291978967//748709478400 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=parse(BigInt,"23154511989")//parse(BigInt,"149741895680")+parse(BigInt,"39398793")//parse(BigInt,"1772093440")*6^(1//2) - A[10,7]=parse(BigInt,"23154511989")//parse(BigInt,"149741895680")-parse(BigInt,"39398793")//parse(BigInt,"1772093440")*6^(1//2) + A[10,6]=23154511989//149741895680+39398793//1772093440*6^(1//2) + A[10,7]=23154511989//149741895680-39398793//1772093440*6^(1//2) A[10,8]=-6251205429//149741895680 A[10,9]=-981041103//4679434240 A[11,1]=1601589807329134144752443//16639785968494158002257920 @@ -4713,74 +4713,74 @@ function constructSharp9(T::Type = Float64) A[11,3]=0 A[11,4]=0 A[11,5]=0 - A[11,6]=-parse(BigInt,"1736562342312744743536201")//parse(BigInt,"1109319064566277200150528")-parse(BigInt,"360257484908262597335743")//parse(BigInt,"511993414415204861607936")*6^(1//2) - A[11,7]=-parse(BigInt,"1736562342312744743536201")//parse(BigInt,"1109319064566277200150528")+parse(BigInt,"360257484908262597335743")//parse(BigInt,"511993414415204861607936")*6^(1//2) + A[11,6]=-1736562342312744743536201//1109319064566277200150528-360257484908262597335743//511993414415204861607936*6^(1//2) + A[11,7]=-1736562342312744743536201//1109319064566277200150528+360257484908262597335743//511993414415204861607936*6^(1//2) A[11,8]=512032742176678555764127//369773021522092400050176 A[11,9]=248233526294563631278471//103998662303088487514112 A[11,10]=-3//20 - A[12,1]=-parse(BigInt,"131987017608786696357225423387594635612719389206128606880670434178321331969627889057541436355642743061150672386594396559")//parse(BigInt,"318753926087995555015147926201612010240447228295789462486798116221476093939683123897279961564118214685494052121351290880") + A[12,1]=-131987017608786696357225423387594635612719389206128606880670434178321331969627889057541436355642743061150672386594396559//318753926087995555015147926201612010240447228295789462486798116221476093939683123897279961564118214685494052121351290880 A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-parse(BigInt,"581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047")//parse(BigInt,"1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352")+parse(BigInt,"71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031")//parse(BigInt,"51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736")*6^(1//2) - A[12,7]=-parse(BigInt,"581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047")//parse(BigInt,"1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352")-parse(BigInt,"71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031")//parse(BigInt,"51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736")*6^(1//2) - A[12,8]=-parse(BigInt,"189357008262607724321683086336517345228379250897103291049044350530935228180690663776657891613652665009511679250229667441")//parse(BigInt,"104902085728430283184879370421906174798708029629619600881898639306750333561102065113284728091471708748347777999725133824") - A[12,9]=-parse(BigInt,"1618350992792815653992284152254111827399426534014847245801101845172567304269189800544372100050869595166981551925667441")//parse(BigInt,"19637518660778297585754649024920739916598981028937029385347383945787366501641192454385997632075140011874187139618963456") - A[12,10]=parse(BigInt,"6883437842714982754414155283530543027800010156600147069119889350771791431366439329656536871565378282089012991331513")//parse(BigInt,"1827181489551794784669860898707808352423218653885642080180242252960011545073999200946066370836641132319880849653760") - A[12,11]=parse(BigInt,"115590271440716912566235566233889746097162479804636463234298604185457969653794053637008425503953091180886565")//parse(BigInt,"315361333249071836330411464879245754163964468656963767284078726004630975015921697525870414526347596936773632") - A[13,1]=parse(BigInt,"5215174783558918407997583468635543407988332719241764605769949554629")//parse(BigInt,"20283132613214812064685094275151111714651171227532533713038580121600") + A[12,6]=-581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047//1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352+71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031//51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736*6^(1//2) + A[12,7]=-581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047//1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352-71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031//51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736*6^(1//2) + A[12,8]=-189357008262607724321683086336517345228379250897103291049044350530935228180690663776657891613652665009511679250229667441//104902085728430283184879370421906174798708029629619600881898639306750333561102065113284728091471708748347777999725133824 + A[12,9]=-1618350992792815653992284152254111827399426534014847245801101845172567304269189800544372100050869595166981551925667441//19637518660778297585754649024920739916598981028937029385347383945787366501641192454385997632075140011874187139618963456 + A[12,10]=6883437842714982754414155283530543027800010156600147069119889350771791431366439329656536871565378282089012991331513//1827181489551794784669860898707808352423218653885642080180242252960011545073999200946066370836641132319880849653760 + A[12,11]=115590271440716912566235566233889746097162479804636463234298604185457969653794053637008425503953091180886565//315361333249071836330411464879245754163964468656963767284078726004630975015921697525870414526347596936773632 + A[13,1]=5215174783558918407997583468635543407988332719241764605769949554629//20283132613214812064685094275151111714651171227532533713038580121600 A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=parse(BigInt,"2843598186227456480865065344408178581293412110128603")//parse(BigInt,"792075053175002139265844335272820716293355019960320")-parse(BigInt,"18227070890226867447840942666790512323422585544257")//parse(BigInt,"121857700488461867579360666965049340968208464609280")*6^(1//2) - A[13,7]=parse(BigInt,"2843598186227456480865065344408178581293412110128603")//parse(BigInt,"792075053175002139265844335272820716293355019960320")+parse(BigInt,"18227070890226867447840942666790512323422585544257")//parse(BigInt,"121857700488461867579360666965049340968208464609280")*6^(1//2) - A[13,8]=parse(BigInt,"9326829464422062118248457481351539504275339476759467047326605595685633")//parse(BigInt,"4901901791858228863857691041029309678010355547895721285919177263022080") - A[13,9]=-parse(BigInt,"741604155090542466856213236072374206251235617068304762316465738169791")//parse(BigInt,"141551673163321136844445993892555326037025917405403892742525852712960") - A[13,10]=-parse(BigInt,"6058504866441219655595548618762485399974773685307046001179355536003")//parse(BigInt,"2252275720815396172726400694965157641073696835574259179818290290400") - A[13,11]=-parse(BigInt,"72917047186465183128180555150230405657138451692847535142343993")//parse(BigInt,"44661747288016218276854771442831738093234145203222656783563600") - A[13,12]=parse(BigInt,"2736153920540927643774133147635296486946660915558253285983742020488887296849241173151960647763453239551016003889152")//parse(BigInt,"2485672110698341015290264470463939203955869249618375406787169018009688457749866177826801192710345262847046284166825") - A[14,1]=parse(BigInt,"1961431625890315687063141575818232405522545898155499982338718373117379429883")//parse(BigInt,"480056647167077429990593568055406093586176318669944422673481728000000000000") + A[13,6]=2843598186227456480865065344408178581293412110128603//792075053175002139265844335272820716293355019960320-18227070890226867447840942666790512323422585544257//121857700488461867579360666965049340968208464609280*6^(1//2) + A[13,7]=2843598186227456480865065344408178581293412110128603//792075053175002139265844335272820716293355019960320+18227070890226867447840942666790512323422585544257//121857700488461867579360666965049340968208464609280*6^(1//2) + A[13,8]=9326829464422062118248457481351539504275339476759467047326605595685633//4901901791858228863857691041029309678010355547895721285919177263022080 + A[13,9]=-741604155090542466856213236072374206251235617068304762316465738169791//141551673163321136844445993892555326037025917405403892742525852712960 + A[13,10]=-6058504866441219655595548618762485399974773685307046001179355536003//2252275720815396172726400694965157641073696835574259179818290290400 + A[13,11]=-72917047186465183128180555150230405657138451692847535142343993//44661747288016218276854771442831738093234145203222656783563600 + A[13,12]=2736153920540927643774133147635296486946660915558253285983742020488887296849241173151960647763453239551016003889152//2485672110698341015290264470463939203955869249618375406787169018009688457749866177826801192710345262847046284166825 + A[14,1]=1961431625890315687063141575818232405522545898155499982338718373117379429883//480056647167077429990593568055406093586176318669944422673481728000000000000 A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=-parse(BigInt,"8688525606146315530022414580346392155721271039")//parse(BigInt,"22386738118754433181814607602481176248320000000")-parse(BigInt,"10256190098435854298655077997613296122112139953")//parse(BigInt,"1148037852243817086246902953973393653760000000")*6^(1//2) - A[14,7]=-parse(BigInt,"8688525606146315530022414580346392155721271039")//parse(BigInt,"22386738118754433181814607602481176248320000000")+parse(BigInt,"10256190098435854298655077997613296122112139953")//parse(BigInt,"1148037852243817086246902953973393653760000000")*6^(1//2) - A[14,8]=-parse(BigInt,"108151392092290424953498836380059772609736403739434481043071361807712075869481")//parse(BigInt,"8600735495194563448316261478331353993230137106756553600705167485829120000000") - A[14,9]=parse(BigInt,"683210554257935462600257975958139742203919396113084127371502375524416129719")//parse(BigInt,"26895337200565243662247103690698994332502640106760065066162305761280000000") - A[14,10]=-parse(BigInt,"125971034051203704183074450363446847441594334546885083244594242327104115033")//parse(BigInt,"5066049934698363488698655054901069679084758735799331062593807151200000000") - A[14,11]=parse(BigInt,"4322338495495152743252505005837177994220267688026960252214552638944423")//parse(BigInt,"236867625787508422152958167179676757535142999000924357630500000000000") - A[14,12]=-parse(BigInt,"88682414394183619425441647866243388112917289239161463940944492930492112547171652363240146123589908870567811533658125375935101390832")//parse(BigInt,"9405104776230176067202383689444499684238639823097650089954333383377958770491999076242219980453370248022825420814384818872314453125") - A[14,13]=parse(BigInt,"26235475641986625187247554297838197168935151270802587")//parse(BigInt,"31781620957198174033817415268740604591106877500000000") - A[15,1]=-parse(BigInt,"2933688768685553737193922190442902414638569907165819426999847151894747")//parse(BigInt,"1423967854813137802350516795065201258930107696470226170813903745843200") + A[14,6]=-8688525606146315530022414580346392155721271039//22386738118754433181814607602481176248320000000-10256190098435854298655077997613296122112139953//1148037852243817086246902953973393653760000000*6^(1//2) + A[14,7]=-8688525606146315530022414580346392155721271039//22386738118754433181814607602481176248320000000+10256190098435854298655077997613296122112139953//1148037852243817086246902953973393653760000000*6^(1//2) + A[14,8]=-108151392092290424953498836380059772609736403739434481043071361807712075869481//8600735495194563448316261478331353993230137106756553600705167485829120000000 + A[14,9]=683210554257935462600257975958139742203919396113084127371502375524416129719//26895337200565243662247103690698994332502640106760065066162305761280000000 + A[14,10]=-125971034051203704183074450363446847441594334546885083244594242327104115033//5066049934698363488698655054901069679084758735799331062593807151200000000 + A[14,11]=4322338495495152743252505005837177994220267688026960252214552638944423//236867625787508422152958167179676757535142999000924357630500000000000 + A[14,12]=-88682414394183619425441647866243388112917289239161463940944492930492112547171652363240146123589908870567811533658125375935101390832//9405104776230176067202383689444499684238639823097650089954333383377958770491999076242219980453370248022825420814384818872314453125 + A[14,13]=26235475641986625187247554297838197168935151270802587//31781620957198174033817415268740604591106877500000000 + A[15,1]=-2933688768685553737193922190442902414638569907165819426999847151894747//1423967854813137802350516795065201258930107696470226170813903745843200 A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-parse(BigInt,"279050827135618188106138704976571118076242172562777")//parse(BigInt,"26980717750745660055932121988692169249262917386240")+parse(BigInt,"59017804198407615229179283246229064921710388893173")//parse(BigInt,"17987145167163773370621414659128112832841944924160")*6^(1//2) - A[15,7]=-parse(BigInt,"279050827135618188106138704976571118076242172562777")//parse(BigInt,"26980717750745660055932121988692169249262917386240")-parse(BigInt,"59017804198407615229179283246229064921710388893173")//parse(BigInt,"17987145167163773370621414659128112832841944924160")*6^(1//2) - A[15,8]=parse(BigInt,"68240477823918559060550996013166770535743446467404475965020846786328901")//parse(BigInt,"69628625900822775316247857716283393138506964199995817446989013471723520") - A[15,9]=parse(BigInt,"48531604865335743440838806675493568975092395234916265724406574203650554879")//parse(BigInt,"7529075569049450724715447951105730327391304314424323559158913160761835520") - A[15,10]=parse(BigInt,"7315898198049114373691779027237206235234893868747090317226910860963581499")//parse(BigInt,"432400219379131684183655517400956805867024783959757582533074834771793600") - A[15,11]=-parse(BigInt,"87035912584683752124645187592152267644073875904388006117245587111831")//parse(BigInt,"41468532532723053663401983927439573730970639521941633396843682248800") - A[15,12]=parse(BigInt,"793006054328041651061360131256412474400253089909554005378332728214806108995212138291759017448087224471716436232175864384424753159293287828190208")//parse(BigInt,"600635305507048430170531323174007915813446499853348186301444535722932552444071789775577508083955280258070844780520371987041149053341617704219325") - A[15,13]=parse(BigInt,"19013238692887784267164981427867630356262081870600946422701364458")//parse(BigInt,"146516308633144198110735805762400905606463733191840985648075179899") - A[15,14]=parse(BigInt,"368176545506575596342007241113258886329861009608750000000")//parse(BigInt,"7515329389098801941975451526298754679007062667248055263091") - A[16,1]=-parse(BigInt,"36388658330162124762200023703074655379362961851837455245313588466117")//parse(BigInt,"299291302137383314536268908335335078201218487321808786511993451315200") + A[15,6]=-279050827135618188106138704976571118076242172562777//26980717750745660055932121988692169249262917386240+59017804198407615229179283246229064921710388893173//17987145167163773370621414659128112832841944924160*6^(1//2) + A[15,7]=-279050827135618188106138704976571118076242172562777//26980717750745660055932121988692169249262917386240-59017804198407615229179283246229064921710388893173//17987145167163773370621414659128112832841944924160*6^(1//2) + A[15,8]=68240477823918559060550996013166770535743446467404475965020846786328901//69628625900822775316247857716283393138506964199995817446989013471723520 + A[15,9]=48531604865335743440838806675493568975092395234916265724406574203650554879//7529075569049450724715447951105730327391304314424323559158913160761835520 + A[15,10]=7315898198049114373691779027237206235234893868747090317226910860963581499//432400219379131684183655517400956805867024783959757582533074834771793600 + A[15,11]=-87035912584683752124645187592152267644073875904388006117245587111831//41468532532723053663401983927439573730970639521941633396843682248800 + A[15,12]=793006054328041651061360131256412474400253089909554005378332728214806108995212138291759017448087224471716436232175864384424753159293287828190208//600635305507048430170531323174007915813446499853348186301444535722932552444071789775577508083955280258070844780520371987041149053341617704219325 + A[15,13]=19013238692887784267164981427867630356262081870600946422701364458//146516308633144198110735805762400905606463733191840985648075179899 + A[15,14]=368176545506575596342007241113258886329861009608750000000//7515329389098801941975451526298754679007062667248055263091 + A[16,1]=-36388658330162124762200023703074655379362961851837455245313588466117//299291302137383314536268908335335078201218487321808786511993451315200 A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-parse(BigInt,"5017294099975580158862668031284197043053591531405121")//parse(BigInt,"432874134925719951608236287739966681862399087083520")-parse(BigInt,"115700422823857939498444446575144266776173664871303")//parse(BigInt,"199788062273409208434570594341523083936491886346240")*6^(1//2) - A[16,7]=-parse(BigInt,"5017294099975580158862668031284197043053591531405121")//parse(BigInt,"432874134925719951608236287739966681862399087083520")+parse(BigInt,"115700422823857939498444446575144266776173664871303")//parse(BigInt,"199788062273409208434570594341523083936491886346240")*6^(1//2) - A[16,8]=-parse(BigInt,"91869384706617020415871523809581333688744319256441669606452442156503951243")//parse(BigInt,"10053990532496870785611049673131231012151168225596329651077879646797168640") - A[16,9]=parse(BigInt,"52862999381403119807509472978743982056878734540171187101666495333163485251")//parse(BigInt,"2399905281474961058988767393522446655063434938667458594324573249770618880") - A[16,10]=parse(BigInt,"11964965861294434337427534231330501089458731146841410298258149571218167")//parse(BigInt,"1974017923973741961134058915802491373563600428420464580517659076868800") - A[16,11]=parse(BigInt,"37167680872257703003686692191635149388479305578570534942584948859")//parse(BigInt,"3913390524272247558198063815920084715858046504866006220243936800") - A[16,12]=-parse(BigInt,"29443955867054347753341026121045589578978185460220369427665634428174791788280117223531690217195051250854008448256016995751289856")//parse(BigInt,"6138364406531943832091734698181735919618182422997726728173639255839442923939727454711783369110119257425239678616468261908910975") - A[16,13]=parse(BigInt,"407816748385172686498153181346812432791118177175769818363629863")//parse(BigInt,"626162397882386095196201629768303759628250075752997120162580989") + A[16,6]=-5017294099975580158862668031284197043053591531405121//432874134925719951608236287739966681862399087083520-115700422823857939498444446575144266776173664871303//199788062273409208434570594341523083936491886346240*6^(1//2) + A[16,7]=-5017294099975580158862668031284197043053591531405121//432874134925719951608236287739966681862399087083520+115700422823857939498444446575144266776173664871303//199788062273409208434570594341523083936491886346240*6^(1//2) + A[16,8]=-91869384706617020415871523809581333688744319256441669606452442156503951243//10053990532496870785611049673131231012151168225596329651077879646797168640 + A[16,9]=52862999381403119807509472978743982056878734540171187101666495333163485251//2399905281474961058988767393522446655063434938667458594324573249770618880 + A[16,10]=11964965861294434337427534231330501089458731146841410298258149571218167//1974017923973741961134058915802491373563600428420464580517659076868800 + A[16,11]=37167680872257703003686692191635149388479305578570534942584948859//3913390524272247558198063815920084715858046504866006220243936800 + A[16,12]=-29443955867054347753341026121045589578978185460220369427665634428174791788280117223531690217195051250854008448256016995751289856//6138364406531943832091734698181735919618182422997726728173639255839442923939727454711783369110119257425239678616468261908910975 + A[16,13]=407816748385172686498153181346812432791118177175769818363629863//626162397882386095196201629768303759628250075752997120162580989 A[16,14]=0 A[16,15]=0 α[1]=30703843389361946002220520407//1036329015084155723633962896000 @@ -4791,11 +4791,11 @@ function constructSharp9(T::Type = Float64) α[6]=0 α[7]=0 α[8]=1516681888913470906364013671875//19423768214582439936604117641536 - α[9]=parse(BigInt,"1929922737998470573359614532470703125")//parse(BigInt,"9295447834009061726737853188569292704") - α[10]=parse(BigInt,"27072397368129209968072433152000000000")//parse(BigInt,"159540891067276798629433718421290211669") - α[11]=parse(BigInt,"3416676287738448149119878197304164096817920457")//parse(BigInt,"22521752441211566270536786917243920830369456000") - α[12]=parse(BigInt,"909034900749411645631439991260524977916886591502548355130330148829066896764151555292038222333366816993556860935646735988456500531298304")//parse(BigInt,"6301978749188979317659380355882211371188146506066543226107226217493443986031316306450151922600620534579104501042337690306078523205079625") - α[13]=parse(BigInt,"9160897746149204383653282352747804858423571")//parse(BigInt,"54934119002888850773584011583391921191449440") + α[9]=1929922737998470573359614532470703125//9295447834009061726737853188569292704 + α[10]=27072397368129209968072433152000000000//159540891067276798629433718421290211669 + α[11]=3416676287738448149119878197304164096817920457//22521752441211566270536786917243920830369456000 + α[12]=909034900749411645631439991260524977916886591502548355130330148829066896764151555292038222333366816993556860935646735988456500531298304//6301978749188979317659380355882211371188146506066543226107226217493443986031316306450151922600620534579104501042337690306078523205079625 + α[13]=9160897746149204383653282352747804858423571//54934119002888850773584011583391921191449440 α[14]=3769686146953412690297035156250000//195792979665408643382362918863397227 α[15]=50782110772148063247179059//1538266148871578545201811280 α[16]=0 @@ -4809,9 +4809,9 @@ function constructSharp9(T::Type = Float64) αEEst[8]=2518169234679274570156341552734375//38284247150941989115046715871467456 αEEst[9]=13171020424136540706261627197265625//61559257178867958455217570785227104 αEEst[10]=33191111003144264098986272000000000//196721197370254992144801132455351679 - αEEst[11]=parse(BigInt,"98603841096694858013088556726735239713679")//parse(BigInt,"574051243626833692823306576536179258032000") - αEEst[12]=parse(BigInt,"5093635768538576107415789300891145054334065554846760039946162068969260804962050605021707042060987973190001839145435136")//parse(BigInt,"40589106364182299226269510371318864016087966429387805447847648739509460272079710913035195393529050583646417571607929125") - αEEst[13]=parse(BigInt,"108010721096523379193662759959856611609133")//parse(BigInt,"570689193181223151553200582051397411377120") + αEEst[11]=98603841096694858013088556726735239713679//574051243626833692823306576536179258032000 + αEEst[12]=5093635768538576107415789300891145054334065554846760039946162068969260804962050605021707042060987973190001839145435136//40589106364182299226269510371318864016087966429387805447847648739509460272079710913035195393529050583646417571607929125 + αEEst[13]=108010721096523379193662759959856611609133//570689193181223151553200582051397411377120 αEEst[14]=0 αEEst[15]=0 αEEst[16]=26859551018855966185191031//763900876650511794556001520 @@ -4834,11 +4834,11 @@ function constructTsitouras9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//49 - c[3]=parse(BigInt,"64")//parse(BigInt,"705")-parse(BigInt,"16")//parse(BigInt,"14805")*6^(1//2) - c[4]=parse(BigInt,"32")//parse(BigInt,"235")-parse(BigInt,"8")//parse(BigInt,"4935")*6^(1//2) + c[3]=64//705-16//14805*6^(1//2) + c[4]=32//235-8//4935*6^(1//2) c[5]=3//7 - c[6]=parse(BigInt,"8")//parse(BigInt,"21")+parse(BigInt,"4")//parse(BigInt,"63")*6^(1//2) - c[7]=parse(BigInt,"8")//parse(BigInt,"21")-parse(BigInt,"4")//parse(BigInt,"63")*6^(1//2) + c[6]=8//21+4//63*6^(1//2) + c[7]=8//21-4//63*6^(1//2) c[8]=40//63 c[9]=10//21 c[10]=19//18 @@ -4849,122 +4849,122 @@ function constructTsitouras9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//49 - A[3,1]=-parse(BigInt,"165952")//parse(BigInt,"1491075")+parse(BigInt,"38896")//parse(BigInt,"10437525")*6^(1//2) - A[3,2]=parse(BigInt,"301312")//parse(BigInt,"1491075")-parse(BigInt,"7168")//parse(BigInt,"1491075")*6^(1//2) - A[4,1]=parse(BigInt,"8")//parse(BigInt,"235")-parse(BigInt,"2")//parse(BigInt,"4935")*6^(1//2) + A[3,1]=-165952//1491075+38896//10437525*6^(1//2) + A[3,2]=301312//1491075-7168//1491075*6^(1//2) + A[4,1]=8//235-2//4935*6^(1//2) A[4,2]=0 - A[4,3]=parse(BigInt,"24")//parse(BigInt,"235")-parse(BigInt,"2")//parse(BigInt,"1645")*6^(1//2) - A[5,1]=parse(BigInt,"38937")//parse(BigInt,"44800")+parse(BigInt,"171")//parse(BigInt,"5600")*6^(1//2) + A[4,3]=24//235-2//1645*6^(1//2) + A[5,1]=38937//44800+171//5600*6^(1//2) A[5,2]=0 - A[5,3]=-parse(BigInt,"149931")//parse(BigInt,"44800")-parse(BigInt,"81")//parse(BigInt,"700")*6^(1//2) - A[5,4]=parse(BigInt,"65097")//parse(BigInt,"22400")+parse(BigInt,"477")//parse(BigInt,"5600")*6^(1//2) - A[6,1]=parse(BigInt,"176")//parse(BigInt,"5103")-parse(BigInt,"29")//parse(BigInt,"5103")*6^(1//2) + A[5,3]=-149931//44800-81//700*6^(1//2) + A[5,4]=65097//22400+477//5600*6^(1//2) + A[6,1]=176//5103-29//5103*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=parse(BigInt,"364520")//parse(BigInt,"1674351")+parse(BigInt,"87715")//parse(BigInt,"5023053")*6^(1//2) - A[6,5]=parse(BigInt,"1940224")//parse(BigInt,"15069159")+parse(BigInt,"779264")//parse(BigInt,"15069159")*6^(1//2) - A[7,1]=parse(BigInt,"4336")//parse(BigInt,"127575")+parse(BigInt,"479")//parse(BigInt,"127575")*6^(1//2) + A[6,4]=364520//1674351+87715//5023053*6^(1//2) + A[6,5]=1940224//15069159+779264//15069159*6^(1//2) + A[7,1]=4336//127575+479//127575*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=parse(BigInt,"90731944")//parse(BigInt,"400648275")-parse(BigInt,"170142739")//parse(BigInt,"8413613775")*6^(1//2) - A[7,5]=parse(BigInt,"8245504")//parse(BigInt,"62429373")-parse(BigInt,"22187008")//parse(BigInt,"437005611")*6^(1//2) - A[7,6]=-parse(BigInt,"3936")//parse(BigInt,"340025")+parse(BigInt,"11464")//parse(BigInt,"3060225")*6^(1//2) + A[7,4]=90731944//400648275-170142739//8413613775*6^(1//2) + A[7,5]=8245504//62429373-22187008//437005611*6^(1//2) + A[7,6]=-3936//340025+11464//3060225*6^(1//2) A[8,1]=40//567 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=parse(BigInt,"160")//parse(BigInt,"567")-parse(BigInt,"10")//parse(BigInt,"567")*6^(1//2) + A[8,6]=160//567-10//567*6^(1//2) A[8,7]=10//567*6^(1//2)+160//567 A[9,1]=95//1344 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=parse(BigInt,"295")//parse(BigInt,"1344")-parse(BigInt,"115")//parse(BigInt,"2688")*6^(1//2) - A[9,7]=parse(BigInt,"295")//parse(BigInt,"1344")+parse(BigInt,"115")//parse(BigInt,"2688")*6^(1//2) + A[9,6]=295//1344-115//2688*6^(1//2) + A[9,7]=295//1344+115//2688*6^(1//2) A[9,8]=-15//448 A[10,1]=52918819//138240000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=-parse(BigInt,"1453047743")//parse(BigInt,"103680000")-parse(BigInt,"4153586941")//parse(BigInt,"829440000")*6^(1//2) - A[10,7]=-parse(BigInt,"1453047743")//parse(BigInt,"103680000")+parse(BigInt,"4153586941")//parse(BigInt,"829440000")*6^(1//2) + A[10,6]=-1453047743//103680000-4153586941//829440000*6^(1//2) + A[10,7]=-1453047743//103680000+4153586941//829440000*6^(1//2) A[10,8]=44599023//5120000 A[10,9]=518179039//25920000 - A[11,1]=parse(BigInt,"258780283")//parse(BigInt,"8618400000")+parse(BigInt,"585428803")//parse(BigInt,"51710400000")*6^(1//2) + A[11,1]=258780283//8618400000+585428803//51710400000*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=19//25 - A[11,7]=parse(BigInt,"1180508473123")//parse(BigInt,"443296800000")-parse(BigInt,"136404911099")//parse(BigInt,"147765600000")*6^(1//2) - A[11,8]=-parse(BigInt,"106856621")//parse(BigInt,"190800000")+parse(BigInt,"585428803")//parse(BigInt,"2289600000")*6^(1//2) - A[11,9]=-parse(BigInt,"1260561943")//parse(BigInt,"591300000")+parse(BigInt,"585428803")//parse(BigInt,"886950000")*6^(1//2) - A[11,10]=parse(BigInt,"13167297224")//parse(BigInt,"792049782825")-parse(BigInt,"9366860848")//parse(BigInt,"2376149348475")*6^(1//2) - A[12,1]=parse(BigInt,"307213395328582867964430765847473084972824867512957518186088963")//parse(BigInt,"5126364212860621132939944111710304798478633358572140981841000000")+parse(BigInt,"119107533326819222510639750832411974467191643469020133053")//parse(BigInt,"29137664905764716334007503363213354847664112851105748578125")*6^(1//2) + A[11,7]=1180508473123//443296800000-136404911099//147765600000*6^(1//2) + A[11,8]=-106856621//190800000+585428803//2289600000*6^(1//2) + A[11,9]=-1260561943//591300000+585428803//886950000*6^(1//2) + A[11,10]=13167297224//792049782825-9366860848//2376149348475*6^(1//2) + A[12,1]=307213395328582867964430765847473084972824867512957518186088963//5126364212860621132939944111710304798478633358572140981841000000+119107533326819222510639750832411974467191643469020133053//29137664905764716334007503363213354847664112851105748578125*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=parse(BigInt,"10354821182100230493026667000379184955505622050895245676387169")//parse(BigInt,"146467548938874889512569831763151565670818095959204028052600000")-parse(BigInt,"3268463788087907168885902319404754223684763360609854606186699")//parse(BigInt,"41847871125392825575019951932329018763090884559772579443600000")*6^(1//2) - A[12,7]=parse(BigInt,"542371157260956891298011197530777699174343335570401188235055068891")//parse(BigInt,"715703215922030799396778727922657043395761853183510539934169000000")-parse(BigInt,"2557103919967567420571445567798380600417779349808054092568810687111")//parse(BigInt,"10019845022908431191554902190917198607540665944569147559078366000000")*6^(1//2) - A[12,8]=-parse(BigInt,"892225578009519154676238995901578841509244882985862325637048827")//parse(BigInt,"38813900468801845720831005417235164902766795429189067433939000000")+parse(BigInt,"20367388198886087049319397392342447633889771033202442752063")//parse(BigInt,"220613748572218566528913954035758258132313997301229239234375")*6^(1//2) - A[12,9]=-parse(BigInt,"550688605235770338034863642917595195825050633798073448796494914")//parse(BigInt,"835322740042020854251374821774223772966384453517335472487484375")+parse(BigInt,"72417380262706087286468968506106480476052519229164240896224")//parse(BigInt,"303864219731546327483221106502082129125640034018674235171875")*6^(1//2) - A[12,10]=parse(BigInt,"123396895115495738434549229715587040998178289648593721222723693824")//parse(BigInt,"16960466422214315122555088502288155618001490986047888958907461648625")-parse(BigInt,"8781560217119727637264447549372070053517105489683916369731584")//parse(BigInt,"6169685857480653009296139869875647732994358307038155314262445125")*6^(1//2) - A[12,11]=-parse(BigInt,"241890129426298647138485610377551406165672225318019246672")//parse(BigInt,"3661688723471872237814245794078789141770452398980100701315") - A[13,1]=parse(BigInt,"45077846760256141387004276823")//parse(BigInt,"110315894143992133591739924480")+parse(BigInt,"1493491403898138129099")//parse(BigInt,"13100021190238236835840")*6^(1//2) + A[12,6]=10354821182100230493026667000379184955505622050895245676387169//146467548938874889512569831763151565670818095959204028052600000-3268463788087907168885902319404754223684763360609854606186699//41847871125392825575019951932329018763090884559772579443600000*6^(1//2) + A[12,7]=542371157260956891298011197530777699174343335570401188235055068891//715703215922030799396778727922657043395761853183510539934169000000-2557103919967567420571445567798380600417779349808054092568810687111//10019845022908431191554902190917198607540665944569147559078366000000*6^(1//2) + A[12,8]=-892225578009519154676238995901578841509244882985862325637048827//38813900468801845720831005417235164902766795429189067433939000000+20367388198886087049319397392342447633889771033202442752063//220613748572218566528913954035758258132313997301229239234375*6^(1//2) + A[12,9]=-550688605235770338034863642917595195825050633798073448796494914//835322740042020854251374821774223772966384453517335472487484375+72417380262706087286468968506106480476052519229164240896224//303864219731546327483221106502082129125640034018674235171875*6^(1//2) + A[12,10]=123396895115495738434549229715587040998178289648593721222723693824//16960466422214315122555088502288155618001490986047888958907461648625-8781560217119727637264447549372070053517105489683916369731584//6169685857480653009296139869875647732994358307038155314262445125*6^(1//2) + A[12,11]=-241890129426298647138485610377551406165672225318019246672//3661688723471872237814245794078789141770452398980100701315 + A[13,1]=45077846760256141387004276823//110315894143992133591739924480+1493491403898138129099//13100021190238236835840*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=parse(BigInt,"28530732123103900185")//parse(BigInt,"9849639992660328448")-parse(BigInt,"15062887306567756845")//parse(BigInt,"5628365710091616256")*6^(1//2) - A[13,7]=parse(BigInt,"530875502237315716994493")//parse(BigInt,"24064781139210466754560")-parse(BigInt,"8920823473649531766699837")//parse(BigInt,"1347627743795786138255360")*6^(1//2) - A[13,8]=-parse(BigInt,"155850251753928802974915857362119")//parse(BigInt,"174015086605340016477040216637440")+parse(BigInt,"13441422635083243161891")//parse(BigInt,"5220309196109974077440")*6^(1//2) - A[13,9]=-parse(BigInt,"493074073683718697930133408597")//parse(BigInt,"27602712116408194083051274240")+parse(BigInt,"1493491403898138129099")//parse(BigInt,"224694912332563742720")*6^(1//2) - A[13,10]=parse(BigInt,"200609996314078300148532240828075")//parse(BigInt,"1019933691979646265167106381709312")-parse(BigInt,"336035565877081079047275")//parse(BigInt,"8465066424794973677551616")*6^(1//2) + A[13,6]=28530732123103900185//9849639992660328448-15062887306567756845//5628365710091616256*6^(1//2) + A[13,7]=530875502237315716994493//24064781139210466754560-8920823473649531766699837//1347627743795786138255360*6^(1//2) + A[13,8]=-155850251753928802974915857362119//174015086605340016477040216637440+13441422635083243161891//5220309196109974077440*6^(1//2) + A[13,9]=-493074073683718697930133408597//27602712116408194083051274240+1493491403898138129099//224694912332563742720*6^(1//2) + A[13,10]=200609996314078300148532240828075//1019933691979646265167106381709312-336035565877081079047275//8465066424794973677551616*6^(1//2) A[13,11]=-1259978731825102407292471875//947642075600343143202947072 - A[13,12]=-parse(BigInt,"193916214235317468987992391599053188049367133486207120889311375")//parse(BigInt,"42748092349455088111344007455417233641020280098816132254793728") - A[14,1]=parse(BigInt,"36716621212098036093935018687105425505961")//parse(BigInt,"72248275402215258274603114496000000000000")+1221461237263884679751555607//9994523002806272000000000000*6^(1//2) + A[13,12]=-193916214235317468987992391599053188049367133486207120889311375//42748092349455088111344007455417233641020280098816132254793728 + A[14,1]=36716621212098036093935018687105425505961//72248275402215258274603114496000000000000+1221461237263884679751555607//9994523002806272000000000000*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=parse(BigInt,"8283471074731862302286097")//parse(BigInt,"7514678949478400000000000")-parse(BigInt,"15668946773152185221466849")//parse(BigInt,"4294102256844800000000000")*6^(1//2) - A[14,7]=parse(BigInt,"397408075485926915758262202639")//parse(BigInt,"18359970961922048000000000000")-parse(BigInt,"6493922587539771225254133441201")//parse(BigInt,"1028158373867634688000000000000")*6^(1//2) - A[14,8]=parse(BigInt,"2435278493903047909370803905780425755549361787")//parse(BigInt,"6951941874960961660657094977773568000000000000")+10993151135374962117764000463//3982779843223552000000000000*6^(1//2) - A[14,9]=-parse(BigInt,"558123239069103416347126929975086912148938889")//parse(BigInt,"34184771406932232290260692794368000000000000")+1221461237263884679751555607//171428613534976000000000000*6^(1//2) - A[14,10]=parse(BigInt,"306734586161727173704146823378382330889519")//parse(BigInt,"1406266800626214225846914661737584000000000")-10993151135374962117764000463//258333325951995046312000000000*6^(1//2) - A[14,11]=-parse(BigInt,"163845778835264660255510638493965671483")//parse(BigInt,"114196173990354810149157741209600000000") - A[14,12]=-parse(BigInt,"379727098691580451304129337662817719784451899678250630685021894233169654109523405323")//parse(BigInt,"74980943726337976053062781324716052947047103330285761853079535691020475760640000000") + A[14,6]=8283471074731862302286097//7514678949478400000000000-15668946773152185221466849//4294102256844800000000000*6^(1//2) + A[14,7]=397408075485926915758262202639//18359970961922048000000000000-6493922587539771225254133441201//1028158373867634688000000000000*6^(1//2) + A[14,8]=2435278493903047909370803905780425755549361787//6951941874960961660657094977773568000000000000+10993151135374962117764000463//3982779843223552000000000000*6^(1//2) + A[14,9]=-558123239069103416347126929975086912148938889//34184771406932232290260692794368000000000000+1221461237263884679751555607//171428613534976000000000000*6^(1//2) + A[14,10]=306734586161727173704146823378382330889519//1406266800626214225846914661737584000000000-10993151135374962117764000463//258333325951995046312000000000*6^(1//2) + A[14,11]=-163845778835264660255510638493965671483//114196173990354810149157741209600000000 + A[14,12]=-379727098691580451304129337662817719784451899678250630685021894233169654109523405323//74980943726337976053062781324716052947047103330285761853079535691020475760640000000 A[14,13]=-235412270220829707518634576//10004921377982463725322265625 - A[15,1]=parse(BigInt,"246936976626965995144662615055843")//parse(BigInt,"458607216908592948032148676000000")+parse(BigInt,"1082690484492446489")//parse(BigInt,"9760276369928000000")*6^(1//2) + A[15,1]=246936976626965995144662615055843//458607216908592948032148676000000+1082690484492446489//9760276369928000000*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-parse(BigInt,"5604689614035063")//parse(BigInt,"3669276830800000")-parse(BigInt,"556441805223969")//parse(BigInt,"131045601100000")*6^(1//2) - A[15,7]=parse(BigInt,"613864878280672501731")//parse(BigInt,"35859318285004000000")-parse(BigInt,"1204548796910252147313")//parse(BigInt,"251015227995028000000")*6^(1//2) - A[15,8]=parse(BigInt,"2797434125723089631989036145593862912367")//parse(BigInt,"1454544479209361363081818944324206000000")+9744214360432018401//3889433440648000000*6^(1//2) - A[15,9]=-parse(BigInt,"78495184115962971170097375833699424291")//parse(BigInt,"6993857040773733071103139785566500000")+1082690484492446489//167410755405250000*6^(1//2) - A[15,10]=parse(BigInt,"38933993403647216169460437449231039304")//parse(BigInt,"187659712667940353060087104196403689875")-155907429766912294416//4036458217999922598625*6^(1//2) + A[15,6]=-5604689614035063//3669276830800000-556441805223969//131045601100000*6^(1//2) + A[15,7]=613864878280672501731//35859318285004000000-1204548796910252147313//251015227995028000000*6^(1//2) + A[15,8]=2797434125723089631989036145593862912367//1454544479209361363081818944324206000000+9744214360432018401//3889433440648000000*6^(1//2) + A[15,9]=-78495184115962971170097375833699424291//6993857040773733071103139785566500000+1082690484492446489//167410755405250000*6^(1//2) + A[15,10]=38933993403647216169460437449231039304//187659712667940353060087104196403689875-155907429766912294416//4036458217999922598625*6^(1//2) A[15,11]=-4116079644901049270506242987//3129604261871291193409631155 - A[15,12]=-parse(BigInt,"869293931367062297302433741250572190497190440843976042585249416347005728190566119731")//parse(BigInt,"185354770907948507678541561399002564941703939116570719233261621774655604595976403844") + A[15,12]=-869293931367062297302433741250572190497190440843976042585249416347005728190566119731//185354770907948507678541561399002564941703939116570719233261621774655604595976403844 A[15,13]=37424319425692041216//5567956245138066768875 A[15,14]=-26637096887808000000//690666426738105277187 - A[16,1]=parse(BigInt,"29766990313562078086727231879295211")//parse(BigInt,"61911974282660047984340071260000000")+parse(BigInt,"13591007763158148317")//parse(BigInt,"146404145548920000000")*6^(1//2) + A[16,1]=29766990313562078086727231879295211//61911974282660047984340071260000000+13591007763158148317//146404145548920000000*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-parse(BigInt,"583353427111301443")//parse(BigInt,"293542146464000000")-parse(BigInt,"40076566638916409")//parse(BigInt,"10483648088000000")*6^(1//2) - A[16,7]=parse(BigInt,"19531933359906438277223")//parse(BigInt,"1434372731400160000000")-parse(BigInt,"9404496119706140958251")//parse(BigInt,"2510152279950280000000")*6^(1//2) - A[16,8]=parse(BigInt,"117813280551292383465368402104818510183261")//parse(BigInt,"58181779168374454523272757772968240000000")+40773023289474444951//19447167203240000000*6^(1//2) - A[16,9]=-parse(BigInt,"2325450203082696961260142930045971433803")//parse(BigInt,"279754281630949322844125591422660000000")+13591007763158148317//2511161331078750000*6^(1//2) - A[16,10]=parse(BigInt,"2829276993010365332321333380796499415893")//parse(BigInt,"15951075576774930010107403856694313639375")-652368372631591119216//20182291089999612993125*6^(1//2) + A[16,6]=-583353427111301443//293542146464000000-40076566638916409//10483648088000000*6^(1//2) + A[16,7]=19531933359906438277223//1434372731400160000000-9404496119706140958251//2510152279950280000000*6^(1//2) + A[16,8]=117813280551292383465368402104818510183261//58181779168374454523272757772968240000000+40773023289474444951//19447167203240000000*6^(1//2) + A[16,9]=-2325450203082696961260142930045971433803//279754281630949322844125591422660000000+13591007763158148317//2511161331078750000*6^(1//2) + A[16,10]=2829276993010365332321333380796499415893//15951075576774930010107403856694313639375-652368372631591119216//20182291089999612993125*6^(1//2) A[16,11]=-64853022020814701128056854079867//63343190260274933754610934577200 - A[16,12]=-parse(BigInt,"5501801061234219240967503472431237166019376078542725490351730718419538863636177307419649")//parse(BigInt,"1398104557705668743632427777409619346988852569336419139359459089957402274666793446137600") + A[16,12]=-5501801061234219240967503472431237166019376078542725490351730718419538863636177307419649//1398104557705668743632427777409619346988852569336419139359459089957402274666793446137600 A[16,13]=-6425519161642982676103168//293904570399612854395066875 A[16,14]=-51926882941360640000//2663999074561263212007 A[16,15]=0 @@ -4979,7 +4979,7 @@ function constructTsitouras9(T::Type = Float64) α[9]=14586697891849999254003//29700462390576849520000 α[10]=102209317997264953344//225042304099487188475 α[11]=1883570537693211021//1872275755054959100 - α[12]=parse(BigInt,"17109990417889849939560223376925306674323804078983341334325755071278367152457480027")//parse(BigInt,"71381427125808828146076534703173195056090466069876919551824450642795947233961810560") + α[12]=17109990417889849939560223376925306674323804078983341334325755071278367152457480027//71381427125808828146076534703173195056090466069876919551824450642795947233961810560 α[13]=-10678264099993989152768//2396652442219114419375 α[14]=1212545712242913280000000//130535954653501897388343 α[15]=-5462519910419447//852178998090420 @@ -4995,7 +4995,7 @@ function constructTsitouras9(T::Type = Float64) αEEst[9]=444432599960137218801//1132275692309381360000 αEEst[10]=-439332801641475586992//417935707613333350025 αEEst[11]=-217759597939752597//869270886275516725 - αEEst[12]=parse(BigInt,"17659727425367474410466504999969566436559834034377723810849746362072595341")//parse(BigInt,"71629450771664553932203312665447432781082741824305141429680586700646203520") + αEEst[12]=17659727425367474410466504999969566436559834034377723810849746362072595341//71629450771664553932203312665447432781082741824305141429680586700646203520 αEEst[13]=982070268140959301632//143578256907135886875 αEEst[14]=-3885243675284052992000000//242423915785074952292637 αEEst[15]=10 @@ -5021,11 +5021,11 @@ function constructTsitouras92(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//46 - c[3]=parse(BigInt,"96755252944")//parse(BigInt,"718444993695")-parse(BigInt,"11256225944")//parse(BigInt,"718444993695")*6^(1//2) - c[4]=parse(BigInt,"48377626472")//parse(BigInt,"239481664565")-parse(BigInt,"5628112972")//parse(BigInt,"239481664565")*6^(1//2) + c[3]=96755252944//718444993695-11256225944//718444993695*6^(1//2) + c[4]=48377626472//239481664565-5628112972//239481664565*6^(1//2) c[5]=71//136 - c[6]=parse(BigInt,"276")//parse(BigInt,"715")-parse(BigInt,"46")//parse(BigInt,"715")*6^(1//2) - c[7]=parse(BigInt,"276")//parse(BigInt,"715")+parse(BigInt,"46")//parse(BigInt,"715")*6^(1//2) + c[6]=276//715-46//715*6^(1//2) + c[7]=276//715+46//715*6^(1//2) c[8]=92//143 c[9]=69//143 c[10]=3//44 @@ -5036,123 +5036,123 @@ function constructTsitouras92(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//46 - A[3,1]=-parse(BigInt,"163287951175938724532816")//parse(BigInt,"516163208965408589753025")+parse(BigInt,"42011574289334042817176")//parse(BigInt,"516163208965408589753025")*6^(1//2) - A[3,2]=parse(BigInt,"232801278267248934720896")//parse(BigInt,"516163208965408589753025")-parse(BigInt,"50098553466700618240256")//parse(BigInt,"516163208965408589753025")*6^(1//2) - A[4,1]=parse(BigInt,"12094406618")//parse(BigInt,"239481664565")-parse(BigInt,"1407028243")//parse(BigInt,"239481664565")*6^(1//2) + A[3,1]=-163287951175938724532816//516163208965408589753025+42011574289334042817176//516163208965408589753025*6^(1//2) + A[3,2]=232801278267248934720896//516163208965408589753025-50098553466700618240256//516163208965408589753025*6^(1//2) + A[4,1]=12094406618//239481664565-1407028243//239481664565*6^(1//2) A[4,2]=0 - A[4,3]=parse(BigInt,"36283219854")//parse(BigInt,"239481664565")-parse(BigInt,"4221084729")//parse(BigInt,"239481664565")*6^(1//2) - A[5,1]=parse(BigInt,"450479172821804238979159483")//parse(BigInt,"489985471732935255816699904")+parse(BigInt,"65404175703680378526395577")//parse(BigInt,"244992735866467627908349952")*6^(1//2) + A[4,3]=36283219854//239481664565-4221084729//239481664565*6^(1//2) + A[5,1]=450479172821804238979159483//489985471732935255816699904+65404175703680378526395577//244992735866467627908349952*6^(1//2) A[5,2]=0 - A[5,3]=-parse(BigInt,"1663285823745576633021875313")//parse(BigInt,"489985471732935255816699904")-parse(BigInt,"258991054585998425691922779")//parse(BigInt,"244992735866467627908349952")*6^(1//2) - A[5,4]=parse(BigInt,"734303944921586208649981787")//parse(BigInt,"244992735866467627908349952")+parse(BigInt,"96793439441159023582763601")//parse(BigInt,"122496367933233813954174976")*6^(1//2) - A[6,1]=parse(BigInt,"188634486760257")//parse(BigInt,"2753187875656075")-parse(BigInt,"40451003556679")//parse(BigInt,"5506375751312150")*6^(1//2) + A[5,3]=-1663285823745576633021875313//489985471732935255816699904-258991054585998425691922779//244992735866467627908349952*6^(1//2) + A[5,4]=734303944921586208649981787//244992735866467627908349952+96793439441159023582763601//122496367933233813954174976*6^(1//2) + A[6,1]=188634486760257//2753187875656075-40451003556679//5506375751312150*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=parse(BigInt,"890541395040155939974909749")//parse(BigInt,"3404930508779360011084250045")-parse(BigInt,"235414842445143790083329443")//parse(BigInt,"6809861017558720022168500090")*6^(1//2) - A[6,5]=parse(BigInt,"127509164130554343284736")//parse(BigInt,"2278805333809176804299525")-parse(BigInt,"51090254569210884816896")//parse(BigInt,"2278805333809176804299525")*6^(1//2) - A[7,1]=parse(BigInt,"523150756520001")//parse(BigInt,"5294592068569375")+parse(BigInt,"372205675002861")//parse(BigInt,"137659393782803750")*6^(1//2) + A[6,4]=890541395040155939974909749//3404930508779360011084250045-235414842445143790083329443//6809861017558720022168500090*6^(1//2) + A[6,5]=127509164130554343284736//2278805333809176804299525-51090254569210884816896//2278805333809176804299525*6^(1//2) + A[7,1]=523150756520001//5294592068569375+372205675002861//137659393782803750*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=parse(BigInt,"121832502441158811994748302664452173")//parse(BigInt,"6319431229672072722127362725145820625")-parse(BigInt,"12054008141355156662680357922224203047")//parse(BigInt,"164305211971473890775311430853791336250")*6^(1//2) - A[7,5]=-parse(BigInt,"7345188891123909155979140554752")//parse(BigInt,"52428978281511938535235507146875")+parse(BigInt,"71382195182457889488943971467264")//parse(BigInt,"681576717659655200958061592909375")*6^(1//2) - A[7,6]=parse(BigInt,"84211752143498940768")//parse(BigInt,"206389046233053165625")+parse(BigInt,"567839841668979868")//parse(BigInt,"18762640566641196875")*6^(1//2) + A[7,4]=121832502441158811994748302664452173//6319431229672072722127362725145820625-12054008141355156662680357922224203047//164305211971473890775311430853791336250*6^(1//2) + A[7,5]=-7345188891123909155979140554752//52428978281511938535235507146875+71382195182457889488943971467264//681576717659655200958061592909375*6^(1//2) + A[7,6]=84211752143498940768//206389046233053165625+567839841668979868//18762640566641196875*6^(1//2) A[8,1]=92//1287 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=parse(BigInt,"368")//parse(BigInt,"1287")+parse(BigInt,"23")//parse(BigInt,"1287")*6^(1//2) - A[8,7]=parse(BigInt,"368")//parse(BigInt,"1287")-parse(BigInt,"23")//parse(BigInt,"1287")*6^(1//2) + A[8,6]=368//1287+23//1287*6^(1//2) + A[8,7]=368//1287-23//1287*6^(1//2) A[9,1]=1311//18304 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=parse(BigInt,"4071")//parse(BigInt,"18304")+parse(BigInt,"1587")//parse(BigInt,"36608")*6^(1//2) - A[9,7]=parse(BigInt,"4071")//parse(BigInt,"18304")-parse(BigInt,"1587")//parse(BigInt,"36608")*6^(1//2) + A[9,6]=4071//18304+1587//36608*6^(1//2) + A[9,7]=4071//18304-1587//36608*6^(1//2) A[9,8]=-621//18304 A[10,1]=2451872601//50434064384 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=parse(BigInt,"84329349")//parse(BigInt,"1146228736")-parse(BigInt,"1383050643")//parse(BigInt,"100868128768")*6^(1//2) - A[10,7]=parse(BigInt,"84329349")//parse(BigInt,"1146228736")+parse(BigInt,"1383050643")//parse(BigInt,"100868128768")*6^(1//2) + A[10,6]=84329349//1146228736-1383050643//100868128768*6^(1//2) + A[10,7]=84329349//1146228736+1383050643//100868128768*6^(1//2) A[10,8]=-1098320769//50434064384 A[10,9]=-333490521//3152129024 - A[11,1]=-parse(BigInt,"11290810941252792923651")//parse(BigInt,"1669469461414577748900000")-parse(BigInt,"76218489460616423924209")//parse(BigInt,"10016816768487466493400000")*6^(1//2) + A[11,1]=-11290810941252792923651//1669469461414577748900000-76218489460616423924209//10016816768487466493400000*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-parse(BigInt,"44608220078798131601386867")//parse(BigInt,"1778327431680661626219300000")-parse(BigInt,"302663621648107819403033939")//parse(BigInt,"5334982295041984878657900000")*6^(1//2) - A[11,8]=parse(BigInt,"4768550623191902657077")//parse(BigInt,"335320789258483564950000")+parse(BigInt,"76218489460616423924209")//parse(BigInt,"9388982099237539818600000")*6^(1//2) - A[11,9]=parse(BigInt,"76371166597983496297729")//parse(BigInt,"1268154687036073482337500")+parse(BigInt,"76218489460616423924209")//parse(BigInt,"1902232030554110223506250")*6^(1//2) - A[11,10]=parse(BigInt,"12837092726068800321242176")//parse(BigInt,"73489499260117750229428125")+parse(BigInt,"224387232972054752032871296")//parse(BigInt,"13889515360162254793361915625")*6^(1//2) - A[12,1]=-parse(BigInt,"355843792738780589211336013211266011894384892859307606673616682840321037292934264483298005378753134077")//parse(BigInt,"6114980501338466999761271314291724602877525435623381536957589416556451501095664913528943447961301150000")+parse(BigInt,"1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761")//parse(BigInt,"62508689569237662664226328990537629273859148897483455711122025147021504233422352449406977468048856200000")*6^(1//2) + A[11,7]=-44608220078798131601386867//1778327431680661626219300000-302663621648107819403033939//5334982295041984878657900000*6^(1//2) + A[11,8]=4768550623191902657077//335320789258483564950000+76218489460616423924209//9388982099237539818600000*6^(1//2) + A[11,9]=76371166597983496297729//1268154687036073482337500+76218489460616423924209//1902232030554110223506250*6^(1//2) + A[11,10]=12837092726068800321242176//73489499260117750229428125+224387232972054752032871296//13889515360162254793361915625*6^(1//2) + A[12,1]=-355843792738780589211336013211266011894384892859307606673616682840321037292934264483298005378753134077//6114980501338466999761271314291724602877525435623381536957589416556451501095664913528943447961301150000+1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761//62508689569237662664226328990537629273859148897483455711122025147021504233422352449406977468048856200000*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-parse(BigInt,"17594918026040863488775323023688367263938903884097169692619657825340943285779242173824532021369934883")//parse(BigInt,"34620197299885474706340736056297763905521990158606221624621429312196525421587764433517710597688597280")-parse(BigInt,"1718800244468971293911190106580576895962584281439946985382458420029691073118839588510586218092229")//parse(BigInt,"134447368154895047403264994393389374390376660810121249027656036163870001637234036635020235330829504")*6^(1//2) - A[12,7]=-parse(BigInt,"138207307502597872414466248711907117101238289950946956575872497287994333538943652935288845283125425999567221")//parse(BigInt,"449445892634106961164222874370868126852218761612180707797390011848931329871568905581758203549930436500950000")+parse(BigInt,"373422609934822782117113512174693455251869921393106586844571126171756173532479385325874622983683540733325899")//parse(BigInt,"1797783570536427844656891497483472507408875046448722831189560047395725319486275622327032814199721746003800000")*6^(1//2) - A[12,8]=parse(BigInt,"12632445836279619113294210780168171565726892406599945732333835965116776912265868042131556830549327654393")//parse(BigInt,"112996477298237313277639902405971868302745384545450862247028276227308103806571175581620305423011393900000")-parse(BigInt,"6303547312203088429495101153246145287920801370707526715790327134571780988988474483681572268319398771221")//parse(BigInt,"225992954596474626555279804811943736605490769090901724494056552454616207613142351163240610846022787800000")*6^(1//2) - A[12,9]=parse(BigInt,"1115379785277627713874987636432084522404410826010464628546537384975239192450316138834225701046102632948257")//parse(BigInt,"3347520639960280405850082108776916598468832017158981794068212683234002575269671076605501548156712544287500")-parse(BigInt,"1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761")//parse(BigInt,"11870640567235036900177596130414597866910751833897098560525576890900718352020110200728728894172739518750")*6^(1//2) - A[12,10]=parse(BigInt,"11195395793619792818419572687595618271094922253700867106612850891912759357989068567623193453186950145251776")//parse(BigInt,"37146762745465379216384266737567863919875050348378042013698628944987922182903823702648363618722076517534375")-parse(BigInt,"687320121745403419867910288709505619542179230939368838936545299414049008577113662220686991034529999350912")//parse(BigInt,"12382254248488459738794755579189287973291683449459347337899542981662640727634607900882787872907358839178125")*6^(1//2) - A[12,11]=parse(BigInt,"73825104187474768875967421005730375156586805528272061538441201406502469378399602291332635087412")//parse(BigInt,"92871272539029599143289144740668914525146202470165909630170359355065425993729905138177287271317") - A[13,1]=-parse(BigInt,"64719070744144335733962214412431202035561004419937320357188840883")//parse(BigInt,"101209800434111984325751891003355158288493635359529771992774000000")+parse(BigInt,"3559372342256314491923633965576963561357143961289")//parse(BigInt,"36357243706101884581258626118802982597639184500000")*6^(1//2) + A[12,6]=-17594918026040863488775323023688367263938903884097169692619657825340943285779242173824532021369934883//34620197299885474706340736056297763905521990158606221624621429312196525421587764433517710597688597280-1718800244468971293911190106580576895962584281439946985382458420029691073118839588510586218092229//134447368154895047403264994393389374390376660810121249027656036163870001637234036635020235330829504*6^(1//2) + A[12,7]=-138207307502597872414466248711907117101238289950946956575872497287994333538943652935288845283125425999567221//449445892634106961164222874370868126852218761612180707797390011848931329871568905581758203549930436500950000+373422609934822782117113512174693455251869921393106586844571126171756173532479385325874622983683540733325899//1797783570536427844656891497483472507408875046448722831189560047395725319486275622327032814199721746003800000*6^(1//2) + A[12,8]=12632445836279619113294210780168171565726892406599945732333835965116776912265868042131556830549327654393//112996477298237313277639902405971868302745384545450862247028276227308103806571175581620305423011393900000-6303547312203088429495101153246145287920801370707526715790327134571780988988474483681572268319398771221//225992954596474626555279804811943736605490769090901724494056552454616207613142351163240610846022787800000*6^(1//2) + A[12,9]=1115379785277627713874987636432084522404410826010464628546537384975239192450316138834225701046102632948257//3347520639960280405850082108776916598468832017158981794068212683234002575269671076605501548156712544287500-1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761//11870640567235036900177596130414597866910751833897098560525576890900718352020110200728728894172739518750*6^(1//2) + A[12,10]=11195395793619792818419572687595618271094922253700867106612850891912759357989068567623193453186950145251776//37146762745465379216384266737567863919875050348378042013698628944987922182903823702648363618722076517534375-687320121745403419867910288709505619542179230939368838936545299414049008577113662220686991034529999350912//12382254248488459738794755579189287973291683449459347337899542981662640727634607900882787872907358839178125*6^(1//2) + A[12,11]=73825104187474768875967421005730375156586805528272061538441201406502469378399602291332635087412//92871272539029599143289144740668914525146202470165909630170359355065425993729905138177287271317 + A[13,1]=-64719070744144335733962214412431202035561004419937320357188840883//101209800434111984325751891003355158288493635359529771992774000000+3559372342256314491923633965576963561357143961289//36357243706101884581258626118802982597639184500000*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-parse(BigInt,"66005588850553492194962577164587068367312330247")//parse(BigInt,"19603612723583140697294028442079849957408380800")-parse(BigInt,"13176568020345600854085799476910283462657777")//parse(BigInt,"76130534848866565814734091037203300805469440")*6^(1//2) - A[13,7]=-parse(BigInt,"9318570701703691930191534222789494006237103047579881711")//parse(BigInt,"3562968864769188061196125478115789029665196590638000000")+parse(BigInt,"6434757944786940764537553522803508307647498263055753667")//parse(BigInt,"7125937729538376122392250956231578059330393181276000000")*6^(1//2) - A[13,8]=-parse(BigInt,"3761276943318114593157887595063197569838926771255702620302334773297")//parse(BigInt,"1464216542935037622889021617525045499738187320641028236799386000000")-parse(BigInt,"3559372342256314491923633965576963561357143961289")//parse(BigInt,"34078442106289230846820763513066043517445275500000")*6^(1//2) - A[13,9]=parse(BigInt,"438696881717332693164574683605145782902979477404432064959580227217")//parse(BigInt,"190320793597985643524049406938231176153947641989529318077977593750")-parse(BigInt,"3559372342256314491923633965576963561357143961289")//parse(BigInt,"6904380415341463658460171786984220252917056671875")*6^(1//2) - A[13,10]=parse(BigInt,"39393077397330623465044422844130393549390670768068628724675776122752")//parse(BigInt,"24104666116749847055078895726017945791587677982957405550119962671875")-parse(BigInt,"911199319617616509932450295187702671707428854089984")//parse(BigInt,"4383797390367410875150919593877143523760184037765625")*6^(1//2) - A[13,11]=parse(BigInt,"1455014345065512890761705230599774567929341275785651")//parse(BigInt,"437274533681980646175086038705021590800143506216585") - A[13,12]=parse(BigInt,"43491235157516875762138510242422928845963515012067399050743561004230490804423974878600834753885909")//parse(BigInt,"15650073716933473532700213239415706508578020603344410725067680963543589421556571669667160279586515") - A[14,1]=parse(BigInt,"1113523038973067377822299106095464437335258246585030516055024186482995053")//parse(BigInt,"1172081821952666268571554825436238158838606320428900711229598548800375000")-parse(BigInt,"9656355719858106181793772673915704646989403181")//parse(BigInt,"42650123991481333817759653132492492758879187500")*6^(1//2) + A[13,6]=-66005588850553492194962577164587068367312330247//19603612723583140697294028442079849957408380800-13176568020345600854085799476910283462657777//76130534848866565814734091037203300805469440*6^(1//2) + A[13,7]=-9318570701703691930191534222789494006237103047579881711//3562968864769188061196125478115789029665196590638000000+6434757944786940764537553522803508307647498263055753667//7125937729538376122392250956231578059330393181276000000*6^(1//2) + A[13,8]=-3761276943318114593157887595063197569838926771255702620302334773297//1464216542935037622889021617525045499738187320641028236799386000000-3559372342256314491923633965576963561357143961289//34078442106289230846820763513066043517445275500000*6^(1//2) + A[13,9]=438696881717332693164574683605145782902979477404432064959580227217//190320793597985643524049406938231176153947641989529318077977593750-3559372342256314491923633965576963561357143961289//6904380415341463658460171786984220252917056671875*6^(1//2) + A[13,10]=39393077397330623465044422844130393549390670768068628724675776122752//24104666116749847055078895726017945791587677982957405550119962671875-911199319617616509932450295187702671707428854089984//4383797390367410875150919593877143523760184037765625*6^(1//2) + A[13,11]=1455014345065512890761705230599774567929341275785651//437274533681980646175086038705021590800143506216585 + A[13,12]=43491235157516875762138510242422928845963515012067399050743561004230490804423974878600834753885909//15650073716933473532700213239415706508578020603344410725067680963543589421556571669667160279586515 + A[14,1]=1113523038973067377822299106095464437335258246585030516055024186482995053//1172081821952666268571554825436238158838606320428900711229598548800375000-9656355719858106181793772673915704646989403181//42650123991481333817759653132492492758879187500*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=parse(BigInt,"65156558806314041332627176859309009839731119")//parse(BigInt,"11498348446055040912040697694327646399463400")+parse(BigInt,"2893908603034923903437694020377944093049")//parse(BigInt,"44653780373029285095303680366320956891120")*6^(1//2) - A[14,7]=parse(BigInt,"8209640140354849710164186531509948506760631106345347")//parse(BigInt,"2089832016538282470163966831380108687881472614625000")-parse(BigInt,"7326425889801057568096943993446608268878122947239059")//parse(BigInt,"4179664033076564940327933662760217375762945229250000")*6^(1//2) - A[14,8]=parse(BigInt,"358387301461393123075253933751833574944722054371964074460462507967392441417")//parse(BigInt,"600381220734980367702253537950121782364502552531871330639897526611625875000")+parse(BigInt,"9656355719858106181793772673915704646989403181")//parse(BigInt,"39976896846716122011518307352108347913593312500")*6^(1//2) - A[14,9]=-parse(BigInt,"642851404125311605101723817200220613720981758568362376903035228606467992291")//parse(BigInt,"274647144865445671171423994203344292862210985060954852952360191727428234375")+parse(BigInt,"77250845758864849454350181391325637175915225448")//parse(BigInt,"64795380679365872530827165335902056306758765625")*6^(1//2) - A[14,10]=-parse(BigInt,"369969589301763518639761285997824520507173970793320519753635225871563412913152")//parse(BigInt,"180850870268987312974476662632186804296491491034759756207691410652763681078125")+parse(BigInt,"454852979828196233587213868032125351691788847437824")//parse(BigInt,"946232027174365750372191179393662736769436409578125")*6^(1//2) - A[14,11]=-parse(BigInt,"7715303458281199041757411869319392732268755939408305903151657039")//parse(BigInt,"1483062857858019956599354292891821472831958379628421680653323310") - A[14,12]=-parse(BigInt,"945432908618140420875128019003679821034774098061354410087876969999388668430388640158852256997513450369741874915618358283")//parse(BigInt,"1183336256073681379271114843949311985569932050547818490887959987766109714104308279282406274069868573023638087923030436570") - A[14,13]=parse(BigInt,"1056911827593717127690972016166243945915857152155")//parse(BigInt,"7359790814129537930306952068888958882079118176267") - A[15,1]=parse(BigInt,"71647807109611556622880429107737597894249449144677487291739567")//parse(BigInt,"4608441750702552040544087416037317498817362012884252849000000")-751354288295256883750046307992744439//260856700304180835921321781903000000*6^(1//2) + A[14,6]=65156558806314041332627176859309009839731119//11498348446055040912040697694327646399463400+2893908603034923903437694020377944093049//44653780373029285095303680366320956891120*6^(1//2) + A[14,7]=8209640140354849710164186531509948506760631106345347//2089832016538282470163966831380108687881472614625000-7326425889801057568096943993446608268878122947239059//4179664033076564940327933662760217375762945229250000*6^(1//2) + A[14,8]=358387301461393123075253933751833574944722054371964074460462507967392441417//600381220734980367702253537950121782364502552531871330639897526611625875000+9656355719858106181793772673915704646989403181//39976896846716122011518307352108347913593312500*6^(1//2) + A[14,9]=-642851404125311605101723817200220613720981758568362376903035228606467992291//274647144865445671171423994203344292862210985060954852952360191727428234375+77250845758864849454350181391325637175915225448//64795380679365872530827165335902056306758765625*6^(1//2) + A[14,10]=-369969589301763518639761285997824520507173970793320519753635225871563412913152//180850870268987312974476662632186804296491491034759756207691410652763681078125+454852979828196233587213868032125351691788847437824//946232027174365750372191179393662736769436409578125*6^(1//2) + A[14,11]=-7715303458281199041757411869319392732268755939408305903151657039//1483062857858019956599354292891821472831958379628421680653323310 + A[14,12]=-945432908618140420875128019003679821034774098061354410087876969999388668430388640158852256997513450369741874915618358283//1183336256073681379271114843949311985569932050547818490887959987766109714104308279282406274069868573023638087923030436570 + A[14,13]=1056911827593717127690972016166243945915857152155//7359790814129537930306952068888958882079118176267 + A[15,1]=71647807109611556622880429107737597894249449144677487291739567//4608441750702552040544087416037317498817362012884252849000000-751354288295256883750046307992744439//260856700304180835921321781903000000*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=parse(BigInt,"538527061627015039205734500467757677")//parse(BigInt,"6645826087749591758241674935867200")+parse(BigInt,"55735563892040165710948254310427")//parse(BigInt,"25809033350483851488317184216960")*6^(1//2) - A[15,7]=parse(BigInt,"10166737271161511304691200043681679377006693")//parse(BigInt,"172554720727113306507896188662956931000000")-parse(BigInt,"8156608278080671316516960851836659322130571")//parse(BigInt,"345109441454226613015792377325913862000000")*6^(1//2) - A[15,8]=parse(BigInt,"13730153329629135442521913725273883916343982389395960187482153016633")//parse(BigInt,"175471617700441378138284361033681728617635976027122756488121000000")+parse(BigInt,"20286565783971935861251250315804099853")//parse(BigInt,"6601681107698115001393451249699000000")*6^(1//2) - A[15,9]=-parse(BigInt,"653480004921889631988496090206918830045333930618354572374567471359")//parse(BigInt,"12778455326756234342932466086484629156552273764794479235501062500")+751354288295256883750046307992744439//49537690682765110667751011467156250*6^(1//2) - A[15,10]=-parse(BigInt,"1892005381291509192972446465852606492709607810610330309174017655027008")//parse(BigInt,"53004882228844808583820366645125601151772763811007845509116404390625")+parse(BigInt,"2211987024741236265760136330730639628416")//parse(BigInt,"361709036854355745656111465938134640625")*6^(1//2) - A[15,11]=-parse(BigInt,"754694656733111129471952033526995126769302954114714957")//parse(BigInt,"10457763407796883263416278675753537185966936455426905") - A[15,12]=-parse(BigInt,"3809310391558597134511116925648017476134448177941143033030907811018093065572169647629059619278510306257177668207871699977487")//parse(BigInt,"49657222601249321414413002320858790760827862034335478005117886015451993139010886447467038877038198587307390592603767686355") - A[15,13]=parse(BigInt,"1329021384022690762809893094055902242790")//parse(BigInt,"314695772164147033634887576401647768207") + A[15,6]=538527061627015039205734500467757677//6645826087749591758241674935867200+55735563892040165710948254310427//25809033350483851488317184216960*6^(1//2) + A[15,7]=10166737271161511304691200043681679377006693//172554720727113306507896188662956931000000-8156608278080671316516960851836659322130571//345109441454226613015792377325913862000000*6^(1//2) + A[15,8]=13730153329629135442521913725273883916343982389395960187482153016633//175471617700441378138284361033681728617635976027122756488121000000+20286565783971935861251250315804099853//6601681107698115001393451249699000000*6^(1//2) + A[15,9]=-653480004921889631988496090206918830045333930618354572374567471359//12778455326756234342932466086484629156552273764794479235501062500+751354288295256883750046307992744439//49537690682765110667751011467156250*6^(1//2) + A[15,10]=-1892005381291509192972446465852606492709607810610330309174017655027008//53004882228844808583820366645125601151772763811007845509116404390625+2211987024741236265760136330730639628416//361709036854355745656111465938134640625*6^(1//2) + A[15,11]=-754694656733111129471952033526995126769302954114714957//10457763407796883263416278675753537185966936455426905 + A[15,12]=-3809310391558597134511116925648017476134448177941143033030907811018093065572169647629059619278510306257177668207871699977487//49657222601249321414413002320858790760827862034335478005117886015451993139010886447467038877038198587307390592603767686355 + A[15,13]=1329021384022690762809893094055902242790//314695772164147033634887576401647768207 A[15,14]=-6893352883273198849981789770//5486160832491820655265629723 - A[16,1]=-parse(BigInt,"2570623236993305537882133348905686861198442251997239696046711165213")//parse(BigInt,"1788444074612646395894349444415762174941041849960120845639920000000")+parse(BigInt,"17049571162138593122630888759407239103637")//parse(BigInt,"41413609740291749510869046094920280000000")*6^(1//2) + A[16,1]=-2570623236993305537882133348905686861198442251997239696046711165213//1788444074612646395894349444415762174941041849960120845639920000000+17049571162138593122630888759407239103637//41413609740291749510869046094920280000000*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-parse(BigInt,"104754859887173191244557803812288138363")//parse(BigInt,"11164987827419314153846013892256896000")+3784288812661530935801759817347107//43359176028812870500372869484492800*6^(1//2) - A[16,7]=-parse(BigInt,"12625417179938563922326639910886861363642731119")//parse(BigInt,"2029243515750852484532859178676373508560000000")+parse(BigInt,"4034430827439578769139663757402876281578669781")//parse(BigInt,"1352829010500568323021906119117582339040000000")*6^(1//2) - A[16,8]=-parse(BigInt,"121185791557797038984865049921261438811435078875133421073861312913308541")//parse(BigInt,"761448556714003333948396687643999840432514259811137574414811792240000000")-parse(BigInt,"17049571162138593122630888759407239103637")//parse(BigInt,"38817884913264916208193493348230120000000")*6^(1//2) - A[16,9]=parse(BigInt,"7831706161943944732903576802308126564075661689777008313099672046941217")//parse(BigInt,"1912115178728933570934305539114995143003765478134474309438025195000000")-parse(BigInt,"17049571162138593122630888759407239103637")//parse(BigInt,"7864603772795788969612150580525726250000")*6^(1//2) - A[16,10]=parse(BigInt,"1231862339518930958878836935481237970791679023430521469669885456183927336")//parse(BigInt,"350627295943808408781971725357505851618976832609816898042805015043984375")-parse(BigInt,"6274242187667002269128167063461863990138416")//parse(BigInt,"7178115836374689772545532041542281943203125")*6^(1//2) - A[16,11]=parse(BigInt,"23975119191644794266115435124846718653445865470965352804548709")//parse(BigInt,"2618162142480251258794523717542364435163988588525025359875200") - A[16,12]=parse(BigInt,"54918621392363748304153623111076473105288800876284517914641326502791860135537567319289496873218100975783896487633335215553248687")//parse(BigInt,"42045763520929825428011777325117555313008167341712535936493416447003511630663297772799291157965783507844913762569462175390505600") - A[16,13]=-parse(BigInt,"35648602464057004250287591332213307928385")//parse(BigInt,"140983705929537871068429634227938200156736") + A[16,6]=-104754859887173191244557803812288138363//11164987827419314153846013892256896000+3784288812661530935801759817347107//43359176028812870500372869484492800*6^(1//2) + A[16,7]=-12625417179938563922326639910886861363642731119//2029243515750852484532859178676373508560000000+4034430827439578769139663757402876281578669781//1352829010500568323021906119117582339040000000*6^(1//2) + A[16,8]=-121185791557797038984865049921261438811435078875133421073861312913308541//761448556714003333948396687643999840432514259811137574414811792240000000-17049571162138593122630888759407239103637//38817884913264916208193493348230120000000*6^(1//2) + A[16,9]=7831706161943944732903576802308126564075661689777008313099672046941217//1912115178728933570934305539114995143003765478134474309438025195000000-17049571162138593122630888759407239103637//7864603772795788969612150580525726250000*6^(1//2) + A[16,10]=1231862339518930958878836935481237970791679023430521469669885456183927336//350627295943808408781971725357505851618976832609816898042805015043984375-6274242187667002269128167063461863990138416//7178115836374689772545532041542281943203125*6^(1//2) + A[16,11]=23975119191644794266115435124846718653445865470965352804548709//2618162142480251258794523717542364435163988588525025359875200 + A[16,12]=54918621392363748304153623111076473105288800876284517914641326502791860135537567319289496873218100975783896487633335215553248687//42045763520929825428011777325117555313008167341712535936493416447003511630663297772799291157965783507844913762569462175390505600 + A[16,13]=-35648602464057004250287591332213307928385//140983705929537871068429634227938200156736 A[16,14]=180996536632507119654644161465573//475057638807131734180761408974016 A[16,15]=0 α[1]=385924436255198461459913//25885297292164750617319296 @@ -5163,10 +5163,10 @@ function constructTsitouras92(T::Type = Float64) α[6]=0 α[7]=0 α[8]=-81508791888782942071778080019859673//399395400777999552787672219983509760 - α[9]=parse(BigInt,"935936315524449978576662571821361001")//parse(BigInt,"4086801409502444670525951816974611200") + α[9]=935936315524449978576662571821361001//4086801409502444670525951816974611200 α[10]=2172547024243858864854526674870272//16972283408414027681310867548214525 - α[11]=parse(BigInt,"1193746724713997342094811077921918673563219")//parse(BigInt,"5333839543124606397779553737025343484595200") - α[12]=parse(BigInt,"78998885900843720607956191287550920802893766832745691186069543513026890766039702331356142187984337094261434894685526783")//parse(BigInt,"199728353759405693383344357357050366806065734043901244628659238274456345277244226082448918708806038102409307770530790400") + α[11]=1193746724713997342094811077921918673563219//5333839543124606397779553737025343484595200 + α[12]=78998885900843720607956191287550920802893766832745691186069543513026890766039702331356142187984337094261434894685526783//199728353759405693383344357357050366806065734043901244628659238274456345277244226082448918708806038102409307770530790400 α[13]=11409994679937666036993318622713183//210646829819316523523317257829664000 α[14]=10048608923923592706010638721995991//79176273134521955696793568162336000 α[15]=-491671864801784912209409//935818304406566046193728000 @@ -5178,11 +5178,11 @@ function constructTsitouras92(T::Type = Float64) αEEst[5]=0 αEEst[6]=0 αEEst[7]=0 - αEEst[8]=parse(BigInt,"29177952541973984236460298638317525091")//parse(BigInt,"1395926082130949417341226925726678720") + αEEst[8]=29177952541973984236460298638317525091//1395926082130949417341226925726678720 αEEst[9]=-481359954433374971820713358519126547//262512559006778653160811139234495296 αEEst[10]=-325585565780649471399541319800832//3935361974048520890008015792480311 - αEEst[11]=parse(BigInt,"828906176711503347732519444777342468824091")//parse(BigInt,"1234749218911637779745721368343853865102720") - αEEst[12]=-parse(BigInt,"19819005742497004038604841557068415948625832456498098356731269808855703554130425034149167680385863035602494067")//parse(BigInt,"944246035063763492934067294951661726695697507391691339725080641234241699449384342323015093676255343392536960") + αEEst[11]=828906176711503347732519444777342468824091//1234749218911637779745721368343853865102720 + αEEst[12]=-19819005742497004038604841557068415948625832456498098356731269808855703554130425034149167680385863035602494067//944246035063763492934067294951661726695697507391691339725080641234241699449384342323015093676255343392536960 αEEst[13]=96762135771288342741313072067956263//15762193817514374346399946534150720 αEEst[14]=-250908066606160220133619476267717281//58399326977497401115669462861805760 αEEst[15]=33//92 @@ -7852,13 +7852,13 @@ function constructDormandPrince8(T::Type = Float64) 3//80 0 0 3//16 3//20 0 0 0 0 0 0 0 0 215595617//4500000000 0 0 202047683//1800000000 -28693883//1125000000 23124283//1800000000 0 0 0 0 0 0 0 14873762658037143//879168438156250000 0 0 3467633544794897//8940695981250000 1474287494383247//40978189914062500 26709270507070017//135600555715625000 -14591655588284//84484570233063 0 0 0 0 0 0 - parse(BigInt,"7586331039021946882049083502441337664277676907617750536566352")//parse(BigInt,"109794461601491217860220353338581031394059220336451160078730445") 0 0 -parse(BigInt,"236057339412812449835946465344221735535939129430991059693568")//parse(BigInt,"372184615598275314780407977418918750488336340123563254504171") -parse(BigInt,"3299739166368883603096250588167927276977533790499480498577408")//parse(BigInt,"20470153857905142312922438758040531276858498706795978997729405") parse(BigInt,"4695919603694846215470554638065271273971468502369170235542016")//parse(BigInt,"33868800019443053645017125945121606294438606951244256159879561") parse(BigInt,"291851811898394201384602939640627532330843113837053004434432000000")//parse(BigInt,"310174233778061645620360730197195350622945922304711702829528117367") parse(BigInt,"6992959981041103840944260661352231159203510904000000")//parse(BigInt,"33042342481018810238716485165383193327572243242031481") 0 0 0 0 0 - 99299034813490800741867453179778547//540971123539151162906952826011200000 0 0 -2493835259080554724582//1010153717930905426875 -48550347897506146536052//166675363458599395434375 -24871192635697392099560348960246//939492072180864357472739828818125 478776089216929482237673925052922000//168119099731629344552415590032785027 6560308981643238155096750//23314158982833116227901307 parse(BigInt,"1586281686644478270321241459439899956623408540189275177")//parse(BigInt,"12818966182821619734532382093543907143647820508227904000") 0 0 0 0 - -parse(BigInt,"102116003386322998978127600084904875522141269364791505043913504184525097818434721165778087547359160299919872547571820573487921693")//parse(BigInt,"84016717385376362440519288454722754561118206109968455863629915569413007015484884082989277327146750610032897620427741658059440288") 0 0 parse(BigInt,"338590872606752219742507143357021902717271169524361004010718467428498066558752974165816979255870352236800")//parse(BigInt,"20308212073515087965058545521329962060416948491603802421256875704911573108931922671691153944392874968051") parse(BigInt,"68189290605616416787948548385820859588684790288743680764422049661712817412461535969920258787664375619072")//parse(BigInt,"74463444269555322538548000244876527554862144469213942211275210918009101399417049796200897796107208216187") -parse(BigInt,"1734282043732424474072631498514610096486835338935534079058145376760622893524503274680375038942168945756187943481380463560951840")//parse(BigInt,"286345537377499805912462279621622489249909215975695809863482134802066603511244489020404711919081949534640172065152437496912477") -parse(BigInt,"3399549280223124443696423490103003766707892326374755946138975000967466690241111348721006509128775254952212682658842765965521154240000000")//parse(BigInt,"212424385105117691648087703103838079790425456287912424851546922389328485500145214289225448961304538830766072442444722564103495915888123") parse(BigInt,"14452808190943733856347403293564049428070036006455540637351575894308889412108389906599600485253194980566957563315340127500000")//parse(BigInt,"973298753951638431793701721528200883789914680313298926814615071301495341142665245758696799918623095581715765886887649741383") -parse(BigInt,"847205714160239289113307424793539077951658318917591980262304042838612275700008766016957700930195545053374220841398660187944621107065829310608865394026418258355")//parse(BigInt,"63358704383980726998416112830322706485300332630289060627019459285960825979588560697460438306253611095891491565590971432387489415884103732012574255897878321824") parse(BigInt,"115188988949323598098458035263894669359112068207548636038131244599058496172710646622536373145562218909633738697549245770000")//parse(BigInt,"22435701423704647109276644681016984863989966659062291511947760084943925084166270812354794844590216383205333034660617626349") 0 0 0 - parse(BigInt,"21969012306961489525323859125985377266525845354279828748")//parse(BigInt,"84868015648089839210997460517819380601933600521692915045") 0 0 -2291872762438069505504//480025046760766258851 -3829018311866050387904//8800459190614048078935 -parse(BigInt,"607977714773374460437401016185253441418120832060126402968")//parse(BigInt,"199370728929424959394190105343852509479613745231838418799") parse(BigInt,"5302029233035772894614097632213626682295966947853615180783170000000")//parse(BigInt,"950538766256052885387161080614691196420735587733978871061913292363") parse(BigInt,"102968047255116137164987219663037502898143843145000000")//parse(BigInt,"16726911019578511096352500731821705820659977305290973") -parse(BigInt,"111383789341965407321602142444917514115800834690201329379027449761759895100011973929185171163615")//parse(BigInt,"22003454775272439861723739055800175619777853128055268766511800511549546753240522083740083243539") parse(BigInt,"44737471541467333111555512048686345065750")//parse(BigInt,"20391511842264262870398286145868618178341") parse(BigInt,"596546910748352988538198147432444829112451075399436970876618894337461087953328002664759407401623072330633057948252")//parse(BigInt,"4431076125983762085449284205348478790535717302043416234911901479328512794465980800998816354448181196721636373483787") 0 0 - parse(BigInt,"1066221205855832326088695778460159015192405644968016897066521076847764032613686056268693633")//parse(BigInt,"1296431693610525557488309197474904206216262654240544950471874305723890174339356551609704000") 0 0 -parse(BigInt,"1335791413506612664643690684478806471077526746614666064")//parse(BigInt,"114574907798601779179110271814903983120429559544320175") -parse(BigInt,"1591415543044168099882026495959288688569084060473110176")//parse(BigInt,"2100539976307699284950354983273239690541208591645869875") parse(BigInt,"33975758488532631832742416857645572913178866704247539610423012370193845167470455176890924")//parse(BigInt,"47586856225469573819304596274208152402640120925455970356063642741972959597009066064956075") parse(BigInt,"12176653428667113090492984656207574633063967759246601254930448409444470870786024235115138527800000")//parse(BigInt,"1008353786145118968620988891518234034224047994442049071310258686840184337101721351612973016221399") -parse(BigInt,"339784374935367314296824613776444883113869450234942131172912300100535979345925250000")//parse(BigInt,"159698690787587746004588725210359673189662237866695585709500421500486548151424426361") parse(BigInt,"4955095692700499418628052380948016677978733013841365878109775677669056866398110949788869771135857671298802131693154421086808143")//parse(BigInt,"2489789885462873158531234022579722982784822257458164105126884288597324542930882581099522281388970940826324647386340365850671680") -parse(BigInt,"563115171027780776675066866318087406247194110301648522108648094708415")//parse(BigInt,"2403532595444498372383116767918060257292523183751650851596520916634577") parse(BigInt,"147332487580158450887955957061658718012538967463083369806963200702426559434915876714751833908862217396388157664714990174448521780809")//parse(BigInt,"837599084085749358149340415048050308970085851893614803629073546048735327947816070400330404870816820234727495143522673498826476267825") 0 0] - α = [ 212810988215683677989664967567559//5097575504458999984164528930580800;0;0;0;0;-570667999368605802515460802224128//10291145812277763122885317774476825;parse(BigInt,"3970894643399159150754126826496000000000000")//parse(BigInt,"16592904867230933191457493387696939021741363");parse(BigInt,"177094288219480472437690862000000000000")//parse(BigInt,"251729356670100506734814442705774463449");-parse(BigInt,"66822609448295850920212176513645119787713273203022994500406050793972052314809461629969645683")//parse(BigInt,"87952305220338336969447643899150816363456821562985998778022435070001091778042097545895594560");314652731163869955629145958568800000//476340207420551356675670184044905167;parse(BigInt,"177014954088789647707522848990757432519504314686067075784476503038212450536095365316360385634933688213244039743969578872631174179769")//parse(BigInt,"1119019983628991838522384101261104859676427163726922121733732080377576616485631933067985100908132443862205090961383250990215178108200");-454665916000392064556420344242099//1909482158429176288068071462671400;1//4] - αEEst = [7136040226482108704342809557217//241464102842794736092004001974880;0;0;0;0;-15349154422148033115423212285265536//18524062462099973621193571994058285;parse(BigInt,"45434521806506196832804182374790400000000")//parse(BigInt,"145978635195580057402851847985603569106229");parse(BigInt,"365696286946774693155766999232150000000")//parse(BigInt,"148214481030059176862554298041717674741");-parse(BigInt,"836336669851503831866889530158468123932231502753408325817124013619515886965077571")//parse(BigInt,"328368994730082689886153304749497093954319862912916225944630536728837081959128864");294694385044387823293019951454286000//204145803180236295718144364590673643;parse(BigInt,"1759482754698187564675489259591170188433054767657805212470918093603353527288272972728828708146708084742711724049636")//parse(BigInt,"22155380629918810427246421026742393952678586510217081174559507396642563972329904004994081772240905983608181867418935");2//45;0] + 7586331039021946882049083502441337664277676907617750536566352//109794461601491217860220353338581031394059220336451160078730445 0 0 -236057339412812449835946465344221735535939129430991059693568//372184615598275314780407977418918750488336340123563254504171 -3299739166368883603096250588167927276977533790499480498577408//20470153857905142312922438758040531276858498706795978997729405 4695919603694846215470554638065271273971468502369170235542016//33868800019443053645017125945121606294438606951244256159879561 291851811898394201384602939640627532330843113837053004434432000000//310174233778061645620360730197195350622945922304711702829528117367 6992959981041103840944260661352231159203510904000000//33042342481018810238716485165383193327572243242031481 0 0 0 0 0 + 99299034813490800741867453179778547//540971123539151162906952826011200000 0 0 -2493835259080554724582//1010153717930905426875 -48550347897506146536052//166675363458599395434375 -24871192635697392099560348960246//939492072180864357472739828818125 478776089216929482237673925052922000//168119099731629344552415590032785027 6560308981643238155096750//23314158982833116227901307 1586281686644478270321241459439899956623408540189275177//12818966182821619734532382093543907143647820508227904000 0 0 0 0 + -102116003386322998978127600084904875522141269364791505043913504184525097818434721165778087547359160299919872547571820573487921693//84016717385376362440519288454722754561118206109968455863629915569413007015484884082989277327146750610032897620427741658059440288 0 0 338590872606752219742507143357021902717271169524361004010718467428498066558752974165816979255870352236800//20308212073515087965058545521329962060416948491603802421256875704911573108931922671691153944392874968051 68189290605616416787948548385820859588684790288743680764422049661712817412461535969920258787664375619072//74463444269555322538548000244876527554862144469213942211275210918009101399417049796200897796107208216187 -1734282043732424474072631498514610096486835338935534079058145376760622893524503274680375038942168945756187943481380463560951840//286345537377499805912462279621622489249909215975695809863482134802066603511244489020404711919081949534640172065152437496912477 -3399549280223124443696423490103003766707892326374755946138975000967466690241111348721006509128775254952212682658842765965521154240000000//212424385105117691648087703103838079790425456287912424851546922389328485500145214289225448961304538830766072442444722564103495915888123 14452808190943733856347403293564049428070036006455540637351575894308889412108389906599600485253194980566957563315340127500000//973298753951638431793701721528200883789914680313298926814615071301495341142665245758696799918623095581715765886887649741383 -847205714160239289113307424793539077951658318917591980262304042838612275700008766016957700930195545053374220841398660187944621107065829310608865394026418258355//63358704383980726998416112830322706485300332630289060627019459285960825979588560697460438306253611095891491565590971432387489415884103732012574255897878321824 115188988949323598098458035263894669359112068207548636038131244599058496172710646622536373145562218909633738697549245770000//22435701423704647109276644681016984863989966659062291511947760084943925084166270812354794844590216383205333034660617626349 0 0 0 + 21969012306961489525323859125985377266525845354279828748//84868015648089839210997460517819380601933600521692915045 0 0 -2291872762438069505504//480025046760766258851 -3829018311866050387904//8800459190614048078935 -607977714773374460437401016185253441418120832060126402968//199370728929424959394190105343852509479613745231838418799 5302029233035772894614097632213626682295966947853615180783170000000//950538766256052885387161080614691196420735587733978871061913292363 102968047255116137164987219663037502898143843145000000//16726911019578511096352500731821705820659977305290973 -111383789341965407321602142444917514115800834690201329379027449761759895100011973929185171163615//22003454775272439861723739055800175619777853128055268766511800511549546753240522083740083243539 44737471541467333111555512048686345065750//20391511842264262870398286145868618178341 596546910748352988538198147432444829112451075399436970876618894337461087953328002664759407401623072330633057948252//4431076125983762085449284205348478790535717302043416234911901479328512794465980800998816354448181196721636373483787 0 0 + 1066221205855832326088695778460159015192405644968016897066521076847764032613686056268693633//1296431693610525557488309197474904206216262654240544950471874305723890174339356551609704000 0 0 -1335791413506612664643690684478806471077526746614666064//114574907798601779179110271814903983120429559544320175 -1591415543044168099882026495959288688569084060473110176//2100539976307699284950354983273239690541208591645869875 33975758488532631832742416857645572913178866704247539610423012370193845167470455176890924//47586856225469573819304596274208152402640120925455970356063642741972959597009066064956075 12176653428667113090492984656207574633063967759246601254930448409444470870786024235115138527800000//1008353786145118968620988891518234034224047994442049071310258686840184337101721351612973016221399 -339784374935367314296824613776444883113869450234942131172912300100535979345925250000//159698690787587746004588725210359673189662237866695585709500421500486548151424426361 4955095692700499418628052380948016677978733013841365878109775677669056866398110949788869771135857671298802131693154421086808143//2489789885462873158531234022579722982784822257458164105126884288597324542930882581099522281388970940826324647386340365850671680 -563115171027780776675066866318087406247194110301648522108648094708415//2403532595444498372383116767918060257292523183751650851596520916634577 147332487580158450887955957061658718012538967463083369806963200702426559434915876714751833908862217396388157664714990174448521780809//837599084085749358149340415048050308970085851893614803629073546048735327947816070400330404870816820234727495143522673498826476267825 0 0] + α = [ 212810988215683677989664967567559//5097575504458999984164528930580800;0;0;0;0;-570667999368605802515460802224128//10291145812277763122885317774476825;3970894643399159150754126826496000000000000//16592904867230933191457493387696939021741363;177094288219480472437690862000000000000//251729356670100506734814442705774463449;-66822609448295850920212176513645119787713273203022994500406050793972052314809461629969645683//87952305220338336969447643899150816363456821562985998778022435070001091778042097545895594560;314652731163869955629145958568800000//476340207420551356675670184044905167;177014954088789647707522848990757432519504314686067075784476503038212450536095365316360385634933688213244039743969578872631174179769//1119019983628991838522384101261104859676427163726922121733732080377576616485631933067985100908132443862205090961383250990215178108200;-454665916000392064556420344242099//1909482158429176288068071462671400;1//4] + αEEst = [7136040226482108704342809557217//241464102842794736092004001974880;0;0;0;0;-15349154422148033115423212285265536//18524062462099973621193571994058285;45434521806506196832804182374790400000000//145978635195580057402851847985603569106229;365696286946774693155766999232150000000//148214481030059176862554298041717674741;-836336669851503831866889530158468123932231502753408325817124013619515886965077571//328368994730082689886153304749497093954319862912916225944630536728837081959128864;294694385044387823293019951454286000//204145803180236295718144364590673643;1759482754698187564675489259591170188433054767657805212470918093603353527288272972728828708146708084742711724049636//22155380629918810427246421026742393952678586510217081174559507396642563972329904004994081772240905983608181867418935;2//45;0] c = [0;1//18;1//12;1//8;5//16;3//8;59//400;93//200;5490023248//9719169821;13//20;30992876149296355//33518267164510641;1;1] A = map(T,A) α = map(T,α) From 295cfdfec2b6fa09f0faee928f38ed2fc51753dd Mon Sep 17 00:00:00 2001 From: Christopher Rackauckas Date: Sat, 28 Jul 2018 07:15:01 -0700 Subject: [PATCH 2/2] Fix possible rational overflow behavior --- src/ode_tableaus.jl | 1408 +++++++++++++++++++++---------------------- 1 file changed, 704 insertions(+), 704 deletions(-) diff --git a/src/ode_tableaus.jl b/src/ode_tableaus.jl index 29539ac..69f5bee 100644 --- a/src/ode_tableaus.jl +++ b/src/ode_tableaus.jl @@ -1749,17 +1749,17 @@ function constructVernerEfficient6(T::Type = Float64) A[6,3]=246134619571490020064824665//1543816496655405117602368 A[6,4]=-13880495956885686234074067279//113663489566254201783474344 A[6,5]=755005057777788994734129//136485922925633667082436 - A[7,1]=-1663299841566102097180506666498880934230261//30558424506156170307020957791311384232000 + A[7,1]=-BigInt(1663299841566102097180506666498880934230261)//BigInt(30558424506156170307020957791311384232000) A[7,2]=0 A[7,3]=130838124195285491799043628811093033//631862949514135618861563657970240 - A[7,4]=-3287100453856023634160618787153901962873//20724314915376755629135711026851409200 + A[7,4]=-BigInt(3287100453856023634160618787153901962873)//BigInt(20724314915376755629135711026851409200) A[7,5]=2771826790140332140865242520369241//396438716042723436917079980147600 A[7,6]=-1799166916139193//96743806114007800 - A[8,1]=-832144750039369683895428386437986853923637763//15222974550069600748763651844667619945204887 + A[8,1]=-BigInt(832144750039369683895428386437986853923637763)//BigInt(15222974550069600748763651844667619945204887) A[8,2]=0 A[8,3]=818622075710363565982285196611368750//3936576237903728151856072395343129 - A[8,4]=-9818985165491658464841194581385463434793741875//61642597962658994069869370923196463581866011 - A[8,5]=31796692141848558720425711042548134769375//4530254033500045975557858016006308628092 + A[8,4]=-BigInt(9818985165491658464841194581385463434793741875)//BigInt(61642597962658994069869370923196463581866011) + A[8,5]=BigInt(31796692141848558720425711042548134769375)//BigInt(4530254033500045975557858016006308628092) A[8,6]=-14064542118843830075//766928748264306853644 A[8,7]=-1424670304836288125//2782839104764768088217 A[9,1]=382735282417//11129397249634 @@ -1818,45 +1818,45 @@ function constructVerner7(T::Type = Float64) A[5,1] = 2454451729//3841600000 A[5,3] = -9433712007//3841600000 A[5,4] = 4364554539//1920800000 - A[6,1] = -6187101755456742839167388910402379177523537620//2324599620333464857202963610201679332423082271 - A[6,3] = 27569888999279458303270493567994248533230000//2551701010245296220859455115479340650299761 - A[6,4] = -37368161901278864592027018689858091583238040000//4473131870960004275166624817435284159975481033 - A[6,5] = 1392547243220807196190880383038194667840000000//1697219131380493083996999253929006193143549863 + A[6,1] = -BigInt(6187101755456742839167388910402379177523537620)//BigInt(2324599620333464857202963610201679332423082271) + A[6,3] = BigInt(27569888999279458303270493567994248533230000)//BigInt(2551701010245296220859455115479340650299761) + A[6,4] = -BigInt(37368161901278864592027018689858091583238040000)//BigInt(4473131870960004275166624817435284159975481033) + A[6,5] = BigInt(1392547243220807196190880383038194667840000000)//BigInt(1697219131380493083996999253929006193143549863) A[7,1] = 11272026205260557297236918526339//1857697188743815510261537500000 A[7,3] = -48265918242888069//1953194276993750 A[7,4] = 26726983360888651136155661781228//1308381343805114800955157615625 A[7,5] = -2090453318815827627666994432//1096684189897834170412307919 - A[7,6] = 1148577938985388929671582486744843844943428041509//1141532118233823914568777901158338927629837500000 - A[8,1] = 1304457204588839386329181466225966641//108211771565488329642169667802016000 + A[7,6] = BigInt(1148577938985388929671582486744843844943428041509)//BigInt(1141532118233823914568777901158338927629837500000) + A[8,1] = BigInt(1304457204588839386329181466225966641)//BigInt(108211771565488329642169667802016000) A[8,3] = -1990261989751005//40001418792832 - A[8,4] = 2392691599894847687194643439066780106875//58155654089143548047476915856270826016 - A[8,5] = -1870932273351008733802814881998561250//419326053051486744762255151208232123 - A[8,6] = 1043329047173803328972823866240311074041739158858792987034783181//510851127745017966999893975119259285040213723744255237522144000 + A[8,4] = BigInt(2392691599894847687194643439066780106875)//BigInt(58155654089143548047476915856270826016) + A[8,5] = -BigInt(1870932273351008733802814881998561250)//BigInt(419326053051486744762255151208232123) + A[8,6] = BigInt(1043329047173803328972823866240311074041739158858792987034783181)//BigInt(510851127745017966999893975119259285040213723744255237522144000) A[8,7] = -311918858557595100410788125//3171569057622789618800376448 - A[9,1] = 17579784273699839132265404100877911157//1734023495717116205617154737841023480 + A[9,1] = BigInt(17579784273699839132265404100877911157)//BigInt(1734023495717116205617154737841023480) A[9,3] = -18539365951217471064750//434776548575709731377 - A[9,4] = 447448655912568142291911830292656995992000//12511202807447096607487664209063950964109 - A[9,5] = -65907597316483030274308429593905808000000//15158061430635748897861852383197382130691 - A[9,6] = 273847823027445129865693702689010278588244606493753883568739168819449761//136252034448398939768371761610231099586032870552034688235302796640584360 - A[9,7] = 694664732797172504668206847646718750//1991875650119463976442052358853258111 + A[9,4] = BigInt(447448655912568142291911830292656995992000)//BigInt(12511202807447096607487664209063950964109) + A[9,5] = -BigInt(65907597316483030274308429593905808000000)//BigInt(15158061430635748897861852383197382130691) + A[9,6] = BigInt(273847823027445129865693702689010278588244606493753883568739168819449761)//BigInt(136252034448398939768371761610231099586032870552034688235302796640584360) + A[9,7] = BigInt(694664732797172504668206847646718750)//BigInt(1991875650119463976442052358853258111) A[9,8] = -19705319055289176355560129234220800//72595753317320295604316217197876507 A[10,1] = -511858190895337044664743508805671//11367030248263048398341724647960 A[10,3] = 2822037469238841750//15064746656776439 - A[10,4] = -23523744880286194122061074624512868000//152723005449262599342117017051789699 - A[10,5] = 10685036369693854448650967542704000000//575558095977344459903303055137999707 - A[10,6] = -6259648732772142303029374363607629515525848829303541906422993//876479353814142962817551241844706205620792843316435566420120 + A[10,4] = -BigInt(23523744880286194122061074624512868000)//BigInt(152723005449262599342117017051789699) + A[10,5] = BigInt(10685036369693854448650967542704000000)//BigInt(575558095977344459903303055137999707) + A[10,6] = -BigInt(6259648732772142303029374363607629515525848829303541906422993)//BigInt(876479353814142962817551241844706205620792843316435566420120) A[10,7] = 17380896627486168667542032602031250//13279937889697320236613879977356033 α[1] = 96762636172307789//2051985304794103980 α[4] = 312188947591288252500000//1212357694274963646019729 α[5] = 13550580884964304000000000000//51686919683339547115937980629 - α[6] = 72367769693133178898676076432831566019684378142853445230956642801//475600216991873963561768100160364792981629064220601844848928537580 + α[6] = BigInt(72367769693133178898676076432831566019684378142853445230956642801)//BigInt(475600216991873963561768100160364792981629064220601844848928537580) α[7] = 1619421054120605468750//3278200730370057108183 α[8] = -66898316144057728000//227310933007074849597 α[9] = 181081444637946577//2226845467039736466 αEEst[1] = 117807213929927//2640907728177740 αEEst[4] = 4758744518816629500000//17812069906509312711137 αEEst[5] = 1730775233574080000000000//7863520414322158392809673 - αEEst[6] = 2682653613028767167314032381891560552585218935572349997//12258338284789875762081637252125169126464880985167722660 + αEEst[6] = BigInt(2682653613028767167314032381891560552585218935572349997)//BigInt(12258338284789875762081637252125169126464880985167722660) αEEst[7] = 40977117022675781250//178949401077111131341 αEEst[10] = 2152106665253777//106040260335225546 A = map(T,A) @@ -1907,49 +1907,49 @@ function constructVerner8(T::Type = Float64) A[8,5] = -1024030607959889//168929280000000 A[8,6] = 1501408353528689//265697280000000 A[8,7] = 6070139212132283//92502016000000 - A[9,1] = -1472514264486215803881384708877264246346044433307094207829051978044531801133057155//1246894801620032001157059621643986024803301558393487900440453636168046069686436608 - A[9,4] = -5172294311085668458375175655246981230039025336933699114138315270772319372469280000//124619381004809145897278630571215298365257079410236252921850936749076487132995191 - A[9,5] = -12070679258469254807978936441733187949484571516120469966534514296406891652614970375//2722031154761657221710478184531100699497284085048389015085076961673446140398628096 - A[9,6] = 780125155843893641323090552530431036567795592568497182701460674803126770111481625//183110425412731972197889874507158786859226102980861859505241443073629143100805376 - A[9,7] = 664113122959911642134782135839106469928140328160577035357155340392950009492511875//15178465598586248136333023107295349175279765150089078301139943253016877823170816 - A[9,8] = 10332848184452015604056836767286656859124007796970668046446015775000000//1312703550036033648073834248740727914537972028638950165249582733679393783 - A[10,1] = -29055573360337415088538618442231036441314060511//22674759891089577691327962602370597632000000000 + A[9,1] = -BigInt(1472514264486215803881384708877264246346044433307094207829051978044531801133057155)//BigInt(1246894801620032001157059621643986024803301558393487900440453636168046069686436608) + A[9,4] = -BigInt(5172294311085668458375175655246981230039025336933699114138315270772319372469280000)//BigInt(124619381004809145897278630571215298365257079410236252921850936749076487132995191) + A[9,5] = -BigInt(12070679258469254807978936441733187949484571516120469966534514296406891652614970375)//BigInt(2722031154761657221710478184531100699497284085048389015085076961673446140398628096) + A[9,6] = BigInt(780125155843893641323090552530431036567795592568497182701460674803126770111481625)//BigInt(183110425412731972197889874507158786859226102980861859505241443073629143100805376) + A[9,7] = BigInt(664113122959911642134782135839106469928140328160577035357155340392950009492511875)//BigInt(15178465598586248136333023107295349175279765150089078301139943253016877823170816) + A[9,8] = BigInt(10332848184452015604056836767286656859124007796970668046446015775000000)//BigInt(1312703550036033648073834248740727914537972028638950165249582733679393783) + A[10,1] = -BigInt(29055573360337415088538618442231036441314060511)//BigInt(22674759891089577691327962602370597632000000000) A[10,4] = -20462749524591049105403365239069//454251913499893469596231268750 A[10,5] = -180269259803172281163724663224981097//38100922558256871086579832832000000 - A[10,6] = 21127670214172802870128286992003940810655221489//4679473877997892906145822697976708633673728000 - A[10,7] = 318607235173649312405151265849660869927653414425413//6714716715558965303132938072935465423910912000000 + A[10,6] = BigInt(21127670214172802870128286992003940810655221489)//BigInt(4679473877997892906145822697976708633673728000) + A[10,7] = BigInt(318607235173649312405151265849660869927653414425413)//BigInt(6714716715558965303132938072935465423910912000000) A[10,8] = 212083202434519082281842245535894//20022426044775672563822865371173879 - A[10,9] = -2698404929400842518721166485087129798562269848229517793703413951226714583//469545674913934315077000442080871141884676035902717550325616728175875000000 - A[11,1] = -2342659845814086836951207140065609179073838476242943917//1358480961351056777022231400139158760857532162795520000 + A[10,9] = -BigInt(2698404929400842518721166485087129798562269848229517793703413951226714583)//BigInt(469545674913934315077000442080871141884676035902717550325616728175875000000) + A[11,1] = -BigInt(2342659845814086836951207140065609179073838476242943917)//BigInt(1358480961351056777022231400139158760857532162795520000) A[11,4] = -996286030132538159613930889652//16353068885996164905464325675 A[11,5] = -26053085959256534152588089363841//4377552804565683061011299942400 - A[11,6] = 20980822345096760292224086794978105312644533925634933539//3775889992007550803878727839115494641972212962174156800 - A[11,7] = 890722993756379186418929622095833835264322635782294899//13921242001395112657501941955594013822830119803764736 - A[11,8] = 161021426143124178389075121929246710833125//10997207722131034650667041364346422894371443 - A[11,9] = 300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513//4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000 + A[11,6] = BigInt(20980822345096760292224086794978105312644533925634933539)//BigInt(3775889992007550803878727839115494641972212962174156800) + A[11,7] = BigInt(890722993756379186418929622095833835264322635782294899)//BigInt(13921242001395112657501941955594013822830119803764736) + A[11,8] = BigInt(161021426143124178389075121929246710833125)//BigInt(10997207722131034650667041364346422894371443) + A[11,9] = BigInt(300760669768102517834232497565452434946672266195876496371874262392684852243925359864884962513)//BigInt(4655443337501346455585065336604505603760824779615521285751892810315680492364106674524398280000) A[11,10] = -31155237437111730665923206875//392862141594230515010338956291 - A[12,1] = -2866556991825663971778295329101033887534912787724034363//868226711619262703011213925016143612030669233795338240 - A[12,4] = -16957088714171468676387054358954754000//143690415119654683326368228101570221 - A[12,5] = -4583493974484572912949314673356033540575//451957703655250747157313034270335135744 - A[12,6] = 2346305388553404258656258473446184419154740172519949575//256726716407895402892744978301151486254183185289662464 - A[12,7] = 1657121559319846802171283690913610698586256573484808662625//13431480411255146477259155104956093505361644432088109056 - A[12,8] = 345685379554677052215495825476969226377187500//74771167436930077221667203179551347546362089 - A[12,9] = -3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011//947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120 - A[12,10] = 40279545832706233433100438588458933210937500//8896460842799482846916972126377338947215101 - A[12,11] = -6122933601070769591613093993993358877250//1050517001510235513198246721302027675953 - A[13,1] = -618675905535482500672800859344538410358660153899637//203544282118214047100119475340667684874292102389760 - A[13,4] = -4411194916804718600478400319122931000//40373053902469967450761491269633019 - A[13,5] = -16734711409449292534539422531728520225//1801243715290088669307203927210237952 - A[13,6] = 135137519757054679098042184152749677761254751865630525//16029587794486289597771326361911895112703716593983488 - A[13,7] = 38937568367409876012548551903492196137929710431584875//340956454090191606099548798001469306974758443147264 - A[13,8] = -6748865855011993037732355335815350667265625//7002880395717424621213565406715087764770357 - A[13,9] = -1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671//348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320 - A[13,10] = 53381024589235611084013897674181629296875//8959357584795694524874969598508592944141 + A[12,1] = -BigInt(2866556991825663971778295329101033887534912787724034363)//BigInt(868226711619262703011213925016143612030669233795338240) + A[12,4] = -BigInt(16957088714171468676387054358954754000)//BigInt(143690415119654683326368228101570221) + A[12,5] = -BigInt(4583493974484572912949314673356033540575)//BigInt(451957703655250747157313034270335135744) + A[12,6] = BigInt(2346305388553404258656258473446184419154740172519949575)//BigInt(256726716407895402892744978301151486254183185289662464) + A[12,7] = BigInt(1657121559319846802171283690913610698586256573484808662625)//BigInt(13431480411255146477259155104956093505361644432088109056) + A[12,8] = BigInt(345685379554677052215495825476969226377187500)//BigInt(74771167436930077221667203179551347546362089) + A[12,9] = -BigInt(3205890962717072542791434312152727534008102774023210240571361570757249056167015230160352087048674542196011)//BigInt(947569549683965814783015124451273604984657747127257615372449205973192657306017239103491074738324033259120) + A[12,10] = BigInt(40279545832706233433100438588458933210937500)//BigInt(8896460842799482846916972126377338947215101) + A[12,11] = -BigInt(6122933601070769591613093993993358877250)//BigInt(1050517001510235513198246721302027675953) + A[13,1] = -BigInt(618675905535482500672800859344538410358660153899637)//BigInt(203544282118214047100119475340667684874292102389760) + A[13,4] = -BigInt(4411194916804718600478400319122931000)//BigInt(40373053902469967450761491269633019) + A[13,5] = -BigInt(16734711409449292534539422531728520225)//BigInt(1801243715290088669307203927210237952) + A[13,6] = BigInt(135137519757054679098042184152749677761254751865630525)//BigInt(16029587794486289597771326361911895112703716593983488) + A[13,7] = BigInt(38937568367409876012548551903492196137929710431584875)//BigInt(340956454090191606099548798001469306974758443147264) + A[13,8] = -BigInt(6748865855011993037732355335815350667265625)//BigInt(7002880395717424621213565406715087764770357) + A[13,9] = -BigInt(1756005520307450928195422767042525091954178296002788308926563193523662404739779789732685671)//BigInt(348767814578469983605688098046186480904607278021030540735333862087061574934154942830062320) + A[13,10] = BigInt(53381024589235611084013897674181629296875)//BigInt(8959357584795694524874969598508592944141) α[1] = 44901867737754616851973//1014046409980231013380680 α[6] = 791638675191615279648100000//2235604725089973126411512319 α[7] = 3847749490868980348119500000//15517045062138271618141237517 α[8] = -13734512432397741476562500000//875132892924995907746928783 - α[9] = 12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141//489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040 + α[9] = BigInt(12274765470313196878428812037740635050319234276006986398294443554969616342274215316330684448207141)//BigInt(489345147493715517650385834143510934888829280686609654482896526796523353052166757299452852166040) α[10] = -9798363684577739445312500000//308722986341456031822630699 α[11] = 282035543183190840068750//12295407629873040425991 α[12] = -306814272936976936753//1299331183183744997286 @@ -1958,7 +1958,7 @@ function constructVerner8(T::Type = Float64) αEEst[6] = 13908189778321895491375000//39221135527894265375640567 αEEst[7] = 73487947527027243487625000//296504045773342769773399443 αEEst[8] = 68293140641257649609375000//15353208647806945749946119 - αEEst[9] = 22060647948996678611017711379974578860522018208949721559448560203338437626022142776381//1111542009262325874512959185795727215759010577565736079641376621381577236680929558640 + αEEst[9] = BigInt(22060647948996678611017711379974578860522018208949721559448560203338437626022142776381)//BigInt(1111542009262325874512959185795727215759010577565736079641376621381577236680929558640) αEEst[10] = -547971229495642458203125000//23237214025700991642563601 αEEst[13] = -28735456870978964189//79783493704265043693 @@ -2224,7 +2224,7 @@ function constructDormandLockyerMcCorriganPrince6(T::Type = Float64) A[8,2]=0 A[8,3]=19247613365107236707//4836252322132133628 A[8,4]=-3627331815384766429266963559//1852940251413900055822878936 - A[8,5]=-1113629335962635330712822690622675431//31397585101055611361934971740947112 + A[8,5]=-BigInt(1113629335962635330712822690622675431)//BigInt(31397585101055611361934971740947112) A[8,6]=7515696221383336//210977455127283 A[8,7]=-2466239729887929744//169565652664150899277 A[9,1]=265211783//3930519060 @@ -2295,30 +2295,30 @@ function constructTanakaKasugaYamashitaYazaki6D(T::Type = Float64) A[5,2]=-5917919395479054157557671728//2612315925376400178578984625 A[5,3]=232280630406488701857197728//1274810171583683287146544497 A[5,4]=5471535080448445690971520//20898527403011201428631877 - A[6,1]=6437510603218083862126582571557692575111484748570978316432703829//462655382163643505993146289902892129798145865902401535270912000 + A[6,1]=BigInt(6437510603218083862126582571557692575111484748570978316432703829)//BigInt(462655382163643505993146289902892129798145865902401535270912000) A[6,2]=-25083125032238929237211514053//1741543950250933452385989750 - A[6,3]=191471592827838703414373042295007003190385413366181230722958611//201998644533947923598793335502244867385083328952030670310246400 - A[6,4]=-723497411149192638041504597211363403675892243966786723532767//584075332429951001052530262062711448991365353250616692288000 - A[6,5]=20368395873479894700136894919415569811519//12245317457885350045378058014027636736000 - A[7,1]=-1053235524590544505552847720336831796873415344431325525436387723231012409077771//151882847900737440255262782278159042659114250070600779935950570906179610869760 + A[6,3]=BigInt(191471592827838703414373042295007003190385413366181230722958611)//BigInt(201998644533947923598793335502244867385083328952030670310246400) + A[6,4]=-BigInt(723497411149192638041504597211363403675892243966786723532767)//BigInt(584075332429951001052530262062711448991365353250616692288000) + A[6,5]=BigInt(20368395873479894700136894919415569811519)//BigInt(12245317457885350045378058014027636736000) + A[7,1]=-BigInt(1053235524590544505552847720336831796873415344431325525436387723231012409077771)//BigInt(151882847900737440255262782278159042659114250070600779935950570906179610869760) A[7,2]=110556263584594415870053017499108315//15711834237341169934278611772340752 - A[7,3]=27883202411953328597139497795565290131372048742640205053329023156822546337651//66313136270946971682878125476803367732416846682610519097035561761715919388672 - A[7,4]=-134178686375307065766767719823759096451245561636180411142603830822435042239//191743203036279335802347994313396039656741862830639889775698722784806666240 - A[7,5]=1192365386732594028658711096219658222748871123673792181//1339984907884349782764828286663427050229770700990709760 + A[7,3]=BigInt(27883202411953328597139497795565290131372048742640205053329023156822546337651)//BigInt(66313136270946971682878125476803367732416846682610519097035561761715919388672) + A[7,4]=-BigInt(134178686375307065766767719823759096451245561636180411142603830822435042239)//BigInt(191743203036279335802347994313396039656741862830639889775698722784806666240) + A[7,5]=BigInt(1192365386732594028658711096219658222748871123673792181)//BigInt(1339984907884349782764828286663427050229770700990709760) A[7,6]=1//16 - A[8,1]=139472860369418680318405579593202554799958275392817771935632674919979204348213061279//37743426679794053215512832350173350810071958850079214921681182582585691688393293824 + A[8,1]=BigInt(139472860369418680318405579593202554799958275392817771935632674919979204348213061279)//BigInt(37743426679794053215512832350173350810071958850079214921681182582585691688393293824) A[8,2]=-764277739442303538051509575419150250//241488900344982122797870353007980909 - A[8,3]=-7371553444464925806572282862981502319484039203525663191183225508630714910425342675//4846779318912629207559289658412491740053883371241789941360845137312080681624033792 - A[8,4]=8801132642676112554927251590711440081546416618547191842516081677278335900180085//2071689842640920660980285733506294870283516476694921779219912685665930091210112 - A[8,5]=-298368164571373898500032163301238477118159212135073380804555//92828694411466377636989261345454987067336292167034303922176 + A[8,3]=-BigInt(7371553444464925806572282862981502319484039203525663191183225508630714910425342675)//BigInt(4846779318912629207559289658412491740053883371241789941360845137312080681624033792) + A[8,4]=BigInt(8801132642676112554927251590711440081546416618547191842516081677278335900180085)//BigInt(2071689842640920660980285733506294870283516476694921779219912685665930091210112) + A[8,5]=-BigInt(298368164571373898500032163301238477118159212135073380804555)//BigInt(92828694411466377636989261345454987067336292167034303922176) A[8,6]=-240786613447142598518650//1482036690339563123748203 A[8,7]=52860332724128242560//47245264125077723987 - A[9,1]=-70335440697678472884389500304621917516220835017456192585613672496070708987720514364185979355621//5219173052726261361794285880851433852375067076864459834761850509124293962243718819226202095616 - A[9,2]=55057602528492150957512473843952756334951250//3825542672812430870769605520946554801303339 - A[9,3]=-77980782561050861485751338404689118536953083418300092316918550174770045337324006382574405615//39424363920896283457695961995433007195554371610645094834381872512385376722954438065398121984 - A[9,4]=2177533338045948502564188609357006384381697842038103984795932632439956259386338338574157919//387582376874948376545286159615164080595940845312336117877987331598679530792396290947668352 - A[9,5]=-1429465993644112145770349737782620061868013755109155817982734692969685809//295236772314145005435682097407317274403116518334589230312060489793912832 - A[9,6]=-162882286796273095967517045376244881875035//1226056358355165076488310595889719561316528 + A[9,1]=-BigInt(70335440697678472884389500304621917516220835017456192585613672496070708987720514364185979355621)//BigInt(5219173052726261361794285880851433852375067076864459834761850509124293962243718819226202095616) + A[9,2]=BigInt(55057602528492150957512473843952756334951250)//BigInt(3825542672812430870769605520946554801303339) + A[9,3]=-BigInt(77980782561050861485751338404689118536953083418300092316918550174770045337324006382574405615)//BigInt(39424363920896283457695961995433007195554371610645094834381872512385376722954438065398121984) + A[9,4]=BigInt(2177533338045948502564188609357006384381697842038103984795932632439956259386338338574157919)//BigInt(387582376874948376545286159615164080595940845312336117877987331598679530792396290947668352) + A[9,5]=-BigInt(1429465993644112145770349737782620061868013755109155817982734692969685809)//BigInt(295236772314145005435682097407317274403116518334589230312060489793912832) + A[9,6]=-BigInt(162882286796273095967517045376244881875035)//BigInt(1226056358355165076488310595889719561316528) A[9,7]=61//43 A[9,8]=0 α[1]=4783097999//163657290888 @@ -2379,29 +2379,29 @@ function constructTanakaKasugaYamashitaYazaki6C(T::Type = Float64) A[5,2]=-2894503641421476941//3306249394253698200 A[5,3]=42536885251557644//181843716683953401 A[5,4]=124767011204926940//545531150051860203 - A[6,1]=2432582077139652291040741961658278931048241123//1042517831971586211298945274530293397770600000 + A[6,1]=BigInt(2432582077139652291040741961658278931048241123)//BigInt(1042517831971586211298945274530293397770600000) A[6,2]=-5086533956627126527//2404545014002689600 - A[6,3]=-28233375209799471901757749652001556425049843//193956805948202085823059585959124353073600000 - A[6,4]=-64143717120482360099075816554051641763250417//80815335811750869092941494149635147114000000 + A[6,3]=-BigInt(28233375209799471901757749652001556425049843)//BigInt(193956805948202085823059585959124353073600000) + A[6,4]=-BigInt(64143717120482360099075816554051641763250417)//BigInt(80815335811750869092941494149635147114000000) A[6,5]=368355687225024998241998861697//229321716687851233749224000000 - A[7,1]=-218146655544801488428299362829574333746140908535614198091//129671440168534479253493745415914920591854154832474480000 + A[7,1]=-BigInt(218146655544801488428299362829574333746140908535614198091)//BigInt(129671440168534479253493745415914920591854154832474480000) A[7,2]=3225815231796122073236882//1899026582543293621912725 - A[7,3]=90474621818961969641326264897298400503244755498598833923//192999352808981550516827900153919881811131765332055040000 - A[7,4]=-1469845402576002022391874744301978646600063888157276277//1827645386448688925348749054487877668666020505038400000 - A[7,5]=236537380548621166783390004339783981292483//228189687334919622052120277661453593600000 + A[7,3]=BigInt(90474621818961969641326264897298400503244755498598833923)//BigInt(192999352808981550516827900153919881811131765332055040000) + A[7,4]=-BigInt(1469845402576002022391874744301978646600063888157276277)//BigInt(1827645386448688925348749054487877668666020505038400000) + A[7,5]=BigInt(236537380548621166783390004339783981292483)//BigInt(228189687334919622052120277661453593600000) A[7,6]=1//16 - A[8,1]=20745045233020258374773011834908499926526821480199726607317//6703021612773885250214340203318686755448684469761576087200 + A[8,1]=BigInt(20745045233020258374773011834908499926526821480199726607317)//BigInt(6703021612773885250214340203318686755448684469761576087200) A[8,2]=-10062163770239468036471200//3356073465031554356885103 - A[8,3]=-6600722659737487671039676673294259975246135762925896417//9474444736357442876691573864537554989039417965607475200 - A[8,4]=80225477702329113082476652949959330669319741271791060069//21801989308095252074205042131464260060005478841312656000 - A[8,5]=-572101553192975384084889663939632620168841743//192662470105149826757328803363450656933632000 + A[8,3]=-BigInt(6600722659737487671039676673294259975246135762925896417)//BigInt(9474444736357442876691573864537554989039417965607475200) + A[8,4]=BigInt(80225477702329113082476652949959330669319741271791060069)//BigInt(21801989308095252074205042131464260060005478841312656000) + A[8,5]=-BigInt(572101553192975384084889663939632620168841743)//BigInt(192662470105149826757328803363450656933632000) A[8,6]=-223351084874296955//945158103640587564 A[8,7]=3931692514354//3491636633667 - A[9,1]=1042961260483134998083167734826788831236189026066652724982180836527//166222076505494822625791597828801737913859767695104851064439232400 + A[9,1]=BigInt(1042961260483134998083167734826788831236189026066652724982180836527)//BigInt(166222076505494822625791597828801737913859767695104851064439232400) A[9,2]=-4754359005740226898713768141325//838855890397374389475867956178 - A[9,3]=-42750676060439966787211838095564987064848978722439603628501619959//27488922212795009426487499382540855882395413779035427566212172800 - A[9,4]=205686747816311239126907254218859168711623965851131881271189228377//77312593723485964011996092013396157169237101253537140029971736000 - A[9,5]=-75946282944430327533335124997772458772050053465158929//62109575359095533697158937720595685916206114892672000 + A[9,3]=-BigInt(42750676060439966787211838095564987064848978722439603628501619959)//BigInt(27488922212795009426487499382540855882395413779035427566212172800) + A[9,4]=BigInt(205686747816311239126907254218859168711623965851131881271189228377)//BigInt(77312593723485964011996092013396157169237101253537140029971736000) + A[9,5]=-BigInt(75946282944430327533335124997772458772050053465158929)//BigInt(62109575359095533697158937720595685916206114892672000) A[9,6]=-264375495891732597330199815785//1220640854393687869579464225198 A[9,7]=8//11 A[9,8]=0 @@ -2549,30 +2549,30 @@ function constructTanakaKasugaYamashitaYazaki6A(T::Type = Float64) A[5,2]=-32049516354411396813791//31633875873558003463200 A[5,3]=415928927703664756394//3202929932197747850649 A[5,4]=4945815476584113561248//16014649660988739253245 - A[6,1]=264364422150553063350374034500534568610052754809099//76594645373513572971811613560122656201571540854400 + A[6,1]=BigInt(264364422150553063350374034500534568610052754809099)//BigInt(76594645373513572971811613560122656201571540854400) A[6,2]=-4942738251715985006237//988558621048687608225 - A[6,3]=857070668647981630049588712158864150151776268553//235675831918503301451728041723454326774066279552 - A[6,4]=-575165070977427883238172569267537197276341339157//157117221279002200967818694482302884516044186368 + A[6,3]=BigInt(857070668647981630049588712158864150151776268553)//BigInt(235675831918503301451728041723454326774066279552) + A[6,4]=-BigInt(575165070977427883238172569267537197276341339157)//BigInt(157117221279002200967818694482302884516044186368) A[6,5]=41539505110086641686706761875//17218030314852652247321445632 - A[7,1]=-7384332843467384251748880311988170834105043085902030057004642579//1315398593371357506652159044711447383311024734178303038737049600 + A[7,1]=-BigInt(7384332843467384251748880311988170834105043085902030057004642579)//BigInt(1315398593371357506652159044711447383311024734178303038737049600) A[7,2]=5656750329476775131209405217353//831860122007390417396028410400 - A[7,3]=-333346623364947547771242996577246247659950898456372585977245839//190226873502934777885081461850578544663440500019631516371204096 - A[7,4]=7100883704616862706920092769411499000150383998766128086388523//4497089208107205150947552289611785925849657210865993294827520 - A[7,5]=-2179578925723796720158217363641743790096295//4632538471751007430155293544377007681933312 + A[7,3]=-BigInt(333346623364947547771242996577246247659950898456372585977245839)//BigInt(190226873502934777885081461850578544663440500019631516371204096) + A[7,4]=BigInt(7100883704616862706920092769411499000150383998766128086388523)//BigInt(4497089208107205150947552289611785925849657210865993294827520) + A[7,5]=-BigInt(2179578925723796720158217363641743790096295)//BigInt(4632538471751007430155293544377007681933312) A[7,6]=1//16 - A[8,1]=-2032945134330261992294105795025746391376544519999264654886089003925834569//370204608795106233716533306294462150635128163745469969879178202980349056 + A[8,1]=-BigInt(2032945134330261992294105795025746391376544519999264654886089003925834569)//BigInt(370204608795106233716533306294462150635128163745469969879178202980349056) A[8,2]=104400636802444703223540033778325//10372562449415222120508569935887 - A[8,3]=-1282736937871158931724790946085686543914309745805108288599439251128389375//121675640652937013878860597173704343215741424447811808281967661119415424 - A[8,4]=69591790067148620077849942355176681820069270105493261193720164528698455//5177686836295192079951514773349120987903890402034545033275219622102784 - A[8,5]=-277247257204675144642737406657510117972977064771225085//32594437558796549389422402191407749206480247247281408 + A[8,3]=-BigInt(1282736937871158931724790946085686543914309745805108288599439251128389375)//BigInt(121675640652937013878860597173704343215741424447811808281967661119415424) + A[8,4]=BigInt(69591790067148620077849942355176681820069270105493261193720164528698455)//BigInt(5177686836295192079951514773349120987903890402034545033275219622102784) + A[8,5]=-BigInt(277247257204675144642737406657510117972977064771225085)//BigInt(32594437558796549389422402191407749206480247247281408) A[8,6]=206057847729988755370340//362497215363232474360143 A[8,7]=482015452915471040//328927231085842477 - A[9,1]=149325572050522001715919965533803802996087500406626797668220209959218571//32753013690352528622466162111781793695504165546622151035212132158026496 - A[9,2]=-2802049259729837394660870725638222600//886389794903952023701108666481909127 - A[9,3]=-247046029472637555138263024224503808349122551711211979490561742618517516481875//62386925133959095591686249139496495395591773904073928005189977758511970759424 - A[9,4]=17088511387117619026306232328319322341432000611501090216270103426420066685195//2654762771657833854965372303808361506195394634215911830008084159936679606784 - A[9,5]=-1905127968294488657830239165534292922200553202371049568415//428517757803501533934438346448102436732262910333700649472 - A[9,6]=348519474109306281943020669241827485//1086125473870224085200713153977775988 + A[9,1]=BigInt(149325572050522001715919965533803802996087500406626797668220209959218571)//BigInt(32753013690352528622466162111781793695504165546622151035212132158026496) + A[9,2]=-BigInt(2802049259729837394660870725638222600)//BigInt(886389794903952023701108666481909127) + A[9,3]=-BigInt(247046029472637555138263024224503808349122551711211979490561742618517516481875)//BigInt(62386925133959095591686249139496495395591773904073928005189977758511970759424) + A[9,4]=BigInt(17088511387117619026306232328319322341432000611501090216270103426420066685195)//BigInt(2654762771657833854965372303808361506195394634215911830008084159936679606784) + A[9,5]=-BigInt(1905127968294488657830239165534292922200553202371049568415)//BigInt(428517757803501533934438346448102436732262910333700649472) + A[9,6]=BigInt(348519474109306281943020669241827485)//BigInt(1086125473870224085200713153977775988) A[9,7]=5//4 A[9,8]=0 α[1]=703450322//19272872619 @@ -2742,11 +2742,11 @@ function constructChummund62(T::Type = Float64) c[6]=1//2+1//10*5^(1//2) c[7]=1 A[2,1]=750557//18870600 - A[3,1]=-2618524936181374161531835574563010037//1243120420984397996179713098690223560+3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) + A[3,1]=-BigInt(2618524936181374161531835574563010037)//BigInt(1243120420984397996179713098690223560)+3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) A[3,2]=79275599164011507825658766043059867//31078010524609949904492827467255589-3789435780183611636743//41406596067467160927808051177*826321815619^(1//2) - A[4,1]=-268026226098849050460940570252841432600176823648465011650077//5150236239747870879984989921782016384957547807596571966124+75921270833932035355544618340621749422299940322072982//1287559059936967719996247480445504096239386951899142991531*826321815619^(1//2) - A[4,2]=31518353641767830515869136922708314461169361966520350023632789875//553066166067338591675176701039997652878686435650554094276321374-35636316203172669679112815645100268396443783685272961209975//553066166067338591675176701039997652878686435650554094276321374*826321815619^(1//2) - A[4,3]=-2316654837809440895270062146979974449795559590002488266576771951//551916642155010749548578353874329493980040828668519599378437454+3018332469640261586051209426912089268215645947971953376787//551916642155010749548578353874329493980040828668519599378437454*826321815619^(1//2) + A[4,1]=-BigInt(268026226098849050460940570252841432600176823648465011650077)//BigInt(5150236239747870879984989921782016384957547807596571966124)+BigInt(75921270833932035355544618340621749422299940322072982)//BigInt(1287559059936967719996247480445504096239386951899142991531)*826321815619^(1//2) + A[4,2]=BigInt(31518353641767830515869136922708314461169361966520350023632789875)//BigInt(553066166067338591675176701039997652878686435650554094276321374)-BigInt(35636316203172669679112815645100268396443783685272961209975)//BigInt(553066166067338591675176701039997652878686435650554094276321374)*826321815619^(1//2) + A[4,3]=-BigInt(2316654837809440895270062146979974449795559590002488266576771951)//BigInt(551916642155010749548578353874329493980040828668519599378437454)+BigInt(3018332469640261586051209426912089268215645947971953376787)//BigInt(551916642155010749548578353874329493980040828668519599378437454)*826321815619^(1//2) A[5,1]=7557928766176693537//21071504819547814620-3808101371666611447//21071504819547814620*5^(1//2)+1830930386299//21071504819547814620*826321815619^(1//2)+2746507673963//21071504819547814620*826321815619^(1//2)*5^(1//2) A[5,2]=-306676166043910279990585069725//1347799564492996272083268634084+281193211701441857849531780175//1347799564492996272083268634084*5^(1//2)-135831974232490143067425//1347799564492996272083268634084*826321815619^(1//2)-203756277349889111562225//1347799564492996272083268634084*826321815619^(1//2)*5^(1//2) A[5,3]=59599519641651017073742851703//154850028368562600922782726012-19070452237413934132405792717//154850028368562600922782726012*5^(1//2)+3249940179998629473139//154850028368562600922782726012*826321815619^(1//2)+4875109240133213731043//154850028368562600922782726012*826321815619^(1//2)*5^(1//2) @@ -2754,12 +2754,12 @@ function constructChummund62(T::Type = Float64) A[6,1]=-6195448976102809771//10535752409773907310-1420753767230413123//10535752409773907310*5^(1//2)+2689284093484//5267876204886953655*826321815619^(1//2)+57223580479//5267876204886953655*826321815619^(1//2)*5^(1//2) A[6,2]=583482891804126952797345387075//673899782246498136041634317042+55992621594804402807018397650//336949891123249068020817158521*5^(1//2)-254249689295131189339575//336949891123249068020817158521*826321815619^(1//2)-49153620024967407924975//673899782246498136041634317042*826321815619^(1//2)*5^(1//2) A[6,3]=19364321623328820251751318839//77425014184281300461391363006+1040656060288496357918934418//38712507092140650230695681503*5^(1//2)-11049041979964718221319//38712507092140650230695681503*826321815619^(1//2)-19382660452189380569035//77425014184281300461391363006*826321815619^(1//2)*5^(1//2) - A[6,4]=115027957037506741565069794992944458832461//237309179139566721503969545043331027555510-19371908299625437579435144814464589438224//118654589569783360751984772521665513777755*5^(1//2)+64263508455127995016232148201271346//118654589569783360751984772521665513777755*826321815619^(1//2)-41163600684913040546114995026601907//237309179139566721503969545043331027555510*826321815619^(1//2)*5^(1//2) + A[6,4]=BigInt(115027957037506741565069794992944458832461)//BigInt(237309179139566721503969545043331027555510)-BigInt(19371908299625437579435144814464589438224)//BigInt(118654589569783360751984772521665513777755)*5^(1//2)+BigInt(64263508455127995016232148201271346)//BigInt(118654589569783360751984772521665513777755)*826321815619^(1//2)-BigInt(41163600684913040546114995026601907)//BigInt(237309179139566721503969545043331027555510)*826321815619^(1//2)*5^(1//2) A[6,5]=43435632261//211822050005*5^(1//2)-43432990301//84728820002+205839//423644100010*826321815619^(1//2)*5^(1//2)-514//42364410001*826321815619^(1//2) A[7,1]=9047270149938488929//4214300963909562924+2216536302042479231//1404766987969854308*5^(1//2)-991800665293//1404766987969854308*826321815619^(1//2)*5^(1//2)-12588066760235//4214300963909562924*826321815619^(1//2) A[7,2]=-4301448087821718128020528522125//1347799564492996272083268634084-2525818490403297345388026853875//1347799564492996272083268634084*5^(1//2)+1510317586999119637060875//1347799564492996272083268634084*826321815619^(1//2)*5^(1//2)+5764153657065074502128625//1347799564492996272083268634084*826321815619^(1//2) A[7,3]=-491640814441543287886227446905//154850028368562600922782726012+752920605871714580844952275//1564141700692551524472552788*5^(1//2)+1711626851729573101365//1564141700692551524472552788*826321815619^(1//2)*5^(1//2)+204731138699301217060685//154850028368562600922782726012*826321815619^(1//2) - A[7,4]=-222449163212150849227576515026323419478375//94923671655826688601587818017332411022204+805495551976820677052288591080735143509//958824966220471602036240586033660717396*5^(1//2)-253684995628220543918448388547756365//94923671655826688601587818017332411022204*826321815619^(1//2)+882636009291931420795306294477883//958824966220471602036240586033660717396*826321815619^(1//2)*5^(1//2) + A[7,4]=-BigInt(222449163212150849227576515026323419478375)//BigInt(94923671655826688601587818017332411022204)+BigInt(805495551976820677052288591080735143509)//BigInt(958824966220471602036240586033660717396)*5^(1//2)-BigInt(253684995628220543918448388547756365)//BigInt(94923671655826688601587818017332411022204)*826321815619^(1//2)+BigInt(882636009291931420795306294477883)//BigInt(958824966220471602036240586033660717396)*826321815619^(1//2)*5^(1//2) A[7,5]=-44506854521//84728820002*5^(1//2)+214493500755//42364410001-205839//84728820002*826321815619^(1//2)*5^(1//2)+2570//42364410001*826321815619^(1//2) A[7,6]=5//2-1//2*5^(1//2) α[1]=1//12 @@ -3035,20 +3035,20 @@ function constructVernerRobust7(T::Type = Float64) A[7,3]=-9852144759099//2364568872400 A[7,4]=15322550932778398907299//3996134347464283007200 A[7,5]=-18338463121898520004//36506562121215938675 - A[7,6]=23340475544602125119307511373519383499//34957329425893779598660175543672800000 + A[7,6]=BigInt(23340475544602125119307511373519383499)//BigInt(34957329425893779598660175543672800000) A[8,1]=81088643022740545033730780169//2975182110231937140152800000 A[8,2]=0 A[8,3]=-2837794586103//67559110640 A[8,4]=-14167575606881316095038341141//1344719188593468553337836000 A[8,5]=2395552232834276839307772//29760062864388068268875 - A[8,6]=-4076715891031001341580357765362043260356514682697//60535801523558513633981092635987721507186400000 + A[8,6]=-BigInt(4076715891031001341580357765362043260356514682697)//BigInt(60535801523558513633981092635987721507186400000) A[8,7]=36551527355459957808//2801171464968864455 A[9,1]=-3347747115771808477876752833599//1101327591307901549464211073280 A[9,2]=0 A[9,3]=1214704878477625125//119815105452943264 A[9,4]=-65581118617864038124456452415//10200342297342072539428709672 A[9,5]=-133373082911575479273298406095//84070826916189821955373830704 - A[9,6]=622515683654039386383701463758952267447736841050281950137693//328994218860140584540186142455568117669077094653332432085760 + A[9,6]=BigInt(622515683654039386383701463758952267447736841050281950137693)//BigInt(328994218860140584540186142455568117669077094653332432085760) A[9,7]=46169188671551441399013763125//2343692704156841275628930358208 A[9,8]=18880867865877597493091875//3469664148196911643475533504 A[10,1]=-74309815528722196127526037//51427190037752065777334640 @@ -3056,7 +3056,7 @@ function constructVernerRobust7(T::Type = Float64) A[10,3]=913722369253875//113761793498234 A[10,4]=-440658227159292602060396890//58109996881684093545238767 A[10,5]=37290888293935763341814380//10411746696360295961914239 - A[10,6]=-645152888113581065780360392105179310452496326847//264735425121804814898131042131367320451487910960 + A[10,6]=-BigInt(645152888113581065780360392105179310452496326847)//BigInt(264735425121804814898131042131367320451487910960) A[10,7]=473757486190086838681892500//556321100802942639360459887 A[10,8]=0 A[10,9]=0 @@ -3065,7 +3065,7 @@ function constructVernerRobust7(T::Type = Float64) α[3]=0 α[4]=18658605936510000//72821569629535727 α[5]=296950875175030000//1101802245630054969 - α[6]=18875276980274212686824835566143151189850553896330009//148780947139609706104394157596648357994575577036224440 + α[6]=BigInt(18875276980274212686824835566143151189850553896330009)//BigInt(148780947139609706104394157596648357994575577036224440) α[7]=18663850606812500//74993696164706319 α[8]=179884749312500//58508928482581269 α[9]=349315176247648//7273791403140339 @@ -3075,7 +3075,7 @@ function constructVernerRobust7(T::Type = Float64) αEEst[3]=0 αEEst[4]=7505178129270000//29317774785916981 αEEst[5]=1851744839320000//6843492208882329 - αEEst[6]=750882778189818437512810407839645051128089//6004363295715536270735789992319176322209240 + αEEst[6]=BigInt(750882778189818437512810407839645051128089)//BigInt(6004363295715536270735789992319176322209240) αEEst[7]=27902602073000000//110704980052661709 αEEst[8]=0 αEEst[9]=0 @@ -3116,39 +3116,39 @@ A[5,1]=13638791441//21333512000 A[5,2]=0 A[5,3]=-10484391993//4266702400 A[5,4]=1212514581//533337800 -A[6,1]=-10566420537453573046911093467384714791794598586757942301092800//3945478828013189718441489268080494867217306323934034936408479 +A[6,1]=-BigInt(10566420537453573046911093467384714791794598586757942301092800)//BigInt(3945478828013189718441489268080494867217306323934034936408479) A[6,2]=0 -A[6,3]=5231021510299954960251585060495720489874110055798400000000//481214639347870437668189933904195007588401795820714103721 -A[6,4]=-53191822847901986858463766895922715840689391279600297600000000//6327491292785148384899029440906260154779895213246569749827429 -A[6,5]=1781287527622331824616139968260471142273403953102720000000//2161611109404685052753814119556349840946763773078759856171 -A[7,1]=40316732614812499600926954604381622079953//6622027015251398289270845012723400000000 +A[6,3]=BigInt(5231021510299954960251585060495720489874110055798400000000)//BigInt(481214639347870437668189933904195007588401795820714103721) +A[6,4]=-BigInt(53191822847901986858463766895922715840689391279600297600000000)//BigInt(6327491292785148384899029440906260154779895213246569749827429) +A[6,5]=BigInt(1781287527622331824616139968260471142273403953102720000000)//BigInt(2161611109404685052753814119556349840946763773078759856171) +A[7,1]=BigInt(40316732614812499600926954604381622079953)//BigInt(6622027015251398289270845012723400000000) A[7,2]=0 A[7,3]=-3102627096349187411472//125153701152335532175 -A[7,4]=24512593611811814197027847310011747907776//1196407956242848578947668299729517712775 +A[7,4]=BigInt(24512593611811814197027847310011747907776)//BigInt(1196407956242848578947668299729517712775) A[7,5]=-27992220377104300725776520574439264//14697934672024287924310069954740819 -A[7,6]=3894588020195704963647351313475389164102598021642890694420881//3885780076153082703909872726256212057602657456212198200000000 -A[8,1]=219473830564834473126851658008599711669913643457//18148581918776897851104105262715070449854720000 +A[7,6]=BigInt(3894588020195704963647351313475389164102598021642890694420881)//BigInt(3885780076153082703909872726256212057602657456212198200000000) +A[8,1]=BigInt(219473830564834473126851658008599711669913643457)//BigInt(18148581918776897851104105262715070449854720000) A[8,2]=0 A[8,3]=-10861924990722808125//217658610699713969 -A[8,4]=119480318847905366486490498699126516657779132592500//2895978969529640099701689414747730700037272591519 -A[8,5]=-1668548580652290279936994936449972411950403625//374242591559339035424931213674065468041890542 -A[8,6]=38257721102788015064997204763622283132936825913246654962493266309964200473188255317//18800609083266437975749341539616748050410201552864110184725432140737391745319680000 +A[8,4]=BigInt(119480318847905366486490498699126516657779132592500)//BigInt(2895978969529640099701689414747730700037272591519) +A[8,5]=-BigInt(1668548580652290279936994936449972411950403625)//BigInt(374242591559339035424931213674065468041890542) +A[8,6]=BigInt(38257721102788015064997204763622283132936825913246654962493266309964200473188255317)//BigInt(18800609083266437975749341539616748050410201552864110184725432140737391745319680000) A[8,7]=-500096105036391897537714558203625//5080166748283963062825254164179392 -A[9,1]=73088758866605608581823594159257042017139758291//7204156842026682625849538837116971615241846400 +A[9,1]=BigInt(73088758866605608581823594159257042017139758291)//BigInt(7204156842026682625849538837116971615241846400) A[9,2]=0 A[9,3]=-69262713771106609055901000000//1623478443813548051039428229 -A[9,4]=14675490755672909998080009537477454813814604865188000000//410204279941884058406992680456716961361878302419014157 -A[9,5]=-56001310541527335660935463926718909867728400000//12914842534226649788973963163793850259828428307 -A[9,6]=1658790111713212343550432782788025386861251060331884987447839679378079088262228191320420318059//829167683860659102329644660243394316974911850817625934703082071608371922272124378570833366400 -A[9,7]=397383910096482616626611556102242919581343750//1139945435719262247312274838475128039778393907 -A[9,8]=-15924946453851683996573317555310225254108800//58718594835565436263767442911746035434825067 -A[10,1]=-14946539621537434020656235571945101642930646111//332010640625300658857148487489318781645129600 +A[9,4]=BigInt(14675490755672909998080009537477454813814604865188000000)//BigInt(410204279941884058406992680456716961361878302419014157) +A[9,5]=-BigInt(56001310541527335660935463926718909867728400000)//BigInt(12914842534226649788973963163793850259828428307) +A[9,6]=BigInt(1658790111713212343550432782788025386861251060331884987447839679378079088262228191320420318059)//BigInt(829167683860659102329644660243394316974911850817625934703082071608371922272124378570833366400) +A[9,7]=BigInt(397383910096482616626611556102242919581343750)//BigInt(1139945435719262247312274838475128039778393907) +A[9,8]=-BigInt(15924946453851683996573317555310225254108800)//BigInt(58718594835565436263767442911746035434825067) +A[10,1]=-BigInt(14946539621537434020656235571945101642930646111)//BigInt(332010640625300658857148487489318781645129600) A[10,2]=0 A[10,3]=171118989155232139053000000//913940284754207909241943 -A[10,4]=-250906345110237533448815794107434670644623116000000//1630126656666301353726306757388291345384354510761 -A[10,5]=100053022832376562190601031855550739901200000//5412177019773639317674437354179369686847329 -A[10,6]=-741124542370420850881498253695230801778840260257881176783159378749906762930019//104572466684527096537276822312914502674692290031200239724554350786783199401600 -A[10,7]=61868781182570033929134892454042771640656250//47410089451637179941093334205322110905900061 +A[10,4]=-BigInt(250906345110237533448815794107434670644623116000000)//BigInt(1630126656666301353726306757388291345384354510761) +A[10,5]=BigInt(100053022832376562190601031855550739901200000)//BigInt(5412177019773639317674437354179369686847329) +A[10,6]=-BigInt(741124542370420850881498253695230801778840260257881176783159378749906762930019)//BigInt(104572466684527096537276822312914502674692290031200239724554350786783199401600) +A[10,7]=BigInt(61868781182570033929134892454042771640656250)//BigInt(47410089451637179941093334205322110905900061) A[10,8]=0 A[10,9]=0 α[1]=23316791871424559928103//494567385514963690893600 @@ -3156,7 +3156,7 @@ A[10,9]=0 α[3]=0 α[4]=167985897310649194506250000000000000//652486332022351662028939973252423307 α[5]=1146393512631783066800000000000//4366210223630112740458758316827 -α[6]=896878436896140749138361006566548336071636396490005664374818159563751598674344336941//5901910841358241153066354693443102222070394003395707585243672949102475401519736720800 +α[6]=BigInt(896878436896140749138361006566548336071636396490005664374818159563751598674344336941)//BigInt(5901910841358241153066354693443102222070394003395707585243672949102475401519736720800) α[7]=7313950190577733068066406250//14824175638294700286557272779 α[8]=-16063489150654390383296000//54687057461871573111333849 α[9]=608799317735794481861//7494797304744605111718 @@ -3166,7 +3166,7 @@ A[10,9]=0 αEEst[3]=0 αEEst[4]=3268266429605273275000000000000//12237407528692429753538888074653 αEEst[5]=1613021830993125656000000000//7306908939590938710641463789 -αEEst[6]=791180295543850558970031000997303838661625778390906982427125664631928//3622667153393802697274794410484953168258089439622231002370760754183025 +αEEst[6]=BigInt(791180295543850558970031000997303838661625778390906982427125664631928)//BigInt(3622667153393802697274794410484953168258089439622231002370760754183025) αEEst[7]=3939837293445123160156250//17217393308123926000647239 αEEst[8]=0 αEEst[9]=0 @@ -3335,7 +3335,7 @@ function constructSharpSmart7(T::Type = Float64) A[6,5]=132023//106200 A[7,1]=25959766877768976976598957736980//487594514129628295945513157189933 A[7,2]=0 - A[7,3]=347890318302644246405985993187156250//1321817402067092875750818220388519949 + A[7,3]=BigInt(347890318302644246405985993187156250)//BigInt(1321817402067092875750818220388519949) A[7,4]=-1717046972617147709491116450178750//7467894926932728111586543618014237 A[7,5]=29780304732725103577764751746216250//258912687002832625147067486467854423 A[7,6]=-302662548054389051180423185000//25662869164717278733974376694207 @@ -3352,7 +3352,7 @@ function constructSharpSmart7(T::Type = Float64) A[9,4]=-50491693720625//29100752640072 A[9,5]=8909776468783164583973193125//6271093223575470807674793192 A[9,6]=-4792324941735635008750//159776107397443897190271 - A[9,7]=-1532806290465891141166096531902118541769245//1203242011387872547807852011647420329982736 + A[9,7]=-BigInt(1532806290465891141166096531902118541769245)//BigInt(1203242011387872547807852011647420329982736) A[9,8]=-7500029126894375//132689679447323376 A[10,1]=36393032615434450612//324390586094889663425 A[10,2]=0 @@ -3360,7 +3360,7 @@ function constructSharpSmart7(T::Type = Float64) A[10,4]=4135780451822750//874504037187843 A[10,5]=-2349378733647002895234008950//1090914599757106529355865311 A[10,6]=-78686605908422443750//52446632451499515953 - A[10,7]=2315079813491204524435067899365885119542372444358703//316169042039527157595235231573788308031260760584200 + A[10,7]=BigInt(2315079813491204524435067899365885119542372444358703)//BigInt(316169042039527157595235231573788308031260760584200) A[10,8]=-33473047374792524975//32907430028856870472 A[10,9]=5594658687556280397846//1893189870520997940175 A[11,1]=2508607706701842363083//197875357745688550590720 @@ -3369,7 +3369,7 @@ function constructSharpSmart7(T::Type = Float64) A[11,4]=13293920580875//2874148408896 A[11,5]=-599188464780493707137440161875//277270064173229869784600732736 A[11,6]=-3601465055348923762849875//2146128454918752594358208 - A[11,7]=606030238246181777051198920509497430523044409408159//74752050141640998967813674460513197348653288024576 + A[11,7]=BigInt(606030238246181777051198920509497430523044409408159)//BigInt(74752050141640998967813674460513197348653288024576) A[11,8]=-1922750201834125//1941504226023936 A[11,9]=12539348439579//3975412795840 A[11,10]=0 @@ -3379,7 +3379,7 @@ function constructSharpSmart7(T::Type = Float64) α[4]=0 α[5]=28304779228000000//53707434325074117 α[6]=-296881060859375//515060733835389 - α[7]=744858303758379680905615939985761920312207508379//2487223884477764590764433396524922145673887618400 + α[7]=BigInt(744858303758379680905615939985761920312207508379)//BigInt(2487223884477764590764433396524922145673887618400) α[8]=-5118512171875//11763620626464 α[9]=136801854099//127885521925 α[10]=103626500437//1717635089268 @@ -3390,7 +3390,7 @@ function constructSharpSmart7(T::Type = Float64) αEEst[4]=0 αEEst[5]=7786773134600000//14452831163890377 αEEst[6]=-408698637296875//567617951573694 - αEEst[7]=4426705150369152638325381078278067803359//14828075230102658203818343670586143438076 + αEEst[7]=BigInt(4426705150369152638325381078278067803359)//BigInt(14828075230102658203818343670586143438076) αEEst[8]=-5004542378125//10330679593521 αEEst[9]=154806770859//124231649870 αEEst[10]=0 @@ -3432,59 +3432,59 @@ function constructTanakaYamashitaEfficient7(T::Type = Float64) A[5,2]=0 A[5,3]=-68331192803887602162951//24112920357813127230992 A[5,4]=7825717455900471140481//3014115044726640903874 - A[6,1]=-2425518501234340256175806929031336393991001205323654593685210322030691047097621496102266496//201073929944556265242953373967503382318096046559546854970564286270157897072030532387737241 + A[6,1]=-BigInt(2425518501234340256175806929031336393991001205323654593685210322030691047097621496102266496)//BigInt(201073929944556265242953373967503382318096046559546854970564286270157897072030532387737241) A[6,2]=0 - A[6,3]=126875939114499086848675646731069753055308007638565564293214808307459627250976287910912//2631823273838775215546306644775636213113650954300949659959480717139276934490785884841 - A[6,4]=-18238165682427587123600563411903599919711680222699338744428834349094610403849667513626245575680//479212348415302218688412787744011607018072627155280851781784515530195350673833210517995172867 - A[6,5]=74777425357290689294313120787550134201356775453356604582280658347816977407509825814840320//27848089034948481594251542168496834020714916243735255636715495143105044359669539013058107 - A[7,1]=42210784012026021620512889337138957588173072058924928398799062235//401168555464694196502745570125544252560955194769351196028554688 + A[6,3]=BigInt(126875939114499086848675646731069753055308007638565564293214808307459627250976287910912)//BigInt(2631823273838775215546306644775636213113650954300949659959480717139276934490785884841) + A[6,4]=-BigInt(18238165682427587123600563411903599919711680222699338744428834349094610403849667513626245575680)//BigInt(479212348415302218688412787744011607018072627155280851781784515530195350673833210517995172867) + A[6,5]=BigInt(74777425357290689294313120787550134201356775453356604582280658347816977407509825814840320)//BigInt(27848089034948481594251542168496834020714916243735255636715495143105044359669539013058107) + A[7,1]=BigInt(42210784012026021620512889337138957588173072058924928398799062235)//BigInt(401168555464694196502745570125544252560955194769351196028554688) A[7,2]=0 - A[7,3]=-53537582181289418572806048482253962781541488//128102133978061070595749084326726258918069 - A[7,4]=6373437319382536771018620806214785516542915567996760353063349991182871200304//19178871740288180724887392022898914045213833131528843480576173243533301485 - A[7,5]=-836513109281956728811652083904588515347012294160401579661057793958992//42189346226535262916910956145917457264775063492307360825161811325023 - A[7,6]=10038768138260655813133796321688310283082351149893792474426644227234755871856831386997923013888351//8279123943002224665888560854425725483235895533066047643118716510648226939201056966728652698557760 - A[8,1]=1454976871505621321312348899226731229297985195430097820532172928754404221419640982320963761//12687546780768188413911065021432924447284583965992535848754097389537051103097048673168256 + A[7,3]=-BigInt(53537582181289418572806048482253962781541488)//BigInt(128102133978061070595749084326726258918069) + A[7,4]=BigInt(6373437319382536771018620806214785516542915567996760353063349991182871200304)//BigInt(19178871740288180724887392022898914045213833131528843480576173243533301485) + A[7,5]=-BigInt(836513109281956728811652083904588515347012294160401579661057793958992)//BigInt(42189346226535262916910956145917457264775063492307360825161811325023) + A[7,6]=BigInt(10038768138260655813133796321688310283082351149893792474426644227234755871856831386997923013888351)//BigInt(8279123943002224665888560854425725483235895533066047643118716510648226939201056966728652698557760) + A[8,1]=BigInt(1454976871505621321312348899226731229297985195430097820532172928754404221419640982320963761)//BigInt(12687546780768188413911065021432924447284583965992535848754097389537051103097048673168256) A[8,2]=0 - A[8,3]=-1452249436938195913836212549773886207822959770792//3187825000852340545619892931005470986913487349 - A[8,4]=3193785703967379485471835519262043520640585789136428552340853315619929163223926155626278646291801931779256//8816743814108800069900425523882492176796603795861854625575345408990649746129323017714575203134405597571 - A[8,5]=-314398569508916946629277462588835135011587938712337655816458752800894863689255534896547161759213480//14507196201560052990013371105817112064769849230048646555812475120383456376679192045076337148816813 - A[8,6]=5021633516852870452803558794670341128133410978274753232000155240629688617274518068065484524425884625107263111090060721584249881611265924113//3807402575192378287101053794016079417728266285278436439472658972755893033722804748992796724254152818232996309281540415603729279478920107136 - A[8,7]=-894451839895008223904010765658125850176064186717638397881061173697811879745//186244934020117483847289332768639722211239803963523669807238114327710091115676 - A[9,1]=152015786770038627019906826956584678402371493198250158080970494807155603994339//1319428594672311986480108760138089275639618425553698631283119461253421932416 + A[8,3]=-BigInt(1452249436938195913836212549773886207822959770792)//BigInt(3187825000852340545619892931005470986913487349) + A[8,4]=BigInt(3193785703967379485471835519262043520640585789136428552340853315619929163223926155626278646291801931779256)//BigInt(8816743814108800069900425523882492176796603795861854625575345408990649746129323017714575203134405597571) + A[8,5]=-BigInt(314398569508916946629277462588835135011587938712337655816458752800894863689255534896547161759213480)//BigInt(14507196201560052990013371105817112064769849230048646555812475120383456376679192045076337148816813) + A[8,6]=BigInt(5021633516852870452803558794670341128133410978274753232000155240629688617274518068065484524425884625107263111090060721584249881611265924113)//BigInt(3807402575192378287101053794016079417728266285278436439472658972755893033722804748992796724254152818232996309281540415603729279478920107136) + A[8,7]=-BigInt(894451839895008223904010765658125850176064186717638397881061173697811879745)//BigInt(186244934020117483847289332768639722211239803963523669807238114327710091115676) + A[9,1]=BigInt(152015786770038627019906826956584678402371493198250158080970494807155603994339)//BigInt(1319428594672311986480108760138089275639618425553698631283119461253421932416) A[9,2]=0 - A[9,3]=-19887569115365707672105043997835466942389220328//43451712251082409470704235239058276887205131 - A[9,4]=6298831527954572673520838478029639446424615570453903300371170696118960335541193275024146681623960//17307483347318198085207889427954666589398911583434527253470846782562794571553580157056644256313 - A[9,5]=-16267621644623777942279856217571823792451732234540266142050307930357537283432611648312520//747020211145282116967827947968990352912884924402891384654470989583659988117513448655559 - A[9,6]=491920517345271821393960134665582163547632868347911487496995665146055538579545277983570189994492481977206720065882583432234119698425636137169515//371241970695441505578374965290296000309261530083026613438333515399198575394818137422626328203755084156959422247928840402063855870066548878130304 - A[9,7]=-17535891839112183607157943692398769696531153719141528498448224128785868799210475//3881175428498724209649715816699297677268154716152409333146177577349474565697791732 - A[9,8]=-31140449219386755112730831706895080247696102690585728771850210691242594436100540310//58531715707220748822628340615174217489020037018063169180406742622693159384762890406389 - A[10,1]=24861126512935523838485032295435745281790804119672244200744512677831357181363//215828469302253893975010055544246846578750854407392771457340001283636121600 + A[9,3]=-BigInt(19887569115365707672105043997835466942389220328)//BigInt(43451712251082409470704235239058276887205131) + A[9,4]=BigInt(6298831527954572673520838478029639446424615570453903300371170696118960335541193275024146681623960)//BigInt(17307483347318198085207889427954666589398911583434527253470846782562794571553580157056644256313) + A[9,5]=-BigInt(16267621644623777942279856217571823792451732234540266142050307930357537283432611648312520)//BigInt(747020211145282116967827947968990352912884924402891384654470989583659988117513448655559) + A[9,6]=BigInt(491920517345271821393960134665582163547632868347911487496995665146055538579545277983570189994492481977206720065882583432234119698425636137169515)//BigInt(371241970695441505578374965290296000309261530083026613438333515399198575394818137422626328203755084156959422247928840402063855870066548878130304) + A[9,7]=-BigInt(17535891839112183607157943692398769696531153719141528498448224128785868799210475)//BigInt(3881175428498724209649715816699297677268154716152409333146177577349474565697791732) + A[9,8]=-BigInt(31140449219386755112730831706895080247696102690585728771850210691242594436100540310)//BigInt(58531715707220748822628340615174217489020037018063169180406742622693159384762890406389) + A[10,1]=BigInt(24861126512935523838485032295435745281790804119672244200744512677831357181363)//BigInt(215828469302253893975010055544246846578750854407392771457340001283636121600) A[10,2]=0 A[10,3]=-76626859319946149305867456329803//167454524692981091214376557800 - A[10,4]=257532657386915224604779230484778835596042580268896440943054087972106955277512448850995064336363//707777528357579864776572552477247532276956780876653359042572831013312547307465249178438602200 - A[10,5]=-103092665221253777021612043042409780416654274677686197534469014507504059634284484983141143//4735075386204034224907103653335170134874540866215348781137359896717512695961598377363000 - A[10,6]=1318945254307068672853031172410281620677291556423152759282406612372948205789241763483098989903852936890735513699395545618802215742952753372919//995520191927224509158660659519643916330847017611189618002256023928790665495276022949114110343406997764203331763292012060684160018593393766400 - A[10,7]=-2175691361381933486174620849991740173349017185199505364607841//482872625303278742130341621563226511344221688759361797916327450 - A[10,8]=-11327601987184122343710458559595782081610122892585097//21251874884678431935286330856983429378055579208005268000 + A[10,4]=BigInt(257532657386915224604779230484778835596042580268896440943054087972106955277512448850995064336363)//BigInt(707777528357579864776572552477247532276956780876653359042572831013312547307465249178438602200) + A[10,5]=-BigInt(103092665221253777021612043042409780416654274677686197534469014507504059634284484983141143)//BigInt(4735075386204034224907103653335170134874540866215348781137359896717512695961598377363000) + A[10,6]=BigInt(1318945254307068672853031172410281620677291556423152759282406612372948205789241763483098989903852936890735513699395545618802215742952753372919)//BigInt(995520191927224509158660659519643916330847017611189618002256023928790665495276022949114110343406997764203331763292012060684160018593393766400) + A[10,7]=-BigInt(2175691361381933486174620849991740173349017185199505364607841)//BigInt(482872625303278742130341621563226511344221688759361797916327450) + A[10,8]=-BigInt(11327601987184122343710458559595782081610122892585097)//BigInt(21251874884678431935286330856983429378055579208005268000) A[10,9]=0 - α[1]=677260699094873524061210073954310211//13212228177645157882237395248920447488 + α[1]=BigInt(677260699094873524061210073954310211)//BigInt(13212228177645157882237395248920447488) α[2]=0 α[3]=0 - α[4]=5627843976805934592544586970647029617399366281651959837492864//20448796992082885248862284273169726631726393791864145954479875 - α[5]=1359735671458057021603668186882234273947181034928034734244224//4035225037829041960922838374222759264846456609494840689395475 - α[6]=3575764371063841994042920363615768888383369782579963896064642431626191680598750790399139608006651160426580137040859330533720256407//18833618269956378326078572170759846509476617594300797062242096554507068838086062412372695473217373611870290738365243380652826304000 - α[7]=14322850798205614664394883796805489119964080948503151//1692788382425178679633337406927131793062126418747780 - α[8]=-16735096417960349589058935251250023138290806176584545269411//128573843052304513208482301684749747737236254208431871400 + α[4]=BigInt(5627843976805934592544586970647029617399366281651959837492864)//BigInt(20448796992082885248862284273169726631726393791864145954479875) + α[5]=BigInt(1359735671458057021603668186882234273947181034928034734244224)//BigInt(4035225037829041960922838374222759264846456609494840689395475) + α[6]=BigInt(3575764371063841994042920363615768888383369782579963896064642431626191680598750790399139608006651160426580137040859330533720256407)//BigInt(18833618269956378326078572170759846509476617594300797062242096554507068838086062412372695473217373611870290738365243380652826304000) + α[7]=BigInt(14322850798205614664394883796805489119964080948503151)//BigInt(1692788382425178679633337406927131793062126418747780) + α[8]=-BigInt(16735096417960349589058935251250023138290806176584545269411)//BigInt(128573843052304513208482301684749747737236254208431871400) α[9]=33050288141543277444692395096256051//271248590133163812341791503489000 α[10]=0 - αEEst[1]=962650826879437817605721930727384851//18874611682350225546053421784172067840 + αEEst[1]=BigInt(962650826879437817605721930727384851)//BigInt(18874611682350225546053421784172067840) αEEst[2]=0 αEEst[3]=0 - αEEst[4]=99703652969826806275610089806158069716600653757297413344//361062893830367886445877712954352019629670588714825566425 - αEEst[5]=17540887447270394964911517553576959050951784592644178144//52550888012671962193116521992300249584518949945887203425 - αEEst[6]=101855668513773837712956593596043266148479443244790887636953159551191054134940671472736229702711787350735239179//504322587935299170723833764883183242017770187561624249681119708768991642691172146267201689787026963930014131200 - αEEst[7]=179578338747395946570172802104016572846366090083599//31203472487100067827342625012481692038011546889360 - αEEst[8]=-500374162579884236288722085953024481890963958534161489781//5844265593286568782203740985670443078965284282201448700 + αEEst[4]=BigInt(99703652969826806275610089806158069716600653757297413344)//BigInt(361062893830367886445877712954352019629670588714825566425) + αEEst[5]=BigInt(17540887447270394964911517553576959050951784592644178144)//BigInt(52550888012671962193116521992300249584518949945887203425) + αEEst[6]=BigInt(101855668513773837712956593596043266148479443244790887636953159551191054134940671472736229702711787350735239179)//BigInt(504322587935299170723833764883183242017770187561624249681119708768991642691172146267201689787026963930014131200) + αEEst[7]=BigInt(179578338747395946570172802104016572846366090083599)//BigInt(31203472487100067827342625012481692038011546889360) + αEEst[8]=-BigInt(500374162579884236288722085953024481890963958534161489781)//BigInt(5844265593286568782203740985670443078965284282201448700) αEEst[9]=0 αEEst[10]=80 @@ -3525,38 +3525,38 @@ function constructTanakaYamashitaStable7(T::Type = Float64) A[5,2]=0 A[5,3]=134004261625//1187078945472 A[5,4]=149425089125//1780618418208 - A[6,1]=874723327324627172137139789673935509613630495//56881344496107103495850556251109088355454531158 + A[6,1]=BigInt(874723327324627172137139789673935509613630495)//BigInt(56881344496107103495850556251109088355454531158) A[6,2]=0 - A[6,3]=140089490273660861720564275306545765967660125//4375488038162084884296196634700699104265733166 - A[6,4]=-2038049847879400647989164901369906650290192935250//47909406273855748440601205051655304842157645301117 - A[6,5]=2992403630086592541124850354372857004595944160//168193972876080132251638040959092347542006316207 + A[6,3]=BigInt(140089490273660861720564275306545765967660125)//BigInt(4375488038162084884296196634700699104265733166) + A[6,4]=-BigInt(2038049847879400647989164901369906650290192935250)//BigInt(47909406273855748440601205051655304842157645301117) + A[6,5]=BigInt(2992403630086592541124850354372857004595944160)//BigInt(168193972876080132251638040959092347542006316207) A[7,1]=-2001378790961964301303250341598299//131178829335937360185206084581250 A[7,2]=0 A[7,3]=-1366679891168526950613//3342867750190010177170 - A[7,4]=-197077954039191584877658472075693196650//14482289235786224954374999272581521053 - A[7,5]=2928205733652489758138852423071126752//289494157432907631631314224968221875 - A[7,6]=32572843800597493853254181634376441943013874856495312//1642002429836009758962688168840520197029337863346875 - A[8,1]=226949925367094612475083609619198193642397605//120406368918742115270494114142742317844627456 + A[7,4]=-BigInt(197077954039191584877658472075693196650)//BigInt(14482289235786224954374999272581521053) + A[7,5]=BigInt(2928205733652489758138852423071126752)//BigInt(289494157432907631631314224968221875) + A[7,6]=BigInt(32572843800597493853254181634376441943013874856495312)//BigInt(1642002429836009758962688168840520197029337863346875) + A[8,1]=BigInt(226949925367094612475083609619198193642397605)//BigInt(120406368918742115270494114142742317844627456) A[8,2]=0 A[8,3]=83451940525721530822125//1129677771714575730562048 - A[8,4]=7035716180093388934005544535766324331669337496890597125//8744668672303692797949525789789288711635037496457428992 - A[8,5]=1783910495800307104322539337559667105512922125//384741540181237650862158213355907627413029681664 - A[8,6]=-84153602056538973791098303633128803165153465256807063611390103929570560775//37282901435832588263568764858094381410386083732352113498074163165795975168 - A[8,7]=529655154424978769932790603243342890625//2074272966571578715335103162383459680256 - A[9,1]=-2220302447236283385210081868020072818509//374126802552343922668161638021420098000 + A[8,4]=BigInt(7035716180093388934005544535766324331669337496890597125)//BigInt(8744668672303692797949525789789288711635037496457428992) + A[8,5]=BigInt(1783910495800307104322539337559667105512922125)//BigInt(384741540181237650862158213355907627413029681664) + A[8,6]=-BigInt(84153602056538973791098303633128803165153465256807063611390103929570560775)//BigInt(37282901435832588263568764858094381410386083732352113498074163165795975168) + A[8,7]=BigInt(529655154424978769932790603243342890625)//BigInt(2074272966571578715335103162383459680256) + A[9,1]=-BigInt(2220302447236283385210081868020072818509)//BigInt(374126802552343922668161638021420098000) A[9,2]=0 A[9,3]=-580875348986851918117575//7422906155739208262352728 - A[9,4]=-10152884092399228192381460837845336141124812794348025//1298474693887469810743537803700532058113206856602944 - A[9,5]=57628597675871150072147324302138021982593246488//8694208064927983865022808524707850651868593125 - A[9,6]=25006323928409346448859146781582297955220041834414805003311931721685248934905197//3116797087097920659891402066923116953398124957660879445267880838924530153376000 - A[9,7]=-991935992163983524020354479671037652370649875//1096924827756227471690652450958041839154828032 - A[9,8]=11028636941861502413824025771962099757599945728//10166706010345110864067934052134974581343819375 - A[10,1]=2847557162233802909802913419338134005277//175580852316165047798631596921711256000 + A[9,4]=-BigInt(10152884092399228192381460837845336141124812794348025)//BigInt(1298474693887469810743537803700532058113206856602944) + A[9,5]=BigInt(57628597675871150072147324302138021982593246488)//BigInt(8694208064927983865022808524707850651868593125) + A[9,6]=BigInt(25006323928409346448859146781582297955220041834414805003311931721685248934905197)//BigInt(3116797087097920659891402066923116953398124957660879445267880838924530153376000) + A[9,7]=-BigInt(991935992163983524020354479671037652370649875)//BigInt(1096924827756227471690652450958041839154828032) + A[9,8]=BigInt(11028636941861502413824025771962099757599945728)//BigInt(10166706010345110864067934052134974581343819375) + A[10,1]=BigInt(2847557162233802909802913419338134005277)//BigInt(175580852316165047798631596921711256000) A[10,2]=0 A[10,3]=1552914837310075//7167358071597822 - A[10,4]=7813795507395804332400817811705117266280297151179075//609385085239477995902119898391644620983028518989568 - A[10,5]=-306358654025510315315806741256227901425369583//37780230596405542839291492772111971777338125 - A[10,6]=-30230616135053261889365940573714713926595600173797519397657905897494488117634591//1462739064177653822206630548583223553011887775071057363338006334613651993472000 + A[10,4]=BigInt(7813795507395804332400817811705117266280297151179075)//BigInt(609385085239477995902119898391644620983028518989568) + A[10,5]=-BigInt(306358654025510315315806741256227901425369583)//BigInt(37780230596405542839291492772111971777338125) + A[10,6]=-BigInt(30230616135053261889365940573714713926595600173797519397657905897494488117634591)//BigInt(1462739064177653822206630548583223553011887775071057363338006334613651993472000) A[10,7]=-3556025825918703192187464108779875//11170666795578957880984290260063232 A[10,8]=2140578935503723938488131712//2556174768949326564363043125 A[10,9]=0 @@ -3565,7 +3565,7 @@ function constructTanakaYamashitaStable7(T::Type = Float64) α[3]=0 α[4]=-5319231056637407390089058139231875//4078513870347642725257280732562048 α[5]=2430832495624902882205404599808//1640677233246140147577399278125 - α[6]=58846832125102891510730576086257275195560457005949780449038492433452787//55051022626529988904867724618756855605285697694381512902783594390080000 + α[6]=BigInt(58846832125102891510730576086257275195560457005949780449038492433452787)//BigInt(55051022626529988904867724618756855605285697694381512902783594390080000) α[7]=8765694250492187515737289375//142862058843931893355781359104 α[8]=282726763309436004945812396032//864839130161188820942829590625 α[9]=35795813026789129771//507885604115513709330 @@ -3575,7 +3575,7 @@ function constructTanakaYamashitaStable7(T::Type = Float64) αEEst[3]=0 αEEst[4]=-2188638181830974432849378205625//2703688346269567600435718085888 αEEst[5]=1313681506776569792299836438//1214416900996402773928496875 - αEEst[6]=3205635250634133320066291736997892470430172563677735127041069//5224293273794925935053617011014728265925425567271645535360000 + αEEst[6]=BigInt(3205635250634133320066291736997892470430172563677735127041069)//BigInt(5224293273794925935053617011014728265925425567271645535360000) αEEst[7]=153260086062341088187716875//1103181921574763655256998912 αEEst[8]=1144102534493369691260897984//4260291281582210940605071875 αEEst[9]=0 @@ -3915,54 +3915,54 @@ function constructEnrightVerner8(T::Type = Float64) A[8,5]=-29670244019740727//6363654238520000 A[8,6]=503350581600824913//125990342179812500 A[8,7]=9 - A[9,1]=-16045918035544526531085666708200976799092954349059102554439418058855237034803138076235914485211856830024864166368323768200//9829483157728664844198544034921655975378257830080951893693520116322068439377446708493269493633244146421522730587295739613 + A[9,1]=-BigInt(16045918035544526531085666708200976799092954349059102554439418058855237034803138076235914485211856830024864166368323768200)//BigInt(9829483157728664844198544034921655975378257830080951893693520116322068439377446708493269493633244146421522730587295739613) A[9,2]=0 A[9,3]=0 - A[9,4]=-2358539147881877873039445811751103289867403691705393271280994482043263320271984518766662589229245453919623760032009543680000000//217835526181955565558022800341429464086385172122906608031349543583863022015887117168566338470163090032498196064101837445053273 - A[9,5]=-991136638972626168678903371416456100093900405535164924683058122802429707354033382826947398158683765324439618282500000000//79848142008846002789298925227605775190331269194726743910364273272231784282184770467794155269096224513726772081370189773 - A[9,6]=99411279821210413387149352497211785829547149358696952646781033905129048593757052549024957474512389085654050445280000000//10219750071154355529199360565479179548497227516418867455143546824991883616697162903707552409044338358355837306818391433 - A[9,7]=194327599672380134095898291719912961363678073793023525007081328425098431574448809779310732532821200046895000000000//11996011488227722649656673931136490891256463292620473601841875115170259043531987881275965965525693289412424400177 - A[9,8]=-4738143867684122189593816244199450540483384372163549951990525387550768038015218275414120082248510000000000//45627381556119209828916528385326434273376137158228892503158792567081801761628344925618992749059885819540261 - A[10,1]=100509763879264306824096153463041174636629364248095333923106653001873//229490324007644628042361756217436155832461488260089524115475000000000 + A[9,4]=-BigInt(2358539147881877873039445811751103289867403691705393271280994482043263320271984518766662589229245453919623760032009543680000000)//BigInt(217835526181955565558022800341429464086385172122906608031349543583863022015887117168566338470163090032498196064101837445053273) + A[9,5]=-BigInt(991136638972626168678903371416456100093900405535164924683058122802429707354033382826947398158683765324439618282500000000)//BigInt(79848142008846002789298925227605775190331269194726743910364273272231784282184770467794155269096224513726772081370189773) + A[9,6]=BigInt(99411279821210413387149352497211785829547149358696952646781033905129048593757052549024957474512389085654050445280000000)//BigInt(10219750071154355529199360565479179548497227516418867455143546824991883616697162903707552409044338358355837306818391433) + A[9,7]=BigInt(194327599672380134095898291719912961363678073793023525007081328425098431574448809779310732532821200046895000000000)//BigInt(11996011488227722649656673931136490891256463292620473601841875115170259043531987881275965965525693289412424400177) + A[9,8]=-BigInt(4738143867684122189593816244199450540483384372163549951990525387550768038015218275414120082248510000000000)//BigInt(45627381556119209828916528385326434273376137158228892503158792567081801761628344925618992749059885819540261) + A[10,1]=BigInt(100509763879264306824096153463041174636629364248095333923106653001873)//BigInt(229490324007644628042361756217436155832461488260089524115475000000000) A[10,2]=0 A[10,3]=0 - A[10,4]=35076261889213578261995286390053983221937920015616//8903662403052468890234321680409039895089390971875 - A[10,5]=29877053472248545227782869189767925950557009//10443709158645362958089905740134206606110000 - A[10,6]=-72602025182798889442893966553844286012776770019588838776297031451//40918439380405007926071673834718276106178863851548244800289187500 - A[10,7]=-15322912063864370512130145988492098605486502994107816190//3130069400645604876183669549605539076333579290524919889 - A[10,8]=66085154677219418645471125072555541174985695924//310222736648235062495097951962638800384203417327 - A[10,9]=-33475654618965607625490266678231230366345830527265525310030016230875755239420324728600957368877132012320553021//563607181486505082775419237614873016043169125130359330269370345097328575740250457475506596993780051575000000000 - A[11,1]=-5101097760197841615137571256611109219669965728737004453654940399435749927779//3460254790065218498025394912113654440547987641021174968985010753183759952128 + A[10,4]=BigInt(35076261889213578261995286390053983221937920015616)//BigInt(8903662403052468890234321680409039895089390971875) + A[10,5]=BigInt(29877053472248545227782869189767925950557009)//BigInt(10443709158645362958089905740134206606110000) + A[10,6]=-BigInt(72602025182798889442893966553844286012776770019588838776297031451)//BigInt(40918439380405007926071673834718276106178863851548244800289187500) + A[10,7]=-BigInt(15322912063864370512130145988492098605486502994107816190)//BigInt(3130069400645604876183669549605539076333579290524919889) + A[10,8]=BigInt(66085154677219418645471125072555541174985695924)//BigInt(310222736648235062495097951962638800384203417327) + A[10,9]=-BigInt(33475654618965607625490266678231230366345830527265525310030016230875755239420324728600957368877132012320553021)//BigInt(563607181486505082775419237614873016043169125130359330269370345097328575740250457475506596993780051575000000000) + A[11,1]=-BigInt(5101097760197841615137571256611109219669965728737004453654940399435749927779)//BigInt(3460254790065218498025394912113654440547987641021174968985010753183759952128) A[11,2]=0 A[11,3]=0 - A[11,4]=-739282853758412257967453242147288028248514875000//67244182875654829098323943713374207709631980757 - A[11,5]=-304301954438407952266341438991435702455078125//26817588459995310678515661957421952038871616 - A[11,6]=7944893992399893116476631697520363855501654462308622798446100145004371780765625//887005161602928659252827604035768657298435884939489754462273147402132735951354 - A[11,7]=271466662889835128614810796916069488062485834784939879774912795880859375//17080057868208807584911919572395871967414618088449127584294090356526117 - A[11,8]=-547671639173493535187249719091874257724281347519101322819710937500//5545897345777551056363997101744668576293320106258184122878184564689 - A[11,9]=278805054229456473051914785770130401056277521071386274820253852826023602554035252878888463451556710568650135086751734733498388408614837563//57032789758993842471673989706725819315996341861372243823982103984407642346136141015055914541200747733442561186185728215790313661884647470336 - A[11,10]=-7641031089620713267943821483116886435546875//1865115549729059107236140767953375513727732867 - A[12,1]=-2173296165244568434534168496725754283210370856714048295955495704392191998074219//826329709817197468253912814996276721297719271873047121496939265708086637102000 + A[11,4]=-BigInt(739282853758412257967453242147288028248514875000)//BigInt(67244182875654829098323943713374207709631980757) + A[11,5]=-BigInt(304301954438407952266341438991435702455078125)//BigInt(26817588459995310678515661957421952038871616) + A[11,6]=BigInt(7944893992399893116476631697520363855501654462308622798446100145004371780765625)//BigInt(887005161602928659252827604035768657298435884939489754462273147402132735951354) + A[11,7]=BigInt(271466662889835128614810796916069488062485834784939879774912795880859375)//BigInt(17080057868208807584911919572395871967414618088449127584294090356526117) + A[11,8]=-BigInt(547671639173493535187249719091874257724281347519101322819710937500)//BigInt(5545897345777551056363997101744668576293320106258184122878184564689) + A[11,9]=BigInt(278805054229456473051914785770130401056277521071386274820253852826023602554035252878888463451556710568650135086751734733498388408614837563)//BigInt(57032789758993842471673989706725819315996341861372243823982103984407642346136141015055914541200747733442561186185728215790313661884647470336) + A[11,10]=-BigInt(7641031089620713267943821483116886435546875)//BigInt(1865115549729059107236140767953375513727732867) + A[12,1]=-BigInt(2173296165244568434534168496725754283210370856714048295955495704392191998074219)//BigInt(826329709817197468253912814996276721297719271873047121496939265708086637102000) A[12,2]=0 A[12,3]=0 - A[12,4]=-1176485889334472345397948024769479865991267657667189808793600000//128238274125745784857395023683055391720808636521055761250085619 - A[12,5]=-901641526273088667293677983960434306145731566007759375000//47006051321531726477650870675115597779536141098588395119 - A[12,6]=44619197709345843038609995810290222092713734357503573021289399188441075277893825000//3047226829867759667805678237083584916028456629069014496162891378892137605913688013 - A[12,7]=948339742665210716931560767459705347432692833888702670755668800833857753125000//54100203068523816523920547203712158257383235486719126879290708372319555115953 - A[12,8]=-469359986530784242367841163967997985280992052062479522694037718750000//1262000068797740029604893636717124646814536106030908513651797310900389 - A[12,9]=-664127481006260866245417353167879111725438608160134129788715555378465573117813001757238260693051901812594341608922016461968723754067215934799054852630446938063//947405313675779327886462044861834846879473861539583479995101168291116168844040438751584392785913224239894029843821464363224405440877235651675827150051218506000 - A[12,10]=124594688949431236718278718078688571245967961641584151713065625000//2442266119995123914599926487344630873565880304003136401896150897137 - A[12,11]=561064742310110985699639624014768981793940948761680464947352//671379391526329055316725343694451428305592235340194400714475 - A[13,1]=2112537365439605317842214400294939600845864356126794907105288476157299972777//9791129992576348954381966935712572673760150144277222568673000574989723295600 + A[12,4]=-BigInt(1176485889334472345397948024769479865991267657667189808793600000)//BigInt(128238274125745784857395023683055391720808636521055761250085619) + A[12,5]=-BigInt(901641526273088667293677983960434306145731566007759375000)//BigInt(47006051321531726477650870675115597779536141098588395119) + A[12,6]=BigInt(44619197709345843038609995810290222092713734357503573021289399188441075277893825000)//BigInt(3047226829867759667805678237083584916028456629069014496162891378892137605913688013) + A[12,7]=BigInt(948339742665210716931560767459705347432692833888702670755668800833857753125000)//BigInt(54100203068523816523920547203712158257383235486719126879290708372319555115953) + A[12,8]=-BigInt(469359986530784242367841163967997985280992052062479522694037718750000)//BigInt(1262000068797740029604893636717124646814536106030908513651797310900389) + A[12,9]=-BigInt(664127481006260866245417353167879111725438608160134129788715555378465573117813001757238260693051901812594341608922016461968723754067215934799054852630446938063)//BigInt(947405313675779327886462044861834846879473861539583479995101168291116168844040438751584392785913224239894029843821464363224405440877235651675827150051218506000) + A[12,10]=BigInt(124594688949431236718278718078688571245967961641584151713065625000)//BigInt(2442266119995123914599926487344630873565880304003136401896150897137) + A[12,11]=BigInt(561064742310110985699639624014768981793940948761680464947352)//BigInt(671379391526329055316725343694451428305592235340194400714475) + A[13,1]=BigInt(2112537365439605317842214400294939600845864356126794907105288476157299972777)//BigInt(9791129992576348954381966935712572673760150144277222568673000574989723295600) A[13,2]=0 A[13,3]=0 - A[13,4]=63401732568650174882469655273037557867024014649473659852800000//7597437179564699900056826682790095876501867794005624909986891 - A[13,5]=6086761737797404637560639819223305802258863489403125000//2784859079002788542258846760345051095481316496802932391 - A[13,6]=-2559665601805637409198888850698428172565517218973577146475607855715703433900000//1517075781450111169555356439342115045941218379260955323225394329122945220575603 - A[13,7]=-3562962724414944757891560164749973139486260772587248231213362868690625000//408976639178968899516222045518619849445955714595234573207901740578867341 - A[13,8]=27274774093948890572327172846505411328624378015249298079900000000//1115922486918625141794316350997246426030217325603407120793811703663 - A[13,9]=1517649980273287794810711480928689762969941359446589355244683243470868873980537462717945530891242892188019850453060256773054273287757818339//17931096351403549517324822951619492690590259109554169692111771494162805088297821242848492102923447532215742446890559805801281057084758250800 - A[13,10]=36524642706569597276845612368244490741747970924877885921875000//67204508345515429491838411146746729660269255184823759889942481 + A[13,4]=BigInt(63401732568650174882469655273037557867024014649473659852800000)//BigInt(7597437179564699900056826682790095876501867794005624909986891) + A[13,5]=BigInt(6086761737797404637560639819223305802258863489403125000)//BigInt(2784859079002788542258846760345051095481316496802932391) + A[13,6]=-BigInt(2559665601805637409198888850698428172565517218973577146475607855715703433900000)//BigInt(1517075781450111169555356439342115045941218379260955323225394329122945220575603) + A[13,7]=-BigInt(3562962724414944757891560164749973139486260772587248231213362868690625000)//BigInt(408976639178968899516222045518619849445955714595234573207901740578867341) + A[13,8]=BigInt(27274774093948890572327172846505411328624378015249298079900000000)//BigInt(1115922486918625141794316350997246426030217325603407120793811703663) + A[13,9]=BigInt(1517649980273287794810711480928689762969941359446589355244683243470868873980537462717945530891242892188019850453060256773054273287757818339)//BigInt(17931096351403549517324822951619492690590259109554169692111771494162805088297821242848492102923447532215742446890559805801281057084758250800) + A[13,10]=BigInt(36524642706569597276845612368244490741747970924877885921875000)//BigInt(67204508345515429491838411146746729660269255184823759889942481) A[13,11]=0 A[13,12]=0 α[1]=55284231195707975647126708111723//1258814250475014554517603612114000 @@ -3970,11 +3970,11 @@ function constructEnrightVerner8(T::Type = Float64) α[3]=0 α[4]=0 α[5]=0 - α[6]=101652048214282205518610445783893750000000//289586658278060310247144250081091360673509 - α[7]=6219731958882093270433753490048828125000000//25268792314562899182186819800834272764054341 - α[8]=471525882014932587321673707929687500000000//523728817391198795728810839649314044495553 - α[9]=63998419659074502960979467027044380533513499562179716145788153981258354882170183557294261050806789914954901252698438375102943237148428019253408419//14067383878224159980676935999500324267727723947516309536464061683130063437616452951326819824531063499969576146304645311203502485409773697867038000 - α[10]=594562755257530592552224345703125000000//123802720910327682301431417435953442122031 + α[6]=BigInt(101652048214282205518610445783893750000000)//BigInt(289586658278060310247144250081091360673509) + α[7]=BigInt(6219731958882093270433753490048828125000000)//BigInt(25268792314562899182186819800834272764054341) + α[8]=BigInt(471525882014932587321673707929687500000000)//BigInt(523728817391198795728810839649314044495553) + α[9]=BigInt(63998419659074502960979467027044380533513499562179716145788153981258354882170183557294261050806789914954901252698438375102943237148428019253408419)//BigInt(14067383878224159980676935999500324267727723947516309536464061683130063437616452951326819824531063499969576146304645311203502485409773697867038000) + α[10]=BigInt(594562755257530592552224345703125000000)//BigInt(123802720910327682301431417435953442122031) α[11]=-1886691133979705639959153870454656//397947585885835383951563312487675 α[12]=-50061468875139778913910254637881//141186641936036184819986782313781 α[13]=0 @@ -3983,11 +3983,11 @@ function constructEnrightVerner8(T::Type = Float64) αEEst[3]=0 αEEst[4]=0 αEEst[5]=0 - αEEst[6]=91472553308336221233020750122000000000//270389036674192633283981559366098375979 - αEEst[7]=31245710879106859500854236329453125000000//125747467177230198813995913261775760852127 - αEEst[8]=7580382785455138868782239796250000000000//33873008089978031564549954803189465564389 - αEEst[9]=-1264668207534772000389416909088295806823076185957298091511366356638145411319432807599860924173256812108555319505561297378438513//31458133682363879376359837328611310990099259233936346807079836410100132902013789877583819562913435723874810037875576750158649200 - αEEst[10]=2363202400377740499662213515625000000//19167474982246118950523520271861502109 + αEEst[6]=BigInt(91472553308336221233020750122000000000)//BigInt(270389036674192633283981559366098375979) + αEEst[7]=BigInt(31245710879106859500854236329453125000000)//BigInt(125747467177230198813995913261775760852127) + αEEst[8]=BigInt(7580382785455138868782239796250000000000)//BigInt(33873008089978031564549954803189465564389) + αEEst[9]=-BigInt(1264668207534772000389416909088295806823076185957298091511366356638145411319432807599860924173256812108555319505561297378438513)//BigInt(31458133682363879376359837328611310990099259233936346807079836410100132902013789877583819562913435723874810037875576750158649200) + αEEst[10]=BigInt(2363202400377740499662213515625000000)//BigInt(19167474982246118950523520271861502109) αEEst[11]=0 αEEst[12]=0 αEEst[13]=2965876353908674111604434604609//47062213978678728273328927437927 @@ -4049,14 +4049,14 @@ function constructdverk78(T::Type = Float64) A[8,5]=-8339128164608//939060038475 A[8,6]=341936800488//47951126225 A[8,7]=1993321838240//380523459069 - A[9,1]=-1840911252282376584438157336464708426954728061551//2991923615171151921596253813483118262195533733898 + A[9,1]=-BigInt(1840911252282376584438157336464708426954728061551)//BigInt(2991923615171151921596253813483118262195533733898) A[9,2]=0 A[9,3]=0 - A[9,4]=-14764960804048657303638372252908780219281424435//2981692102565021975611711269209606363661854518 - A[9,5]=-875325048502130441118613421785266742862694404520560000//170212030428894418395571677575961339495435011888324169 - A[9,6]=7632051964154290925661849798370645637589377834346780//1734087257418811583049800347581865260479233950396659 - A[9,7]=7519834791971137517048532179652347729899303513750000//1045677303502317596597890707812349832637339039997351 - A[9,8]=1366042683489166351293315549358278750//144631418224267718165055326464180836641 + A[9,4]=-BigInt(14764960804048657303638372252908780219281424435)//BigInt(2981692102565021975611711269209606363661854518) + A[9,5]=-BigInt(875325048502130441118613421785266742862694404520560000)//BigInt(170212030428894418395571677575961339495435011888324169) + A[9,6]=BigInt(7632051964154290925661849798370645637589377834346780)//BigInt(1734087257418811583049800347581865260479233950396659) + A[9,7]=BigInt(7519834791971137517048532179652347729899303513750000)//BigInt(1045677303502317596597890707812349832637339039997351) + A[9,8]=BigInt(1366042683489166351293315549358278750)//BigInt(144631418224267718165055326464180836641) A[10,1]=-63077736705254280154824845013881//78369357853786633855112190394368 A[10,2]=0 A[10,3]=0 @@ -4065,26 +4065,26 @@ function constructdverk78(T::Type = Float64) A[10,6]=1001587844183325981198091450220795//184232684207722503701669953872896 A[10,7]=187023075231349900768014890274453125//25224698849808178010752575653374848 A[10,8]=1908158550070998850625//117087067039189929394176 - A[10,9]=-52956818288156668227044990077324877908565//2912779959477433986349822224412353951940608 - A[11,1]=-10116106591826909534781157993685116703//9562819945036894030442231411871744000 + A[10,9]=-BigInt(52956818288156668227044990077324877908565)//BigInt(2912779959477433986349822224412353951940608) + A[11,1]=-BigInt(10116106591826909534781157993685116703)//BigInt(9562819945036894030442231411871744000) A[11,2]=0 A[11,3]=0 A[11,4]=-9623541317323077848129//3864449564977792573440 A[11,5]=-4823348333146829406881375//576413233634141239944816 - A[11,6]=6566119246514996884067001154977284529//970305487021846325473990863582315520 - A[11,7]=2226455130519213549256016892506730559375//364880443159675255577435648380047355776 + A[11,6]=BigInt(6566119246514996884067001154977284529)//BigInt(970305487021846325473990863582315520) + A[11,7]=BigInt(2226455130519213549256016892506730559375)//BigInt(364880443159675255577435648380047355776) A[11,8]=39747262782380466933662225//1756032802431424164410720256 - A[11,9]=48175771419260955335244683805171548038966866545122229//1989786420513815146528880165952064118903852843612160000 + A[11,9]=BigInt(48175771419260955335244683805171548038966866545122229)//BigInt(1989786420513815146528880165952064118903852843612160000) A[11,10]=-2378292068163246//47768728487211875 A[12,1]=-3218022174758599831659045535578571//1453396753634469525663775847094384 A[12,2]=0 A[12,3]=0 A[12,4]=26290092604284231996745//5760876126062860430544 A[12,5]=-697069297560926452045586710000//41107967755245430594036502319 - A[12,6]=1827357820434213461438077550902273440//139381013914245317709567680839641697 - A[12,7]=643504802814241550941949227194107500000//242124609118836550860494007545333945331 + A[12,6]=BigInt(1827357820434213461438077550902273440)//BigInt(139381013914245317709567680839641697) + A[12,7]=BigInt(643504802814241550941949227194107500000)//BigInt(242124609118836550860494007545333945331) A[12,8]=162259938151380266113750//59091082835244183497007 - A[12,9]=-23028251632873523818545414856857015616678575554130463402//20013169183191444503443905240405603349978424504151629055 + A[12,9]=-BigInt(23028251632873523818545414856857015616678575554130463402)//BigInt(20013169183191444503443905240405603349978424504151629055) A[12,10]=7958341351371843889152//3284467988443203581305 A[12,11]=-507974327957860843878400//121555654819179042718967 A[13,1]=-549080624436801105208519835138333//353987109028707139687100885600400 @@ -4093,9 +4093,9 @@ function constructdverk78(T::Type = Float64) A[13,4]=29116675312186033956481//5331818957833865866320 A[13,5]=-91153092961177216058210567600//7609267653017028089793994539 A[13,6]=1540775569495234383390307262972464//164751248733597841985831445059895 - A[13,7]=-2027488254536386321212021357622300000//7563800784313191306927092359781550321 + A[13,7]=-BigInt(2027488254536386321212021357622300000)//BigInt(7563800784313191306927092359781550321) A[13,8]=-707592954577756600025//2430671607007101253926 - A[13,9]=-315869406877370103440389763510384832076674110731//550845901016714794114516357859531754926300500125 + A[13,9]=-BigInt(315869406877370103440389763510384832076674110731)//BigInt(550845901016714794114516357859531754926300500125) A[13,10]=4305840920849725632512//5066413598663346018375 A[13,11]=0 A[13,12]=0 @@ -4107,7 +4107,7 @@ function constructdverk78(T::Type = Float64) α[6]=14327219974204125//40489566827933216 α[7]=2720762324010009765625000//10917367480696813922225349 α[8]=-498533005859375//95352091037424 - α[9]=405932030463777247926705030596175437402459637909765779//78803919436321841083201886041201537229769115088303952 + α[9]=BigInt(405932030463777247926705030596175437402459637909765779)//BigInt(78803919436321841083201886041201537229769115088303952) α[10]=-10290327637248//1082076946951 α[11]=863264105888000//85814662253313 α[12]=-29746300739//247142463456 @@ -4120,7 +4120,7 @@ function constructdverk78(T::Type = Float64) αEEst[6]=495437430316125//1396191959583904 αEEst[7]=760741072216796875000//3055518466469861159313 αEEst[8]=1186143278515625//444976424841312 - αEEst[9]=13791579353894559147128282108092181066885426809//3515333032435874239702147176443897942760320040 + αEEst[9]=BigInt(13791579353894559147128282108092181066885426809)//BigInt(3515333032435874239702147176443897942760320040) αEEst[10]=-30733299644928//5410384734755 αEEst[11]=0 αEEst[12]=0 @@ -4184,53 +4184,53 @@ function constructTsitourasPapakostas8(T::Type = Float64) A[8,5]=-318556182235222634647116091//27172411532484037214054400 A[8,6]=1205563885850790193966807//132365727505912221222912 A[8,7]=254//39 - A[9,1]=-20629396399716689122801179264428539394462855874226604463554767070845753369//42881759662770155956657513470012114488076017981128105307375594963152353200 + A[9,1]=-BigInt(20629396399716689122801179264428539394462855874226604463554767070845753369)//BigInt(42881759662770155956657513470012114488076017981128105307375594963152353200) A[9,2]=0 A[9,3]=0 - A[9,4]=-3315443074343659404779422149387397712986453181141168247590906370819301077749322753//498517112641608872807821838566847987729514312398278633788185835348997643218553476 - A[9,5]=-273749409411654060286948141164828452109898379203526945684314474186724062841643//60427583951377552503967840653825589117167443021628367691773162913607984889600 - A[9,6]=16656372518874512738268060504309924900437672263609245028809229865738327731797537//4276990138533930522782076385771016009097627930550149628282203007913538394549504 - A[9,7]=42008080033354305590804322944084805264441066760038302359736803632//4865302423216534910074823287811605599629170295030631799935804001 - A[9,8]=668459780930716338000066627236927417191947396177093524377824//71100452948884643779799087713322002499799983434685642170251833 - A[10,1]=-1793603946322260900828212460706877142477132870159527//2313097568511990753781649719556084665131024900300800 + A[9,4]=-BigInt(3315443074343659404779422149387397712986453181141168247590906370819301077749322753)//BigInt(498517112641608872807821838566847987729514312398278633788185835348997643218553476) + A[9,5]=-BigInt(273749409411654060286948141164828452109898379203526945684314474186724062841643)//BigInt(60427583951377552503967840653825589117167443021628367691773162913607984889600) + A[9,6]=BigInt(16656372518874512738268060504309924900437672263609245028809229865738327731797537)//BigInt(4276990138533930522782076385771016009097627930550149628282203007913538394549504) + A[9,7]=BigInt(42008080033354305590804322944084805264441066760038302359736803632)//BigInt(4865302423216534910074823287811605599629170295030631799935804001) + A[9,8]=BigInt(668459780930716338000066627236927417191947396177093524377824)//BigInt(71100452948884643779799087713322002499799983434685642170251833) + A[10,1]=-BigInt(1793603946322260900828212460706877142477132870159527)//BigInt(2313097568511990753781649719556084665131024900300800) A[10,2]=0 A[10,3]=0 - A[10,4]=-14776874123722838192315406145167687512425345723701//1847893530366076701102014146927696206329050105856 - A[10,5]=-19587020919884661714856757105130246995757906603//2911893296942532038566182868170393629789388800 - A[10,6]=6364380863259071677112259236455506477417699780613300364807//1150428174584942133406579091549443438814988349188394057728 - A[10,7]=27725164402569748756040320433848245155581006369//2544159473655547770881695354241256106302348256 - A[10,8]=10744247163960019876833255044784609639//534761804739901348825491947768304503296 - A[10,9]=-50977737930792808232204417497248979399878217280011103197862899//1300915694564913675613280314081837358644964393191337994183389184 - A[11,1]=-3587625717068952487214493441966897048737050755812600710793//3015733164033229624772006086429467685046639983706974412800 + A[10,4]=-BigInt(14776874123722838192315406145167687512425345723701)//BigInt(1847893530366076701102014146927696206329050105856) + A[10,5]=-BigInt(19587020919884661714856757105130246995757906603)//BigInt(2911893296942532038566182868170393629789388800) + A[10,6]=BigInt(6364380863259071677112259236455506477417699780613300364807)//BigInt(1150428174584942133406579091549443438814988349188394057728) + A[10,7]=BigInt(27725164402569748756040320433848245155581006369)//BigInt(2544159473655547770881695354241256106302348256) + A[10,8]=BigInt(10744247163960019876833255044784609639)//BigInt(534761804739901348825491947768304503296) + A[10,9]=-BigInt(50977737930792808232204417497248979399878217280011103197862899)//BigInt(1300915694564913675613280314081837358644964393191337994183389184) + A[11,1]=-BigInt(3587625717068952487214493441966897048737050755812600710793)//BigInt(3015733164033229624772006086429467685046639983706974412800) A[11,2]=0 A[11,3]=0 - A[11,4]=-5453011711267804731211501837262816944661201619903//764973320899716397072448644710733101329290196992 - A[11,5]=-884348836774584715070440485633026464653487653//92725983515963799584249219499787659014963200 - A[11,6]=26823469063654084387375587616552322383082061411417182757389742951//3541299744763681675473620647087123057228744296123642301654630400 - A[11,7]=142363419491686507162007051071007722765323162710521029//12634887202368261565807449771335728082273587905775840 - A[11,8]=64747617454909275289531520412519442831235890581//1269317188117975960996670628974453443777854830080 - A[11,9]=112633808253272720979874303367503891597499261046700689572459050065039333987335667//1404514291245034532812181377119034501014039830518218465064579291611563374608650240 - A[11,10]=-10612202518573994431153697720606405883//67082546658259846778754594976831647575 - A[12,1]=-7534081165544982478296202335922049210803875045423//19219575665440848756074598051658416387002479820800 + A[11,4]=-BigInt(5453011711267804731211501837262816944661201619903)//BigInt(764973320899716397072448644710733101329290196992) + A[11,5]=-BigInt(884348836774584715070440485633026464653487653)//BigInt(92725983515963799584249219499787659014963200) + A[11,6]=BigInt(26823469063654084387375587616552322383082061411417182757389742951)//BigInt(3541299744763681675473620647087123057228744296123642301654630400) + A[11,7]=BigInt(142363419491686507162007051071007722765323162710521029)//BigInt(12634887202368261565807449771335728082273587905775840) + A[11,8]=BigInt(64747617454909275289531520412519442831235890581)//BigInt(1269317188117975960996670628974453443777854830080) + A[11,9]=BigInt(112633808253272720979874303367503891597499261046700689572459050065039333987335667)//BigInt(1404514291245034532812181377119034501014039830518218465064579291611563374608650240) + A[11,10]=-BigInt(10612202518573994431153697720606405883)//BigInt(67082546658259846778754594976831647575) + A[12,1]=-BigInt(7534081165544982478296202335922049210803875045423)//BigInt(19219575665440848756074598051658416387002479820800) A[12,2]=0 A[12,3]=0 - A[12,4]=237696087452786717802270375283034262859273455//60688480889936839261131818793519097177034752 - A[12,5]=-20610578209826329263318986584876108069323//7356333776438834884293014575840932659200 - A[12,6]=51260471529841028040709654458903254781320136131844164563//20998023776318546907382302106788168158765514131585630208 - A[12,7]=-3077214437173472971196810795615384000211457151011//1272435592582280820597059432060116893200684680384 - A[12,8]=-1539218116260541896259682954580256454049//4534670830750360983422999946409310393344 - A[12,9]=241886539350268429372116296787271276553970618941104594460614948326132797451456131//1240669632662465892528916120041123051054026283188324780101555345343662316090597376 + A[12,4]=BigInt(237696087452786717802270375283034262859273455)//BigInt(60688480889936839261131818793519097177034752) + A[12,5]=-BigInt(20610578209826329263318986584876108069323)//BigInt(7356333776438834884293014575840932659200) + A[12,6]=BigInt(51260471529841028040709654458903254781320136131844164563)//BigInt(20998023776318546907382302106788168158765514131585630208) + A[12,7]=-BigInt(3077214437173472971196810795615384000211457151011)//BigInt(1272435592582280820597059432060116893200684680384) + A[12,8]=-BigInt(1539218116260541896259682954580256454049)//BigInt(4534670830750360983422999946409310393344) + A[12,9]=BigInt(241886539350268429372116296787271276553970618941104594460614948326132797451456131)//BigInt(1240669632662465892528916120041123051054026283188324780101555345343662316090597376) A[12,10]=-80556486832245966191717452425924975//414445409518676597565032008051106461 - A[12,11]=2944781680874500347594142792814463350//4965161383073676983610218096030654529 - A[13,1]=-7757739937862944832927743694336116203639371542761//5225100678421794325654850845451340473577260032000 + A[12,11]=BigInt(2944781680874500347594142792814463350)//BigInt(4965161383073676983610218096030654529) + A[13,1]=-BigInt(7757739937862944832927743694336116203639371542761)//BigInt(5225100678421794325654850845451340473577260032000) A[13,2]=0 A[13,3]=0 - A[13,4]=-433889546009521405913741133329446636837810749//181488796115643001621310691169322233346938880 - A[13,5]=-246044720162308748108107126829066792329071//21999103311417807170100413255475150848000 - A[13,6]=2140331235425829844389060818616719848637810765257179167//245428182036011897638028252815369258646052549878743040 - A[13,7]=1573990926219809229258666534611598771063240529//214535514317495538101650508596881057760818080 - A[13,8]=62408280667309375445301959066100433563//4838320046251983849512355559327451645440 - A[13,9]=1145609822249493677618113725359506642998153205603226883141207089968379//26902802166822768476367427840835743139559294105398677975568538466119680 + A[13,4]=-BigInt(433889546009521405913741133329446636837810749)//BigInt(181488796115643001621310691169322233346938880) + A[13,5]=-BigInt(246044720162308748108107126829066792329071)//BigInt(21999103311417807170100413255475150848000) + A[13,6]=BigInt(2140331235425829844389060818616719848637810765257179167)//BigInt(245428182036011897638028252815369258646052549878743040) + A[13,7]=BigInt(1573990926219809229258666534611598771063240529)//BigInt(214535514317495538101650508596881057760818080) + A[13,8]=BigInt(62408280667309375445301959066100433563)//BigInt(4838320046251983849512355559327451645440) + A[13,9]=BigInt(1145609822249493677618113725359506642998153205603226883141207089968379)//BigInt(26902802166822768476367427840835743139559294105398677975568538466119680) A[13,10]=-408950356875874683139089678053832//7674292714443204070455739595109785 A[13,11]=0 A[13,12]=0 @@ -4242,7 +4242,7 @@ function constructTsitourasPapakostas8(T::Type = Float64) α[6]=2335496795323782464411846394611//6598368783294020109895379936256 α[7]=7636073376527143565375240869888//30725949199261296642046754748645 α[8]=-4237087214169934312729607487//12735791394214625116604076160 - α[9]=408505291291133241760995514121984335914363927884426780078325258228227984174126699//212624874612193697466655159405635202123821166475348052734199905546455860773575680 + α[9]=BigInt(408505291291133241760995514121984335914363927884426780078325258228227984174126699)//BigInt(212624874612193697466655159405635202123821166475348052734199905546455860773575680) α[10]=-1108225296327029096435947//405679075893979729103310 α[11]=2460988291206213825688467985//1756342789520947764222671739 α[12]=4808707937311//50545545388065 @@ -4255,7 +4255,7 @@ function constructTsitourasPapakostas8(T::Type = Float64) αEEst[6]=62284335162928966987066121//175437206755843240272669696 αEEst[7]=184309146777472302831695872//742417767522160213324368465 αEEst[8]=-509771598215811385123057257//210282269969085698264101760 - αEEst[9]=2701602489646143640362891402924962500766379885231830470264478480621389//1688575269294196295712420798364925687791337062814161130291144634516480 + αEEst[9]=BigInt(2701602489646143640362891402924962500766379885231830470264478480621389)//BigInt(1688575269294196295712420798364925687791337062814161130291144634516480) αEEst[10]=-7218534073012286740367561//3986456306153224954098780 αEEst[11]=0 αEEst[12]=0 @@ -4278,11 +4278,11 @@ function constructVernerRobust9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//25 - c[3]=48//335-32//1675*6^(1//2) - c[4]=72//335-48//1675*6^(1//2) + c[3]=BigInt(48)//BigInt(335)-BigInt(32)//BigInt(1675)*6^(1//2) + c[4]=BigInt(72)//BigInt(335)-BigInt(48)//BigInt(1675)*6^(1//2) c[5]=72//125 - c[6]=48//125-8//125*6^(1//2) - c[7]=48//125+8//125*6^(1//2) + c[6]=BigInt(48)//BigInt(125)-BigInt(8)//BigInt(125)*6^(1//2) + c[7]=BigInt(48)//BigInt(125)+BigInt(8)//BigInt(125)*6^(1//2) c[8]=16//25 c[9]=12//25 c[10]=3377//50000 @@ -4293,123 +4293,123 @@ function constructVernerRobust9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//25 - A[3,1]=-15792//112225+5536//112225*6^(1//2) - A[3,2]=31872//112225-1536//22445*6^(1//2) - A[4,1]=18//335-12//1675*6^(1//2) + A[3,1]=-BigInt(15792)//BigInt(112225)+BigInt(5536)//BigInt(112225)*6^(1//2) + A[3,2]=BigInt(31872)//BigInt(112225)-BigInt(1536)//BigInt(22445)*6^(1//2) + A[4,1]=BigInt(18)//BigInt(335)-BigInt(12)//BigInt(1675)*6^(1//2) A[4,2]=0 - A[4,3]=54//335-36//1675*6^(1//2) - A[5,1]=4014//3125+252//625*6^(1//2) + A[4,3]=BigInt(54)//BigInt(335)-BigInt(36)//BigInt(1675)*6^(1//2) + A[5,1]=BigInt(4014)//BigInt(3125)+BigInt(252)//BigInt(625)*6^(1//2) A[5,2]=0 - A[5,3]=-14742//3125-972//625*6^(1//2) - A[5,4]=12528//3125+144//125*6^(1//2) - A[6,1]=1232//16875-152//16875*6^(1//2) + A[5,3]=-BigInt(14742)//BigInt(3125)-BigInt(972)//BigInt(625)*6^(1//2) + A[5,4]=BigInt(12528)//BigInt(3125)+BigInt(144)//BigInt(125)*6^(1//2) + A[6,1]=BigInt(1232)//BigInt(16875)-BigInt(152)//BigInt(16875)*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=29684//106875-13372//320625*6^(1//2) - A[6,5]=2132//64125-284//21375*6^(1//2) - A[7,1]=2032//16875+152//16875*6^(1//2) + A[6,4]=BigInt(29684)//BigInt(106875)-BigInt(13372)//BigInt(320625)*6^(1//2) + A[6,5]=BigInt(2132)//BigInt(64125)-BigInt(284)//BigInt(21375)*6^(1//2) + A[7,1]=BigInt(2032)//BigInt(16875)+BigInt(152)//BigInt(16875)*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=-7348//98325-33652//294975*6^(1//2) - A[7,5]=10132//64125-716//21375*6^(1//2) - A[7,6]=2592//14375+2912//14375*6^(1//2) + A[7,4]=-BigInt(7348)//BigInt(98325)-BigInt(33652)//BigInt(294975)*6^(1//2) + A[7,5]=BigInt(10132)//BigInt(64125)-BigInt(716)//BigInt(21375)*6^(1//2) + A[7,6]=BigInt(2592)//BigInt(14375)+BigInt(2912)//BigInt(14375)*6^(1//2) A[8,1]=16//225 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=64//225+4//225*6^(1//2) - A[8,7]=64//225-4//225*6^(1//2) + A[8,6]=BigInt(64)//BigInt(225)+BigInt(4)//BigInt(225)*6^(1//2) + A[8,7]=BigInt(64)//BigInt(225)-BigInt(4)//BigInt(225)*6^(1//2) A[9,1]=57//800 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=177//800+69//1600*6^(1//2) - A[9,7]=177//800-69//1600*6^(1//2) + A[9,6]=BigInt(177)//BigInt(800)+BigInt(69)//BigInt(1600)*6^(1//2) + A[9,7]=BigInt(177)//BigInt(800)-BigInt(69)//BigInt(1600)*6^(1//2) A[9,8]=-27//800 A[10,1]=2844530829046074022657//58982400000000000000000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=4287156859652598464203//58982400000000000000000-1598864762333658025459//117964800000000000000000*6^(1//2) - A[10,7]=4287156859652598464203//58982400000000000000000+1598864762333658025459//117964800000000000000000*6^(1//2) + A[10,6]=BigInt(4287156859652598464203)//BigInt(58982400000000000000000)-BigInt(1598864762333658025459)//BigInt(117964800000000000000000)*6^(1//2) + A[10,7]=BigInt(4287156859652598464203)//BigInt(58982400000000000000000)+BigInt(1598864762333658025459)//BigInt(117964800000000000000000)*6^(1//2) A[10,8]=-141033886218604337343//6553600000000000000000 A[10,9]=-21409264848554971927//204800000000000000000 - A[11,1]=-72189389771//9959178240000-459663572789//59755069440000*6^(1//2) + A[11,1]=-BigInt(72189389771)//BigInt(9959178240000)-BigInt(459663572789)//BigInt(59755069440000)*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-14201240926266911//557169364500480000-31790792357660029//557169364500480000*6^(1//2) - A[11,8]=22414436941//1563197440000+459663572789//56275107840000*6^(1//2) - A[11,9]=154180604903//2534154240000+459663572789//11403694080000*6^(1//2) - A[11,10]=21871487332435000000//125536952879579583419+18386542911560000000//1129832575916216250771*6^(1//2) - A[12,1]=-178144571353393080183496267158614821877982611914666395752937745405391408707734804982447062502773//1247718010112994054746145516410425353598134947600568397156373491324203879120405304413829778240000+352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357//8110167065734461355849945856667764798387877159403694581516427693607325214282634478689893558560000*6^(1//2) + A[11,7]=-BigInt(14201240926266911)//BigInt(557169364500480000)-BigInt(31790792357660029)//BigInt(557169364500480000)*6^(1//2) + A[11,8]=BigInt(22414436941)//BigInt(1563197440000)+BigInt(459663572789)//BigInt(56275107840000)*6^(1//2) + A[11,9]=BigInt(154180604903)//BigInt(2534154240000)+BigInt(459663572789)//BigInt(11403694080000)*6^(1//2) + A[11,10]=BigInt(21871487332435000000)//BigInt(125536952879579583419)+BigInt(18386542911560000000)//BigInt(1129832575916216250771)*6^(1//2) + A[12,1]=-BigInt(178144571353393080183496267158614821877982611914666395752937745405391408707734804982447062502773)//BigInt(1247718010112994054746145516410425353598134947600568397156373491324203879120405304413829778240000)+BigInt(352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357)//BigInt(8110167065734461355849945856667764798387877159403694581516427693607325214282634478689893558560000)*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-39115022545645779688585831988975140882502245161831122703201435591036520210945751850583137867//38425428798268102367071108589483043166777031255688218331140907046999467997785653437677908480-490826700396287454540598331961129757400186839154291202145347161815801053957874498846640625//15370171519307240946828443435793217266710812502275287332456362818799787199114261375071163392*6^(1//2) - A[12,7]=-622064296680932516193525865473060264652463486635595667447855699920023546211607797417635623004817316459//907451703567059050763665262359998604536360756710836393258911136378360869155327677312519401429106240000+643210041535328932923955834959360270277930780334485030265105750796567439186095378077346484617022694073//1814903407134118101527330524719997209072721513421672786517822272756721738310655354625038802858212480000*6^(1//2) - A[12,8]=1203943546728385294644268186854769106596033156989737459970836017592684437096940490927391123081521//6546732431504927940789740125933173479539636700187880198168132038132534360122730704444373657280000-151110511960958278763850506139095613011386663021919350564690684891134877118069370443383945077153//3273366215752463970394870062966586739769818350093940099084066019066267180061365352222186828640000*6^(1//2) - A[12,9]=63681466156701378449525903160928961790100434377497936201427140303316098275608362465676059840449//119057634931893490852780569777780769114850167606078444507680127107913165342297705956314829715000-352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357//1547749254114615381086147407111149998493052178879019778599841652402871149449870177432092786295000*6^(1//2) - A[12,10]=10278934048763239705668635930656276438279802537812076691952406255660602976082835598179622579836784640000000//20706607333558650004563853916074751077994608347553087587301432465002027701979512351053114927376343490460197-24757946279683404392669266925829425235785590869511266396518921812563538267024485653444025561440747520000000//269185895336262450059330100908971764013929908518190138634918622045026360125733660563690494055892465375982561*6^(1//2) - A[12,11]=19635000096509466380843956455829094932847113883632439882926745444809822658280742880787456//15009933124323477487137151792766813737022277834253210285601916815234167186635020874092933 - A[13,1]=-25488511950948766602163761842966272037005387677568247//25343364340644945281003771622773961523200000000000000+2525608241949563386308964624438617443527//12416017897756354830807859200000000000000*6^(1//2) + A[12,6]=-BigInt(39115022545645779688585831988975140882502245161831122703201435591036520210945751850583137867)//BigInt(38425428798268102367071108589483043166777031255688218331140907046999467997785653437677908480)-BigInt(490826700396287454540598331961129757400186839154291202145347161815801053957874498846640625)//BigInt(15370171519307240946828443435793217266710812502275287332456362818799787199114261375071163392)*6^(1//2) + A[12,7]=-BigInt(622064296680932516193525865473060264652463486635595667447855699920023546211607797417635623004817316459)//BigInt(907451703567059050763665262359998604536360756710836393258911136378360869155327677312519401429106240000)+BigInt(643210041535328932923955834959360270277930780334485030265105750796567439186095378077346484617022694073)//BigInt(1814903407134118101527330524719997209072721513421672786517822272756721738310655354625038802858212480000)*6^(1//2) + A[12,8]=BigInt(1203943546728385294644268186854769106596033156989737459970836017592684437096940490927391123081521)//BigInt(6546732431504927940789740125933173479539636700187880198168132038132534360122730704444373657280000)-BigInt(151110511960958278763850506139095613011386663021919350564690684891134877118069370443383945077153)//BigInt(3273366215752463970394870062966586739769818350093940099084066019066267180061365352222186828640000)*6^(1//2) + A[12,9]=BigInt(63681466156701378449525903160928961790100434377497936201427140303316098275608362465676059840449)//BigInt(119057634931893490852780569777780769114850167606078444507680127107913165342297705956314829715000)-BigInt(352591194575569317115651180991223097026568880384478484650944931412648046608828531034562538513357)//BigInt(1547749254114615381086147407111149998493052178879019778599841652402871149449870177432092786295000)*6^(1//2) + A[12,10]=BigInt(10278934048763239705668635930656276438279802537812076691952406255660602976082835598179622579836784640000000)//BigInt(20706607333558650004563853916074751077994608347553087587301432465002027701979512351053114927376343490460197)-BigInt(24757946279683404392669266925829425235785590869511266396518921812563538267024485653444025561440747520000000)//BigInt(269185895336262450059330100908971764013929908518190138634918622045026360125733660563690494055892465375982561)*6^(1//2) + A[12,11]=BigInt(19635000096509466380843956455829094932847113883632439882926745444809822658280742880787456)//BigInt(15009933124323477487137151792766813737022277834253210285601916815234167186635020874092933) + A[13,1]=-BigInt(25488511950948766602163761842966272037005387677568247)//BigInt(25343364340644945281003771622773961523200000000000000)+BigInt(2525608241949563386308964624438617443527)//BigInt(12416017897756354830807859200000000000000)*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-2617546081675469247418718340204655213//431392587109884206933606400000000000-552470350996365859393640759989//2400793528263703412500070400000*6^(1//2) - A[13,7]=-45969294618407232267578352626581642155421231201//10187731154133781589406192186163200000000000000+1540493536582818303738906021531546510663696889//885889665576850572991842798796800000000000000*6^(1//2) - A[13,8]=203013873418014401588800777489550153682185921397719//6003783517480134311881093736968119910400000000000000-3968812951635028178485515838403541696971//18374628007211630439078297600000000000000*6^(1//2) - A[13,9]=57340072791914637839492204156400815228449519011392389//19744238839693126186283635091213610188800000000000000-677602211254760908521917338264019314117//635714271434389910412902400000000000000*6^(1//2) - A[13,10]=24100788715039192225758197856261740786803059875758180717//9662717001210818114953908042643919942065136939286292000-8800028717594297513271653743688562521//20449362746897197076153911415852248500*6^(1//2) - A[13,11]=124358916033523439225154730110040589545064737//19935912449945669485002510178704400000000000 - A[13,12]=594716139297486674475082356103592029886330739685357945223223985387172161751824241784555387316314439//818019847119678359631725769101238313386585208743795596694052943582031156000597320370585600000000000 - A[14,1]=184592679361470753674594239208189459317466722387929369596771//127891217091830656233364014205731655064571321600000000000000-293880952873230803935166416296767553377//866938749696854853908947200000000000000*6^(1//2) + A[13,6]=-BigInt(2617546081675469247418718340204655213)//BigInt(431392587109884206933606400000000000)-552470350996365859393640759989//2400793528263703412500070400000*6^(1//2) + A[13,7]=-BigInt(45969294618407232267578352626581642155421231201)//BigInt(10187731154133781589406192186163200000000000000)+BigInt(1540493536582818303738906021531546510663696889)//BigInt(885889665576850572991842798796800000000000000)*6^(1//2) + A[13,8]=BigInt(203013873418014401588800777489550153682185921397719)//BigInt(6003783517480134311881093736968119910400000000000000)-BigInt(3968812951635028178485515838403541696971)//BigInt(18374628007211630439078297600000000000000)*6^(1//2) + A[13,9]=BigInt(57340072791914637839492204156400815228449519011392389)//BigInt(19744238839693126186283635091213610188800000000000000)-BigInt(677602211254760908521917338264019314117)//BigInt(635714271434389910412902400000000000000)*6^(1//2) + A[13,10]=BigInt(24100788715039192225758197856261740786803059875758180717)//BigInt(9662717001210818114953908042643919942065136939286292000)-BigInt(8800028717594297513271653743688562521)//BigInt(20449362746897197076153911415852248500)*6^(1//2) + A[13,11]=BigInt(124358916033523439225154730110040589545064737)//BigInt(19935912449945669485002510178704400000000000) + A[13,12]=BigInt(594716139297486674475082356103592029886330739685357945223223985387172161751824241784555387316314439)//BigInt(818019847119678359631725769101238313386585208743795596694052943582031156000597320370585600000000000) + A[14,1]=BigInt(184592679361470753674594239208189459317466722387929369596771)//BigInt(127891217091830656233364014205731655064571321600000000000000)-BigInt(293880952873230803935166416296767553377)//BigInt(866938749696854853908947200000000000000)*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=5966995986367380181027852718263477//684582962942931480729600000000000+2897291244884828193281565089//19049265055803310768128000000*6^(1//2) - A[14,7]=99009240614446727611594225452277068906413179//16167053833464253010532287404800000000000000-3748619435624523040662096435375495632409181//1405830768127326348741938035200000000000000*6^(1//2) - A[14,8]=4632645823113234486269357844283603936661991916850927460433//5096189922215990577140952099757378096638035200000000000000+41982993267604400562166630899538221911//116635822311401951029305600000000000000*6^(1//2) - A[14,9]=-12135475677184688070559819501757154968443992507349800863475059//3337534088557268857775113382843672473526974754800000000000000+293880952873230803935166416296767553377//165447122399672764770545400000000000000*6^(1//2) - A[14,10]=-8031428603597180964147750321204281053557209400385686643427859804352//2513586440178391306900178164909088113749933981949109368563389778875+21495292553013453087829315020563569618432//29973653446264566614372595657785433238875*6^(1//2) - A[14,11]=-44866632128961269158599595825347949153517725172080973//5429607175821308141232283339099249860726338769531250 - A[14,12]=-359988533934752543813368225945058137961504440675167771570563740579175484411998973149563531328527853237660249760109643//234128137445668240736067711662442379892483470931740696615716602345729933343308008758732590194294958617150200000000000 + A[14,6]=BigInt(5966995986367380181027852718263477)//BigInt(684582962942931480729600000000000)+BigInt(2897291244884828193281565089)//BigInt(19049265055803310768128000000)*6^(1//2) + A[14,7]=BigInt(99009240614446727611594225452277068906413179)//BigInt(16167053833464253010532287404800000000000000)-BigInt(3748619435624523040662096435375495632409181)//BigInt(1405830768127326348741938035200000000000000)*6^(1//2) + A[14,8]=BigInt(4632645823113234486269357844283603936661991916850927460433)//BigInt(5096189922215990577140952099757378096638035200000000000000)+BigInt(41982993267604400562166630899538221911)//BigInt(116635822311401951029305600000000000000)*6^(1//2) + A[14,9]=-BigInt(12135475677184688070559819501757154968443992507349800863475059)//BigInt(3337534088557268857775113382843672473526974754800000000000000)+BigInt(293880952873230803935166416296767553377)//BigInt(165447122399672764770545400000000000000)*6^(1//2) + A[14,10]=-BigInt(8031428603597180964147750321204281053557209400385686643427859804352)//BigInt(2513586440178391306900178164909088113749933981949109368563389778875)+BigInt(21495292553013453087829315020563569618432)//BigInt(29973653446264566614372595657785433238875)*6^(1//2) + A[14,11]=-BigInt(44866632128961269158599595825347949153517725172080973)//BigInt(5429607175821308141232283339099249860726338769531250) + A[14,12]=-BigInt(359988533934752543813368225945058137961504440675167771570563740579175484411998973149563531328527853237660249760109643)//BigInt(234128137445668240736067711662442379892483470931740696615716602345729933343308008758732590194294958617150200000000000) A[14,13]=1011136807359189181222571916914688//2927578889427871359661497484969729 - A[15,1]=-43117938494612449223384237106139955697243762787772847383//14030104862294690648579566521727488445420965260989440000+4220334940168717525563719481764309232553//5553268895030690235789996003491120640000*6^(1//2) + A[15,1]=-BigInt(43117938494612449223384237106139955697243762787772847383)//BigInt(14030104862294690648579566521727488445420965260989440000)+BigInt(4220334940168717525563719481764309232553)//BigInt(5553268895030690235789996003491120640000)*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-492170504431044248358505817476691843//26311016381549020957251979880325120-65372649360291914372644744384375//457582893592156886213077910962176*6^(1//2) - A[15,7]=-60242025722206083647640080390153021797730167//4671870346091448695506240355969515576320000+312292306982904450161582808948983992497619279//54031196176535884913246084116864832317440000*6^(1//2) - A[15,8]=-10128486019754425336362855829794634260766582925227304979//2051440458733049774272501566471676463052668060718080000-4220334940168717525563719481764309232553//5229862652007483519857107084128791040000*6^(1//2) - A[15,9]=90164396775224825317874747969895939573106537263617688583//9932194582195572820411492715910530662743409752296080000-4220334940168717525563719481764309232553//1059789239915401287502749181781142480000*6^(1//2) - A[15,10]=822220421784353922416106346105112190310210366765138782108892460117760000000//112539961436930436130682455392076582934435837857314380718907401253008522853-43216229787327667461772487493266526541342720000000//26879922067906624005297106621487120800647611685231*6^(1//2) - A[15,11]=209814213871916216679569640811090009729840605120//11651974660960738096987230622554824075229159217 - A[15,12]=3941550892863952281184122715485813150214519858148244578543766661999079625453432169420046111603168071904019820197053706993310801913//576348806945747835561749398160966945390916610765210182493857593996732757363976976471505530337022074730630638475548489174498085584 - A[15,13]=-4759443892077050695292772766912275498897121280000000000//4614026158486489304426198097242323507384603506591241137 - A[15,14]=38733614144315448443538220691259283298308750000000//93806291160324220065540465392781147766752569954001 - A[16,1]=18092408213832965447840389945226814727838921316097789//4568260908663202892681034746459555501706277524480000-156317653995567850184921063401246768027//212359240683067701291661898043594240000*6^(1//2) + A[15,6]=-BigInt(492170504431044248358505817476691843)//BigInt(26311016381549020957251979880325120)-BigInt(65372649360291914372644744384375)//BigInt(457582893592156886213077910962176)*6^(1//2) + A[15,7]=-BigInt(60242025722206083647640080390153021797730167)//BigInt(4671870346091448695506240355969515576320000)+BigInt(312292306982904450161582808948983992497619279)//BigInt(54031196176535884913246084116864832317440000)*6^(1//2) + A[15,8]=-BigInt(10128486019754425336362855829794634260766582925227304979)//BigInt(2051440458733049774272501566471676463052668060718080000)-BigInt(4220334940168717525563719481764309232553)//BigInt(5229862652007483519857107084128791040000)*6^(1//2) + A[15,9]=BigInt(90164396775224825317874747969895939573106537263617688583)//BigInt(9932194582195572820411492715910530662743409752296080000)-BigInt(4220334940168717525563719481764309232553)//BigInt(1059789239915401287502749181781142480000)*6^(1//2) + A[15,10]=BigInt(822220421784353922416106346105112190310210366765138782108892460117760000000)//BigInt(112539961436930436130682455392076582934435837857314380718907401253008522853)-BigInt(43216229787327667461772487493266526541342720000000)//BigInt(26879922067906624005297106621487120800647611685231)*6^(1//2) + A[15,11]=BigInt(209814213871916216679569640811090009729840605120)//BigInt(11651974660960738096987230622554824075229159217) + A[15,12]=BigInt(3941550892863952281184122715485813150214519858148244578543766661999079625453432169420046111603168071904019820197053706993310801913)//BigInt(576348806945747835561749398160966945390916610765210182493857593996732757363976976471505530337022074730630638475548489174498085584) + A[15,13]=-BigInt(4759443892077050695292772766912275498897121280000000000)//BigInt(4614026158486489304426198097242323507384603506591241137) + A[15,14]=BigInt(38733614144315448443538220691259283298308750000000)//BigInt(93806291160324220065540465392781147766752569954001) + A[16,1]=BigInt(18092408213832965447840389945226814727838921316097789)//BigInt(4568260908663202892681034746459555501706277524480000)-BigInt(156317653995567850184921063401246768027)//BigInt(212359240683067701291661898043594240000)*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=65946837846509057750066287355594411//3018431611722608724311451319541760+41984484090942118562371132909375//52494462812567108248894805557248*6^(1//2) - A[16,7]=8692965898134239206513518248119006769975359//535962614823230784958890847664050959360000-38800907634871851557429961190168666395776983//6198524154042582121698476759940763269120000*6^(1//2) - A[16,8]=2641630262222426284468500071736583566105608571199325883//235343729805469979809271071241826755571130067491840000+156317653995567850184921063401246768027//199992055607259790546219146109360640000*6^(1//2) - A[16,9]=-193422103474923353694542105476136625982637168991506421//16048357343710211432072833749116213173856151273040000+156317653995567850184921063401246768027//40526767661819895652001992553977680000*6^(1//2) - A[16,10]=-19419587503350096681694941672242361995243037384025897671049255680000000//2155738929233095407456284002740551925607350553898010429805538450410571+1600692776914614785893591689228766904596480000000//1027899053306897212338272667278244239283200723671*6^(1//2) - A[16,11]=-27285760059113968837908932750404506400064658240//1336728621411169422812695849204871581103756891 - A[16,12]=-194853016061874333335484555436551917329750324944158872786342511110263341294405932910123138589192221578993200454377//15840605894584140753571150900860666508000461134947537749588341642048479030548925808450142813874420689113167632464 - A[16,13]=89488735256675489275877211680603518179732480000000000//58814073298029244653337926984054935524805348324518339 + A[16,6]=BigInt(65946837846509057750066287355594411)//BigInt(3018431611722608724311451319541760)+BigInt(41984484090942118562371132909375)//BigInt(52494462812567108248894805557248)*6^(1//2) + A[16,7]=BigInt(8692965898134239206513518248119006769975359)//BigInt(535962614823230784958890847664050959360000)-BigInt(38800907634871851557429961190168666395776983)//BigInt(6198524154042582121698476759940763269120000)*6^(1//2) + A[16,8]=BigInt(2641630262222426284468500071736583566105608571199325883)//BigInt(235343729805469979809271071241826755571130067491840000)+BigInt(156317653995567850184921063401246768027)//BigInt(199992055607259790546219146109360640000)*6^(1//2) + A[16,9]=-BigInt(193422103474923353694542105476136625982637168991506421)//BigInt(16048357343710211432072833749116213173856151273040000)+BigInt(156317653995567850184921063401246768027)//BigInt(40526767661819895652001992553977680000)*6^(1//2) + A[16,10]=-BigInt(19419587503350096681694941672242361995243037384025897671049255680000000)//BigInt(2155738929233095407456284002740551925607350553898010429805538450410571)+BigInt(1600692776914614785893591689228766904596480000000)//BigInt(1027899053306897212338272667278244239283200723671)*6^(1//2) + A[16,11]=-BigInt(27285760059113968837908932750404506400064658240)//BigInt(1336728621411169422812695849204871581103756891) + A[16,12]=-BigInt(194853016061874333335484555436551917329750324944158872786342511110263341294405932910123138589192221578993200454377)//BigInt(15840605894584140753571150900860666508000461134947537749588341642048479030548925808450142813874420689113167632464) + A[16,13]=BigInt(89488735256675489275877211680603518179732480000000000)//BigInt(58814073298029244653337926984054935524805348324518339) A[16,14]=0 A[16,15]=0 α[1]=100976787617015984669475787//6921502952403262310437464576 @@ -4421,10 +4421,10 @@ function constructVernerRobust9(T::Type = Float64) α[7]=0 α[8]=8877148253451235588984375//4385514038208782482187638272 α[9]=961916572949681511747758515625//4416417715504587515036809762176 - α[10]=1967337516701564001434375000000000000000000000000//15431364863119854943071851131903908575429289017877 + α[10]=BigInt(1967337516701564001434375000000000000000000000000)//BigInt(15431364863119854943071851131903908575429289017877) α[11]=2323713252076974806855457536//10352378514220126928031114081 - α[12]=28308600293241456954311939117138937391141264054325158121088859798090056999504636993802634122671806566061266984631226363619//158391546540670080968065757007173890885877631132509858232987982213169380898029758612356596464561682203552186100842929847264 - α[13]=296136352341197653422080000000000000//3899432561650270968394778037550931439 + α[12]=BigInt(28308600293241456954311939117138937391141264054325158121088859798090056999504636993802634122671806566061266984631226363619)//BigInt(158391546540670080968065757007173890885877631132509858232987982213169380898029758612356596464561682203552186100842929847264) + α[13]=BigInt(296136352341197653422080000000000000)//BigInt(3899432561650270968394778037550931439) α[14]=117048651891177050452812500000000//903958175807874008864483503817601 α[15]=145778296653275182685983//4945417885871057962703934 α[16]=0 @@ -4437,9 +4437,9 @@ function constructVernerRobust9(T::Type = Float64) αEEst[7]=0 αEEst[8]=11089416604965799654140625//10367645480399012960254464 αEEst[9]=19661377435148646805703125//255979697183364488207083392 - αEEst[10]=688790393936688343750000000000000000000000//6091295374506475008386869675533556427693991 + αEEst[10]=BigInt(688790393936688343750000000000000000000000)//BigInt(6091295374506475008386869675533556427693991) αEEst[11]=2387113868151976968347648//9351742108599933990994683 - αEEst[12]=-12428699133337309103655890990808226652772000718643045082918121983471100560973332724469319414156511978021429//12648919237095643063555422745116719205173888728920704277722434371356124846214898200346632677347950735102176 + αEEst[12]=-BigInt(12428699133337309103655890990808226652772000718643045082918121983471100560973332724469319414156511978021429)//BigInt(12648919237095643063555422745116719205173888728920704277722434371356124846214898200346632677347950735102176) αEEst[13]=185286960316915979617280000000000000//465364379785423284294027008596613217 αEEst[14]=0 αEEst[15]=0 @@ -4463,11 +4463,11 @@ function constructVernerEfficient9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1731//50000 - c[3]=7630049//53810000-983539//53810000*6^(1//2) - c[4]=22890147//107620000-2950617//107620000*6^(1//2) + c[3]=BigInt(7630049)//BigInt(53810000)-BigInt(983539)//BigInt(53810000)*6^(1//2) + c[4]=BigInt(22890147)//BigInt(107620000)-BigInt(2950617)//BigInt(107620000)*6^(1//2) c[5]=561//1000 - c[6]=387//1000-129//2000*6^(1//2) - c[7]=387//1000+129//2000*6^(1//2) + c[6]=BigInt(387)//BigInt(1000)-BigInt(129)//BigInt(2000)*6^(1//2) + c[7]=BigInt(387)//BigInt(1000)+BigInt(129)//BigInt(2000)*6^(1//2) c[8]=129//200 c[9]=387//800 c[10]=6757//100000 @@ -4478,123 +4478,123 @@ function constructVernerEfficient9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1731//50000 - A[3,1]=-177968356965557//1002427673820000+14180534491313//250606918455000*6^(1//2) - A[3,2]=64021741529527//200485534764000-7504450763411//100242767382000*6^(1//2) - A[4,1]=22890147//430480000-2950617//430480000*6^(1//2) + A[3,1]=-BigInt(177968356965557)//BigInt(1002427673820000)+BigInt(14180534491313)//BigInt(250606918455000)*6^(1//2) + A[3,2]=BigInt(64021741529527)//BigInt(200485534764000)-BigInt(7504450763411)//BigInt(100242767382000)*6^(1//2) + A[4,1]=BigInt(22890147)//BigInt(430480000)-BigInt(2950617)//BigInt(430480000)*6^(1//2) A[4,2]=0 - A[4,3]=68670441//430480000-8851851//430480000*6^(1//2) - A[5,1]=592203994261020339//513126355505556250+730386990293623641//2052505422022225000*6^(1//2) + A[4,3]=BigInt(68670441)//BigInt(430480000)-BigInt(8851851)//BigInt(430480000)*6^(1//2) + A[5,1]=BigInt(592203994261020339)//BigInt(513126355505556250)+BigInt(730386990293623641)//BigInt(2052505422022225000)*6^(1//2) A[5,2]=0 - A[5,3]=-8712153884182794903//2052505422022225000-2843421359195851533//2052505422022225000*6^(1//2) - A[5,4]=1873698362223295443//513126355505556250+528258592225556973//513126355505556250*6^(1//2) - A[6,1]=11380823631//157617812000-339148869//39404453000*6^(1//2) + A[5,3]=-BigInt(8712153884182794903)//BigInt(2052505422022225000)-BigInt(2843421359195851533)//BigInt(2052505422022225000)*6^(1//2) + A[5,4]=BigInt(1873698362223295443)//BigInt(513126355505556250)+BigInt(528258592225556973)//BigInt(513126355505556250)*6^(1//2) + A[6,1]=BigInt(11380823631)//BigInt(157617812000)-BigInt(339148869)//BigInt(39404453000)*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=16193232887091831//58864341808507450-2355345717024309//58864341808507450*6^(1//2) - A[6,5]=165912282616977//4179075230308000-33181894472511//2089537615154000*6^(1//2) - A[7,1]=26523528363//231790900000+863255358//123138915625*6^(1//2) + A[6,4]=BigInt(16193232887091831)//BigInt(58864341808507450)-BigInt(2355345717024309)//BigInt(58864341808507450)*6^(1//2) + A[6,5]=BigInt(165912282616977)//BigInt(4179075230308000)-BigInt(33181894472511)//BigInt(2089537615154000)*6^(1//2) + A[7,1]=BigInt(26523528363)//BigInt(231790900000)+BigInt(863255358)//BigInt(123138915625)*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=-38208748178016484817787//842517966262441068418750-86118788556282369822807//842517966262441068418750*6^(1//2) - A[7,5]=92362336407446913//290322814529044000-232039320950012997//2467743923496874000*6^(1//2) - A[7,6]=-362925891//1690350537500+857800423623//3380701075000*6^(1//2) + A[7,4]=-BigInt(38208748178016484817787)//BigInt(842517966262441068418750)-BigInt(86118788556282369822807)//BigInt(842517966262441068418750)*6^(1//2) + A[7,5]=BigInt(92362336407446913)//BigInt(290322814529044000)-BigInt(232039320950012997)//BigInt(2467743923496874000)*6^(1//2) + A[7,6]=-BigInt(362925891)//BigInt(1690350537500)+BigInt(857800423623)//BigInt(3380701075000)*6^(1//2) A[8,1]=43//600 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=43//150+43//2400*6^(1//2) - A[8,7]=43//150-43//2400*6^(1//2) + A[8,6]=BigInt(43)//BigInt(150)+BigInt(43)//BigInt(2400)*6^(1//2) + A[8,7]=BigInt(43)//BigInt(150)-BigInt(43)//BigInt(2400)*6^(1//2) A[9,1]=7353//102400 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=22833//102400+8901//204800*6^(1//2) - A[9,7]=22833//102400-8901//204800*6^(1//2) + A[9,6]=BigInt(22833)//BigInt(102400)+BigInt(8901)//BigInt(204800)*6^(1//2) + A[9,7]=BigInt(22833)//BigInt(102400)-BigInt(8901)//BigInt(204800)*6^(1//2) A[9,8]=-3483//102400 A[10,1]=376708742472214988700853//7788456028125000000000000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=187914666753956840195279//2596152009375000000000000-210440846556290693268911//15576912056250000000000000*6^(1//2) - A[10,7]=187914666753956840195279//2596152009375000000000000+210440846556290693268911//15576912056250000000000000*6^(1//2) + A[10,6]=BigInt(187914666753956840195279)//BigInt(2596152009375000000000000)-BigInt(210440846556290693268911)//BigInt(15576912056250000000000000)*6^(1//2) + A[10,7]=BigInt(187914666753956840195279)//BigInt(2596152009375000000000000)+BigInt(210440846556290693268911)//BigInt(15576912056250000000000000)*6^(1//2) A[10,8]=-18552667221896744226647//865384003125000000000000 A[10,9]=-3167799860072183913409//30423656359863281250000 - A[11,1]=-426968570497//54394415898750-92754382349//12087647977500*6^(1//2) + A[11,1]=-BigInt(426968570497)//BigInt(54394415898750)-BigInt(92754382349)//BigInt(12087647977500)*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-2865012129681958//114898584332330625-12962517687655099//229797168664661250*6^(1//2) - A[11,8]=4389715333607//309890657317500+92754382349//11477431752500*6^(1//2) - A[11,9]=4990058173976//83757096376875+371017529396//9306344041875*6^(1//2) - A[11,10]=1099523524595993125000//6257667909869756018891+100957348037989687500//6257667909869756018891*6^(1//2) - A[12,1]=18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756//13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375+407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536//28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875*6^(1//2) + A[11,7]=-BigInt(2865012129681958)//BigInt(114898584332330625)-BigInt(12962517687655099)//BigInt(229797168664661250)*6^(1//2) + A[11,8]=BigInt(4389715333607)//BigInt(309890657317500)+BigInt(92754382349)//BigInt(11477431752500)*6^(1//2) + A[11,9]=BigInt(4990058173976)//BigInt(83757096376875)+BigInt(371017529396)//BigInt(9306344041875)*6^(1//2) + A[11,10]=BigInt(1099523524595993125000)//BigInt(6257667909869756018891)+BigInt(100957348037989687500)//BigInt(6257667909869756018891)*6^(1//2) + A[12,1]=BigInt(18382031104798403869938539009154656587521498573595595063164077882800315372787284683238439478955141517997198007108623761931447163756)//BigInt(13974256944499724344918960993890933614161025322970450047932688998095008528620821239604734608111291769444706187497807869179550841329375)+BigInt(407885778185158609210793892517582595305896470756467612636796259611491408260896413446883450891351622914818800693274034252252905536)//BigInt(28084926388601226073624096169175002956970191576455110633226765141161372294098693275117181239385312198137508846535933127837167926875)*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904//2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635+4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000//23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877*6^(1//2) - A[12,7]=-136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416//3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375+169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904//1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875*6^(1//2) - A[12,8]=5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208//92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875-5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432//365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625*6^(1//2) - A[12,9]=54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328//301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125-6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576//86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375*6^(1//2) - A[12,10]=9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000//58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783-8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000//265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757*6^(1//2) - A[12,11]=123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952//281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461 - A[13,1]=-56042772675322042139227629978042586330633622706053363946766144416933631//58808540772323190525590122613223430507352118534557342666015625000000000+281404579734699232141455524604487724159024972527//1478009944832743180452316204077188415527343750000*6^(1//2) + A[12,6]=-BigInt(333881311789849411971573472868128281438202210721723123251742145367734582887577395547778228760174068758086134389952015563403904)//BigInt(2270872004608103037127689848604039623086639035441372934050180593816493796129405349914148981460714202232988727738778494557727635)+BigInt(4819272892477768171373308666720689121421091953625792970278044071549950640195056472955523769829034800621890424847009130000000)//BigInt(23162894447002650978702436455761204155483718161502003927311842056928236720519934569124319610899284862776485022935540644488821877)*6^(1//2) + A[12,7]=-BigInt(136666607496463622270135608863772076443625468798139480390426740993024803946981763209348364716108721312822619845726151693667598437699964416)//BigInt(3719286465342404274788585327254180828195282427342057650194855634917821113563432870681372043512520401887141437067106105683944802332422369375)+BigInt(169845085565361336805556009296394374527636952379388961026066628725155521832762086875632366996477567928657535912191396155566765457826139904)//BigInt(1593979913718173260623679425966077497797978183146596135797795272107637620098614087434873732933937315094489187314474045293119200999609586875)*6^(1//2) + A[12,8]=BigInt(5610987899273278525411960528081442902198567594809764379756195673673265700551076812883925583370253765702553235594764427173637673766208)//BigInt(92881598198144033018278804740626334135423356791639598109358867770361609232846012626732332450844264293840456574956036349633197336361875)-BigInt(5587476413495323413846491678323049250765705078855720721052003556321800113162964567765526724539063327600257543743479921263738432)//BigInt(365303089362201664516413596925286161494473575337115296250511752859728108868696929614024803255122785403232359817965288739565550625)*6^(1//2) + A[12,9]=BigInt(54598539818083615233566148602203244896696958910734339754065270985433507945162707737759469214674480807272210648148477499238783276259328)//BigInt(301247919092298852634886875129959310794662932014184499827145075851637298698312074030567479239502011693447423026416040794479934024058125)-BigInt(6526172450962537747372702280281321524894343532103481802188740153783862532174342615150135214261625966637100811092384548036046488576)//BigInt(86490932843037281836028387921320502668579653176624892284566487468170341285762869374265713247057712228954184044334206372230816544375)*6^(1//2) + A[12,10]=BigInt(9391667348404584010955422210328707125006120661611061908889750805619418785820948002455890360939221912190524731087070645107486913457760000000)//BigInt(58157266968773020612419028503738708303515285854970725662326801531295387265784849843172223645193277229358434488742203091272981931739152584783)-BigInt(8108825145085088104344721048166325225173729495689364696426720161112012414227752328969720658987315654179873760357725235734000399440000000)//BigInt(265558296661064021061274102756797754810572081529546692522040189640618206693081506133206500662983001047298787619827411375675716583283801757)*6^(1//2) + A[12,11]=BigInt(123461712659887915177271339396606860810479028777869348014870450606260914019560285661288212498128400476015695960341952)//BigInt(281629106670320674754245209358840703704235147307838896741075511220826056829047205614324978253226176275078922716132461) + A[13,1]=-BigInt(56042772675322042139227629978042586330633622706053363946766144416933631)//BigInt(58808540772323190525590122613223430507352118534557342666015625000000000)+BigInt(281404579734699232141455524604487724159024972527)//BigInt(1478009944832743180452316204077188415527343750000)*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-1027163900229750356561238237947225332675621517//179261894431132664078747698292867431640625000-2745292391641202525373103979336813513372321//11702216468464340311060649744558385937500000*6^(1//2) - A[13,7]=-157229999853748227305165773364426925282378072238332930121//36699907367985458573273204094330716033963413238525390625+5757606442802795095318986067317837904184278650664590252101//3523191107326604023034227593055748739260487670898437500000*6^(1//2) - A[13,8]=-9311448168593934146015965019904013602133802943325818346622781285907057//4255970849010124217193135449668739985401313363005576159362792968750000-844213739204097696424366573813463172477074917581//4210188359946578336976868164966163024902343750000*6^(1//2) - A[13,9]=885774233856672590222951867695327816457340130391639153070521335485617578//301098541380295011015469248465465290112505656143757799934635162353515625-281404579734699232141455524604487724159024972527//284481916364737983221402322504830303192138671875*6^(1//2) - A[13,10]=315479116729780153956412124052199685097744239386639023787359107959254802182//134481850506505848012587842215515574380212543200894932329128471154748828125-2940396453647872276646068776592292229737651937934623//7345465058781983710795837429530784777245286520703125*6^(1//2) - A[13,11]=2250996163406545378616532039018846586217631599453822541//382491303797095993563304148204275636433504028320312500 - A[13,12]=2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493//959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000 - A[14,1]=47342003848024391498707976847688893013083074441159779465719863625051668939887702630319//44802546873926050730401222636656855760802419993852060264615320801485392456054687500000-866369530987077991125562402829092187100493209601//3325522375873672156017711459173673934936523437500*6^(1//2) + A[13,6]=-BigInt(1027163900229750356561238237947225332675621517)//BigInt(179261894431132664078747698292867431640625000)-BigInt(2745292391641202525373103979336813513372321)//BigInt(11702216468464340311060649744558385937500000)*6^(1//2) + A[13,7]=-BigInt(157229999853748227305165773364426925282378072238332930121)//BigInt(36699907367985458573273204094330716033963413238525390625)+BigInt(5757606442802795095318986067317837904184278650664590252101)//BigInt(3523191107326604023034227593055748739260487670898437500000)*6^(1//2) + A[13,8]=-BigInt(9311448168593934146015965019904013602133802943325818346622781285907057)//BigInt(4255970849010124217193135449668739985401313363005576159362792968750000)-BigInt(844213739204097696424366573813463172477074917581)//BigInt(4210188359946578336976868164966163024902343750000)*6^(1//2) + A[13,9]=BigInt(885774233856672590222951867695327816457340130391639153070521335485617578)//BigInt(301098541380295011015469248465465290112505656143757799934635162353515625)-BigInt(281404579734699232141455524604487724159024972527)//BigInt(284481916364737983221402322504830303192138671875)*6^(1//2) + A[13,10]=BigInt(315479116729780153956412124052199685097744239386639023787359107959254802182)//BigInt(134481850506505848012587842215515574380212543200894932329128471154748828125)-BigInt(2940396453647872276646068776592292229737651937934623)//BigInt(7345465058781983710795837429530784777245286520703125)*6^(1//2) + A[13,11]=BigInt(2250996163406545378616532039018846586217631599453822541)//BigInt(382491303797095993563304148204275636433504028320312500) + A[13,12]=BigInt(2689340957307691853294902388334454003959378146957529866233529251986359392336044151708949720958809747970514366293458424272174024493)//BigInt(959516386019578808500569114780871708466894752280482835105408027815194895319055443842782227102120493960805649575561796875000000000) + A[14,1]=BigInt(47342003848024391498707976847688893013083074441159779465719863625051668939887702630319)//BigInt(44802546873926050730401222636656855760802419993852060264615320801485392456054687500000)-BigInt(866369530987077991125562402829092187100493209601)//BigInt(3325522375873672156017711459173673934936523437500)*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=871779321807802447463310035318238762878527157//134446420823349498059060773719650573730468750+107641268480999396081848975271849857994818//1097082793918531904161935913552348681640625*6^(1//2) - A[14,7]=496103786351862292800034805114190705484800743513354117014//110099722103956375719819612282992148101890239715576171875-1329938412606197485769312599390307351191540891599374831099//660598332623738254318917673697952888611341438293457031250*6^(1//2) - A[14,8]=40774077277747636354598451708891165494123131383777235229538611989392175193285994266471//15264290546248162101058985941588079518256741255377031736357946125713524703979492187500+123767075855296855875080343261298883871499029943//451091609994276250390378731960660324096679687500*6^(1//2) - A[14,9]=-10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664//3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375+3465478123948311964502249611316368748401972838404//2560337247282641848992620902543472728729248046875*6^(1//2) - A[14,10]=-27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984//12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375+574774300271998598683873114105472016699241495055292//1049352151254569101542262489932969253892183788671875*6^(1//2) - A[14,11]=-34241134351848245624232809437676889009431930503529853032576417589898516//5613347824358651981100985009024281007603230062439942682713165283203125 - A[14,12]=-3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609//1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000 - A[14,13]=4746930876023919335079451612726717649218264199984//18592065538407049755200144388134089346432755594877 - A[15,1]=-25188329249258825443748527038142409879923012133738985313265430932280250855708601//11370641325574469312056961874077298550827642308774647316995717036347558064286250+1234273058981860170179592598535508631343082535549881956//2105633771469628744518390642968552144069898845895808125*6^(1//2) + A[14,6]=BigInt(871779321807802447463310035318238762878527157)//BigInt(134446420823349498059060773719650573730468750)+BigInt(107641268480999396081848975271849857994818)//BigInt(1097082793918531904161935913552348681640625)*6^(1//2) + A[14,7]=BigInt(496103786351862292800034805114190705484800743513354117014)//BigInt(110099722103956375719819612282992148101890239715576171875)-BigInt(1329938412606197485769312599390307351191540891599374831099)//BigInt(660598332623738254318917673697952888611341438293457031250)*6^(1//2) + A[14,8]=BigInt(40774077277747636354598451708891165494123131383777235229538611989392175193285994266471)//BigInt(15264290546248162101058985941588079518256741255377031736357946125713524703979492187500)+BigInt(123767075855296855875080343261298883871499029943)//BigInt(451091609994276250390378731960660324096679687500)*6^(1//2) + A[14,9]=-BigInt(10522038608500556459828649038302068473735749030796372764961618751973793724796364606986664)//BigInt(3899417425005422254034574000397382862235892829653375835197340918271556055507659912109375)+BigInt(3465478123948311964502249611316368748401972838404)//BigInt(2560337247282641848992620902543472728729248046875)*6^(1//2) + A[14,10]=-BigInt(27843764471262693189365201135620670490328475323282820219474851621693895769527094334687108984)//BigInt(12257041066285164222002594300605593929434139193022166317802121412999357024704596261133984375)+BigInt(574774300271998598683873114105472016699241495055292)//BigInt(1049352151254569101542262489932969253892183788671875)*6^(1//2) + A[14,11]=-BigInt(34241134351848245624232809437676889009431930503529853032576417589898516)//BigInt(5613347824358651981100985009024281007603230062439942682713165283203125) + A[14,12]=-BigInt(3432044375893932378102368568052286501033850910516999202088532705211633432793920547702800961532438008401883737341854688972639605334600163938610268855705742764072609)//BigInt(1143174106341682260971647690410567292143926198650927778920823267461111371275907599801714870165813394147519068210931766844494994616580258435518181434575195312500000) + A[14,13]=BigInt(4746930876023919335079451612726717649218264199984)//BigInt(18592065538407049755200144388134089346432755594877) + A[15,1]=-BigInt(25188329249258825443748527038142409879923012133738985313265430932280250855708601)//BigInt(11370641325574469312056961874077298550827642308774647316995717036347558064286250)+BigInt(1234273058981860170179592598535508631343082535549881956)//BigInt(2105633771469628744518390642968552144069898845895808125)*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-54821142119685055562477216205428613949905430396088//3959439837009461289085587746748097947393101278095-1511276753825982856072891469504471256664975925000//40386286337496505148672995016830599063409633036569*6^(1//2) - A[15,7]=-60922424274061599918603524049390657305431262635197540405697952//6484861747489032169774584624759953148531564032417461909516875+84558575751635978733109961893984238786929550462615375699341616//19454585242467096509323753874279859445594692097252385728550625*6^(1//2) - A[15,8]=-116118147575045169733222875835719955334334798191459879782123534889390467935109772//8810626901954835245672275131295870892503713957512170681453300814988417642493125-176324722711694310025656085505072661620440362221411708//285619406719829107485771207042040133465420149964555625*6^(1//2) - A[15,9]=17769448722513898342276837490665097286927607247073335618566987143467294900183033216//2551217008137889615056342146084561867122485163596619283719957742418751029506356875-19748368943709762722873481576568138101489320568798111296//6484554262322259071286545935997129135111813687175650625*6^(1//2) - A[15,10]=97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000//18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599-85297084611782122474911131363078900058888025224607913745000000//69210659450201393843166746722954036326338355649915383851733911*6^(1//2) - A[15,11]=473389749049752963256114649231353822492912259509649519870869750525//35412440882360341799798842428365422941216508121322622479260846291 - A[15,12]=33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637//2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966 - A[15,13]=-38714992656958413389743252726016897599283911682945255636643554687500000//48540494926971587499294589382572212036169135429877901702347521300421767 - A[15,14]=14800250200940323717124616175641261235119295795768814717803955078125//33565577125141877760287380588632421223433194078156948298488471160489 - A[16,1]=2305785696086397561080858186939897173645641331085041313944389849986584101287//617508244345282265819087370078275122671246164669900462139876057008239440000-85404623305589712632165905233974183137607899140719//124822287169084833758410283469525117460541643292500*6^(1//2) + A[15,6]=-BigInt(54821142119685055562477216205428613949905430396088)//BigInt(3959439837009461289085587746748097947393101278095)-BigInt(1511276753825982856072891469504471256664975925000)//BigInt(40386286337496505148672995016830599063409633036569)*6^(1//2) + A[15,7]=-BigInt(60922424274061599918603524049390657305431262635197540405697952)//BigInt(6484861747489032169774584624759953148531564032417461909516875)+BigInt(84558575751635978733109961893984238786929550462615375699341616)//BigInt(19454585242467096509323753874279859445594692097252385728550625)*6^(1//2) + A[15,8]=-BigInt(116118147575045169733222875835719955334334798191459879782123534889390467935109772)//BigInt(8810626901954835245672275131295870892503713957512170681453300814988417642493125)-BigInt(176324722711694310025656085505072661620440362221411708)//BigInt(285619406719829107485771207042040133465420149964555625)*6^(1//2) + A[15,9]=BigInt(17769448722513898342276837490665097286927607247073335618566987143467294900183033216)//BigInt(2551217008137889615056342146084561867122485163596619283719957742418751029506356875)-BigInt(19748368943709762722873481576568138101489320568798111296)//BigInt(6484554262322259071286545935997129135111813687175650625)*6^(1//2) + A[15,10]=BigInt(97659266139124074818193264801929547781659926543786381510190954184218570746215033823993530000000)//BigInt(18560076654469706205963482908787056850812308205603127326855360961727608242796551101182080033599)-BigInt(85297084611782122474911131363078900058888025224607913745000000)//BigInt(69210659450201393843166746722954036326338355649915383851733911)*6^(1//2) + A[15,11]=BigInt(473389749049752963256114649231353822492912259509649519870869750525)//BigInt(35412440882360341799798842428365422941216508121322622479260846291) + A[15,12]=BigInt(33351439245158438248073494056784144097872912773415904536400728387690334563968394114702414108807505158106385116468732853458202899966748488718531545706559142895903144848764637)//BigInt(2316611025327287427714802011322252886090793904989900621592365627649097578102163572190502232425490606773312310665593424982745744299371285598588298606088543376742054644818966) + A[15,13]=-BigInt(38714992656958413389743252726016897599283911682945255636643554687500000)//BigInt(48540494926971587499294589382572212036169135429877901702347521300421767) + A[15,14]=BigInt(14800250200940323717124616175641261235119295795768814717803955078125)//BigInt(33565577125141877760287380588632421223433194078156948298488471160489) + A[16,1]=BigInt(2305785696086397561080858186939897173645641331085041313944389849986584101287)//BigInt(617508244345282265819087370078275122671246164669900462139876057008239440000)-BigInt(85404623305589712632165905233974183137607899140719)//BigInt(124822287169084833758410283469525117460541643292500)*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=102903996961580448264190625267026062654799259083//5046398084890004857481629999673320438819484730+41320925487304219313300272052128374567081128125//51473260465878049546312625996667868475958744246*6^(1//2) - A[16,7]=62798443349876457506718920843975661399949564598018488144466//4132553498782573324058263582553715220777051359780141380625-72308807081932961554425711089716771013571419950657300729103//12397660496347719972174790747661145662331154079340424141875*6^(1//2) - A[16,8]=1794909142126482564390848522924225553221469019751470544959297614654661293377//52596481193994264435601626109752988674679691644275456716633975785978672500+12200660472227101804595129319139169019658271305817//16931561456559959115207709344056578263397760602500*6^(1//2) - A[16,9]=-2775244732780109667342845612394739319115662636371477300455747022423270475907256//228417153675584029725018045422706955827996328208181619436454383447149337555625+341618493222358850528663620935896732550431596562876//96101338378773357469245211954911505447551097205625*6^(1//2) - A[16,10]=-27680554659769016623530979176727448251292244310769996015342190819068970556083063125000//3299557777429648960576561382256606844677258438797072955341581354051375036522231471437+4426552127579895373479670356100179759944766558141730312500//3077113738667320707748877199804636746494977000658967987677*6^(1//2) - A[16,11]=-292603171929706291053929402159930330736639136252680853622275//15473622826279161150227076887290262443510550964275858143964 - A[16,12]=-9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431//286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992 - A[16,13]=2729491144709837905799148766650782532906050298971406518524169921875//2158115888622139473142775812109447802920656149243127309253686951469 + A[16,6]=BigInt(102903996961580448264190625267026062654799259083)//BigInt(5046398084890004857481629999673320438819484730)+BigInt(41320925487304219313300272052128374567081128125)//BigInt(51473260465878049546312625996667868475958744246)*6^(1//2) + A[16,7]=BigInt(62798443349876457506718920843975661399949564598018488144466)//BigInt(4132553498782573324058263582553715220777051359780141380625)-BigInt(72308807081932961554425711089716771013571419950657300729103)//BigInt(12397660496347719972174790747661145662331154079340424141875)*6^(1//2) + A[16,8]=BigInt(1794909142126482564390848522924225553221469019751470544959297614654661293377)//BigInt(52596481193994264435601626109752988674679691644275456716633975785978672500)+BigInt(12200660472227101804595129319139169019658271305817)//BigInt(16931561456559959115207709344056578263397760602500)*6^(1//2) + A[16,9]=-BigInt(2775244732780109667342845612394739319115662636371477300455747022423270475907256)//BigInt(228417153675584029725018045422706955827996328208181619436454383447149337555625)+BigInt(341618493222358850528663620935896732550431596562876)//BigInt(96101338378773357469245211954911505447551097205625)*6^(1//2) + A[16,10]=-BigInt(27680554659769016623530979176727448251292244310769996015342190819068970556083063125000)//BigInt(3299557777429648960576561382256606844677258438797072955341581354051375036522231471437)+BigInt(4426552127579895373479670356100179759944766558141730312500)//BigInt(3077113738667320707748877199804636746494977000658967987677)*6^(1//2) + A[16,11]=-BigInt(292603171929706291053929402159930330736639136252680853622275)//BigInt(15473622826279161150227076887290262443510550964275858143964) + A[16,12]=-BigInt(9815717129569106988569302193220999343824932084582093647596086931754666098662594153095258988516305165794739744873539829069617203523509136682216933020431)//BigInt(286476991170934153076146641094402171801937250068596542931028678669501762253287693294397689327797388113854588113430063939405071979092547998950955940992) + A[16,13]=BigInt(2729491144709837905799148766650782532906050298971406518524169921875)//BigInt(2158115888622139473142775812109447802920656149243127309253686951469) A[16,14]=0 A[16,15]=0 α[1]=8198160366203173411119943711500331//561057579384085860167277847128765528 @@ -4604,13 +4604,13 @@ function constructVernerEfficient9(T::Type = Float64) α[5]=0 α[6]=0 α[7]=0 - α[8]=-455655493073428838813281446213740000000//1163808011150910561240464225837312497869 - α[9]=19965163648706008081135075746915614720000000//86394404190537086868394686205782432516544599 - α[10]=89231107919981418705566970804343750000000000000000000000//699979870988335674445594679856445060562597693583175985391 + α[8]=-BigInt(455655493073428838813281446213740000000)//BigInt(1163808011150910561240464225837312497869) + α[9]=BigInt(19965163648706008081135075746915614720000000)//BigInt(86394404190537086868394686205782432516544599) + α[10]=BigInt(89231107919981418705566970804343750000000000000000000000)//BigInt(699979870988335674445594679856445060562597693583175985391) α[11]=47104273954945906713184913871143492//209684639122339601934631113492763467 - α[12]=20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083//36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608 - α[13]=6053037282142306509795911286909179687500000000//103899257350518063455290077573775162739725126989 - α[14]=917401104920993498360358406096725463867187500//6724249815911346653315790737453607382989551463 + α[12]=BigInt(20845004421404500464010584740796750650832176798370383084226351294730731196673647311062330972740734737279503119387627146381678677156136042524139311907482802844083)//BigInt(36670849891136373020238225328265100250605144718501926305140966586758054847604681466336103169284755987753542321202462371554120593858149755539878561976786592389608) + α[13]=BigInt(6053037282142306509795911286909179687500000000)//BigInt(103899257350518063455290077573775162739725126989) + α[14]=BigInt(917401104920993498360358406096725463867187500)//BigInt(6724249815911346653315790737453607382989551463) α[15]=2585449557665268951371699596493957//84574345160764140163208606048427531 α[16]=0 αEEst[1]=552562031208180939317806684253//27669654257734667858523344041464 @@ -4621,11 +4621,11 @@ function constructVernerEfficient9(T::Type = Float64) αEEst[6]=0 αEEst[7]=0 αEEst[8]=221223388631423597589898601690000000//100946136798587090054685074667127461 - αEEst[9]=101835408791305297984657812561920000000//1149763833200743759976506650241312100139 - αEEst[10]=1313720309077630014453239843750000000000000000000//11518201923215510989126466531107437037395719117133 + αEEst[9]=BigInt(101835408791305297984657812561920000000)//BigInt(1149763833200743759976506650241312100139) + αEEst[10]=BigInt(1313720309077630014453239843750000000000000000000)//BigInt(11518201923215510989126466531107437037395719117133) αEEst[11]=4833611232701440504508086151728//19081321241454145230196661524503 - αEEst[12]=-2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957//1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568 - αEEst[13]=1084761591753640855844358063964843750000000//3182895486031249071938549691320502488733423 + αEEst[12]=-BigInt(2129662374582324648106919795703373645353118273066742230724172731025813964712473647144010599206669825382719359113196238857709025512340589957)//BigInt(1035543739272367080885190546201097218891268728118207332592595987554851882972292670881794178380097716583123063485287435793657425889233080568) + αEEst[13]=BigInt(1084761591753640855844358063964843750000000)//BigInt(3182895486031249071938549691320502488733423) αEEst[14]=0 αEEst[15]=0 αEEst[16]=1839190071060649887127895100784//38045139523510634351420875415397 @@ -4649,11 +4649,11 @@ function constructSharp9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//50 - c[3]=3837236//48429375+1031368//145288125*6^(1//2) - c[4]=1918618//16143125+515684//48429375*6^(1//2) + c[3]=BigInt(3837236)//BigInt(48429375)+BigInt(1031368)//BigInt(145288125)*6^(1//2) + c[4]=BigInt(1918618)//BigInt(16143125)+BigInt(515684)//BigInt(48429375)*6^(1//2) c[5]=14//45 - c[6]=156//625+26//625*6^(1//2) - c[7]=156//625-26//625*6^(1//2) + c[6]=BigInt(156)//BigInt(625)+BigInt(26)//BigInt(625)*6^(1//2) + c[7]=BigInt(156)//BigInt(625)-BigInt(26)//BigInt(625)*6^(1//2) c[8]=52//125 c[9]=39//125 c[10]=21//200 @@ -4664,48 +4664,48 @@ function constructSharp9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//50 - A[3,1]=-24000387317036//281448523546875-5917264532296//281448523546875*6^(1//2) - A[3,2]=46300580261936//281448523546875+7915204837696//281448523546875*6^(1//2) - A[4,1]=959309//32286250+128921//48429375*6^(1//2) + A[3,1]=-BigInt(24000387317036)//BigInt(281448523546875)-BigInt(5917264532296)//BigInt(281448523546875)*6^(1//2) + A[3,2]=BigInt(46300580261936)//BigInt(281448523546875)+BigInt(7915204837696)//BigInt(281448523546875)*6^(1//2) + A[4,1]=BigInt(959309)//BigInt(32286250)+BigInt(128921)//BigInt(48429375)*6^(1//2) A[4,2]=0 - A[4,3]=2877927//32286250+128921//16143125*6^(1//2) - A[5,1]=2826523628723851//5953434698904030-68459492317475//595343469890403*6^(1//2) + A[4,3]=BigInt(2877927)//BigInt(32286250)+BigInt(128921)//BigInt(16143125)*6^(1//2) + A[5,1]=BigInt(2826523628723851)//BigInt(5953434698904030)-BigInt(68459492317475)//BigInt(595343469890403)*6^(1//2) A[5,2]=0 - A[5,3]=-704240024458145//396895646593602+91277530807085//198447823296801*6^(1//2) - A[5,4]=958925642225180//595343469890403-205373100103780//595343469890403*6^(1//2) - A[6,1]=376341108//9406484375+207933466//65845390625*6^(1//2) + A[5,3]=-BigInt(704240024458145)//BigInt(396895646593602)+BigInt(91277530807085)//BigInt(198447823296801)*6^(1//2) + A[5,4]=BigInt(958925642225180)//BigInt(595343469890403)-BigInt(205373100103780)//BigInt(595343469890403)*6^(1//2) + A[6,1]=BigInt(376341108)//BigInt(9406484375)+BigInt(207933466)//BigInt(65845390625)*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=4343545768844529//27892881885795625+469265141246109//27892881885795625*6^(1//2) - A[6,5]=1559927818449//28957835234375+4382126882523//202704846640625*6^(1//2) - A[7,1]=11781705468//235162109375+2328587014//1646134765625*6^(1//2) + A[6,4]=BigInt(4343545768844529)//BigInt(27892881885795625)+BigInt(469265141246109)//BigInt(27892881885795625)*6^(1//2) + A[6,5]=BigInt(1559927818449)//BigInt(28957835234375)+BigInt(4382126882523)//BigInt(202704846640625)*6^(1//2) + A[7,1]=BigInt(11781705468)//BigInt(235162109375)+BigInt(2328587014)//BigInt(1646134765625)*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=23459106068523828440829//354298872323611753203125+7870375504052283205581//354298872323611753203125*6^(1//2) - A[7,5]=146263465360621089//7558718942052734375-1881455818308499953//52911032594369140625*6^(1//2) - A[7,6]=9444124356888//82889304453125-2459298027368//82889304453125*6^(1//2) + A[7,4]=BigInt(23459106068523828440829)//BigInt(354298872323611753203125)+BigInt(7870375504052283205581)//BigInt(354298872323611753203125)*6^(1//2) + A[7,5]=BigInt(146263465360621089)//BigInt(7558718942052734375)-BigInt(1881455818308499953)//BigInt(52911032594369140625)*6^(1//2) + A[7,6]=BigInt(9444124356888)//BigInt(82889304453125)-BigInt(2459298027368)//BigInt(82889304453125)*6^(1//2) A[8,1]=52//1125 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=208//1125-13//1125*6^(1//2) - A[8,7]=208//1125+13//1125*6^(1//2) + A[8,6]=BigInt(208)//BigInt(1125)-BigInt(13)//BigInt(1125)*6^(1//2) + A[8,7]=BigInt(208)//BigInt(1125)+BigInt(13)//BigInt(1125)*6^(1//2) A[9,1]=741//16000 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=2301//16000-897//32000*6^(1//2) - A[9,7]=2301//16000+897//32000*6^(1//2) + A[9,6]=BigInt(2301)//BigInt(16000)-BigInt(897)//BigInt(32000)*6^(1//2) + A[9,7]=BigInt(2301)//BigInt(16000)+BigInt(897)//BigInt(32000)*6^(1//2) A[9,8]=-351//16000 A[10,1]=35291978967//748709478400 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=23154511989//149741895680+39398793//1772093440*6^(1//2) - A[10,7]=23154511989//149741895680-39398793//1772093440*6^(1//2) + A[10,6]=BigInt(23154511989)//BigInt(149741895680)+BigInt(39398793)//BigInt(1772093440)*6^(1//2) + A[10,7]=BigInt(23154511989)//BigInt(149741895680)-BigInt(39398793)//BigInt(1772093440)*6^(1//2) A[10,8]=-6251205429//149741895680 A[10,9]=-981041103//4679434240 A[11,1]=1601589807329134144752443//16639785968494158002257920 @@ -4713,74 +4713,74 @@ function constructSharp9(T::Type = Float64) A[11,3]=0 A[11,4]=0 A[11,5]=0 - A[11,6]=-1736562342312744743536201//1109319064566277200150528-360257484908262597335743//511993414415204861607936*6^(1//2) - A[11,7]=-1736562342312744743536201//1109319064566277200150528+360257484908262597335743//511993414415204861607936*6^(1//2) + A[11,6]=-BigInt(1736562342312744743536201)//BigInt(1109319064566277200150528)-BigInt(360257484908262597335743)//BigInt(511993414415204861607936)*6^(1//2) + A[11,7]=-BigInt(1736562342312744743536201)//BigInt(1109319064566277200150528)+BigInt(360257484908262597335743)//BigInt(511993414415204861607936)*6^(1//2) A[11,8]=512032742176678555764127//369773021522092400050176 A[11,9]=248233526294563631278471//103998662303088487514112 A[11,10]=-3//20 - A[12,1]=-131987017608786696357225423387594635612719389206128606880670434178321331969627889057541436355642743061150672386594396559//318753926087995555015147926201612010240447228295789462486798116221476093939683123897279961564118214685494052121351290880 + A[12,1]=-BigInt(131987017608786696357225423387594635612719389206128606880670434178321331969627889057541436355642743061150672386594396559)//BigInt(318753926087995555015147926201612010240447228295789462486798116221476093939683123897279961564118214685494052121351290880) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047//1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352+71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031//51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736*6^(1//2) - A[12,7]=-581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047//1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352-71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031//51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736*6^(1//2) - A[12,8]=-189357008262607724321683086336517345228379250897103291049044350530935228180690663776657891613652665009511679250229667441//104902085728430283184879370421906174798708029629619600881898639306750333561102065113284728091471708748347777999725133824 - A[12,9]=-1618350992792815653992284152254111827399426534014847245801101845172567304269189800544372100050869595166981551925667441//19637518660778297585754649024920739916598981028937029385347383945787366501641192454385997632075140011874187139618963456 - A[12,10]=6883437842714982754414155283530543027800010156600147069119889350771791431366439329656536871565378282089012991331513//1827181489551794784669860898707808352423218653885642080180242252960011545073999200946066370836641132319880849653760 - A[12,11]=115590271440716912566235566233889746097162479804636463234298604185457969653794053637008425503953091180886565//315361333249071836330411464879245754163964468656963767284078726004630975015921697525870414526347596936773632 - A[13,1]=5215174783558918407997583468635543407988332719241764605769949554629//20283132613214812064685094275151111714651171227532533713038580121600 + A[12,6]=-BigInt(581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047)//BigInt(1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352)+BigInt(71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031)//BigInt(51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736)*6^(1//2) + A[12,7]=-BigInt(581038619225160876203856834629458675128926705143465192450716448466169075797359178616021045291080972121429188543592047)//BigInt(1011917225676176365127453733973371461080784851732664960275549575306273314094232139356444322425772110112679530543972352)-BigInt(71348279807898814965088233729737906656351096659541311591981953238552744805776480028282602780942939988708855996996031)//BigInt(51893191060316736673202755588378023645168453935008459501310234631090939184319596890074067816706262057060488745844736)*6^(1//2) + A[12,8]=-BigInt(189357008262607724321683086336517345228379250897103291049044350530935228180690663776657891613652665009511679250229667441)//BigInt(104902085728430283184879370421906174798708029629619600881898639306750333561102065113284728091471708748347777999725133824) + A[12,9]=-BigInt(1618350992792815653992284152254111827399426534014847245801101845172567304269189800544372100050869595166981551925667441)//BigInt(19637518660778297585754649024920739916598981028937029385347383945787366501641192454385997632075140011874187139618963456) + A[12,10]=BigInt(6883437842714982754414155283530543027800010156600147069119889350771791431366439329656536871565378282089012991331513)//BigInt(1827181489551794784669860898707808352423218653885642080180242252960011545073999200946066370836641132319880849653760) + A[12,11]=BigInt(115590271440716912566235566233889746097162479804636463234298604185457969653794053637008425503953091180886565)//BigInt(315361333249071836330411464879245754163964468656963767284078726004630975015921697525870414526347596936773632) + A[13,1]=BigInt(5215174783558918407997583468635543407988332719241764605769949554629)//BigInt(20283132613214812064685094275151111714651171227532533713038580121600) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=2843598186227456480865065344408178581293412110128603//792075053175002139265844335272820716293355019960320-18227070890226867447840942666790512323422585544257//121857700488461867579360666965049340968208464609280*6^(1//2) - A[13,7]=2843598186227456480865065344408178581293412110128603//792075053175002139265844335272820716293355019960320+18227070890226867447840942666790512323422585544257//121857700488461867579360666965049340968208464609280*6^(1//2) - A[13,8]=9326829464422062118248457481351539504275339476759467047326605595685633//4901901791858228863857691041029309678010355547895721285919177263022080 - A[13,9]=-741604155090542466856213236072374206251235617068304762316465738169791//141551673163321136844445993892555326037025917405403892742525852712960 - A[13,10]=-6058504866441219655595548618762485399974773685307046001179355536003//2252275720815396172726400694965157641073696835574259179818290290400 - A[13,11]=-72917047186465183128180555150230405657138451692847535142343993//44661747288016218276854771442831738093234145203222656783563600 - A[13,12]=2736153920540927643774133147635296486946660915558253285983742020488887296849241173151960647763453239551016003889152//2485672110698341015290264470463939203955869249618375406787169018009688457749866177826801192710345262847046284166825 - A[14,1]=1961431625890315687063141575818232405522545898155499982338718373117379429883//480056647167077429990593568055406093586176318669944422673481728000000000000 + A[13,6]=BigInt(2843598186227456480865065344408178581293412110128603)//BigInt(792075053175002139265844335272820716293355019960320)-BigInt(18227070890226867447840942666790512323422585544257)//BigInt(121857700488461867579360666965049340968208464609280)*6^(1//2) + A[13,7]=BigInt(2843598186227456480865065344408178581293412110128603)//BigInt(792075053175002139265844335272820716293355019960320)+BigInt(18227070890226867447840942666790512323422585544257)//BigInt(121857700488461867579360666965049340968208464609280)*6^(1//2) + A[13,8]=BigInt(9326829464422062118248457481351539504275339476759467047326605595685633)//BigInt(4901901791858228863857691041029309678010355547895721285919177263022080) + A[13,9]=-BigInt(741604155090542466856213236072374206251235617068304762316465738169791)//BigInt(141551673163321136844445993892555326037025917405403892742525852712960) + A[13,10]=-BigInt(6058504866441219655595548618762485399974773685307046001179355536003)//BigInt(2252275720815396172726400694965157641073696835574259179818290290400) + A[13,11]=-BigInt(72917047186465183128180555150230405657138451692847535142343993)//BigInt(44661747288016218276854771442831738093234145203222656783563600) + A[13,12]=BigInt(2736153920540927643774133147635296486946660915558253285983742020488887296849241173151960647763453239551016003889152)//BigInt(2485672110698341015290264470463939203955869249618375406787169018009688457749866177826801192710345262847046284166825) + A[14,1]=BigInt(1961431625890315687063141575818232405522545898155499982338718373117379429883)//BigInt(480056647167077429990593568055406093586176318669944422673481728000000000000) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=-8688525606146315530022414580346392155721271039//22386738118754433181814607602481176248320000000-10256190098435854298655077997613296122112139953//1148037852243817086246902953973393653760000000*6^(1//2) - A[14,7]=-8688525606146315530022414580346392155721271039//22386738118754433181814607602481176248320000000+10256190098435854298655077997613296122112139953//1148037852243817086246902953973393653760000000*6^(1//2) - A[14,8]=-108151392092290424953498836380059772609736403739434481043071361807712075869481//8600735495194563448316261478331353993230137106756553600705167485829120000000 - A[14,9]=683210554257935462600257975958139742203919396113084127371502375524416129719//26895337200565243662247103690698994332502640106760065066162305761280000000 - A[14,10]=-125971034051203704183074450363446847441594334546885083244594242327104115033//5066049934698363488698655054901069679084758735799331062593807151200000000 - A[14,11]=4322338495495152743252505005837177994220267688026960252214552638944423//236867625787508422152958167179676757535142999000924357630500000000000 - A[14,12]=-88682414394183619425441647866243388112917289239161463940944492930492112547171652363240146123589908870567811533658125375935101390832//9405104776230176067202383689444499684238639823097650089954333383377958770491999076242219980453370248022825420814384818872314453125 - A[14,13]=26235475641986625187247554297838197168935151270802587//31781620957198174033817415268740604591106877500000000 - A[15,1]=-2933688768685553737193922190442902414638569907165819426999847151894747//1423967854813137802350516795065201258930107696470226170813903745843200 + A[14,6]=-BigInt(8688525606146315530022414580346392155721271039)//BigInt(22386738118754433181814607602481176248320000000)-BigInt(10256190098435854298655077997613296122112139953)//BigInt(1148037852243817086246902953973393653760000000)*6^(1//2) + A[14,7]=-BigInt(8688525606146315530022414580346392155721271039)//BigInt(22386738118754433181814607602481176248320000000)+BigInt(10256190098435854298655077997613296122112139953)//BigInt(1148037852243817086246902953973393653760000000)*6^(1//2) + A[14,8]=-BigInt(108151392092290424953498836380059772609736403739434481043071361807712075869481)//BigInt(8600735495194563448316261478331353993230137106756553600705167485829120000000) + A[14,9]=BigInt(683210554257935462600257975958139742203919396113084127371502375524416129719)//BigInt(26895337200565243662247103690698994332502640106760065066162305761280000000) + A[14,10]=-BigInt(125971034051203704183074450363446847441594334546885083244594242327104115033)//BigInt(5066049934698363488698655054901069679084758735799331062593807151200000000) + A[14,11]=BigInt(4322338495495152743252505005837177994220267688026960252214552638944423)//BigInt(236867625787508422152958167179676757535142999000924357630500000000000) + A[14,12]=-BigInt(88682414394183619425441647866243388112917289239161463940944492930492112547171652363240146123589908870567811533658125375935101390832)//BigInt(9405104776230176067202383689444499684238639823097650089954333383377958770491999076242219980453370248022825420814384818872314453125) + A[14,13]=BigInt(26235475641986625187247554297838197168935151270802587)//BigInt(31781620957198174033817415268740604591106877500000000) + A[15,1]=-BigInt(2933688768685553737193922190442902414638569907165819426999847151894747)//BigInt(1423967854813137802350516795065201258930107696470226170813903745843200) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-279050827135618188106138704976571118076242172562777//26980717750745660055932121988692169249262917386240+59017804198407615229179283246229064921710388893173//17987145167163773370621414659128112832841944924160*6^(1//2) - A[15,7]=-279050827135618188106138704976571118076242172562777//26980717750745660055932121988692169249262917386240-59017804198407615229179283246229064921710388893173//17987145167163773370621414659128112832841944924160*6^(1//2) - A[15,8]=68240477823918559060550996013166770535743446467404475965020846786328901//69628625900822775316247857716283393138506964199995817446989013471723520 - A[15,9]=48531604865335743440838806675493568975092395234916265724406574203650554879//7529075569049450724715447951105730327391304314424323559158913160761835520 - A[15,10]=7315898198049114373691779027237206235234893868747090317226910860963581499//432400219379131684183655517400956805867024783959757582533074834771793600 - A[15,11]=-87035912584683752124645187592152267644073875904388006117245587111831//41468532532723053663401983927439573730970639521941633396843682248800 - A[15,12]=793006054328041651061360131256412474400253089909554005378332728214806108995212138291759017448087224471716436232175864384424753159293287828190208//600635305507048430170531323174007915813446499853348186301444535722932552444071789775577508083955280258070844780520371987041149053341617704219325 - A[15,13]=19013238692887784267164981427867630356262081870600946422701364458//146516308633144198110735805762400905606463733191840985648075179899 - A[15,14]=368176545506575596342007241113258886329861009608750000000//7515329389098801941975451526298754679007062667248055263091 - A[16,1]=-36388658330162124762200023703074655379362961851837455245313588466117//299291302137383314536268908335335078201218487321808786511993451315200 + A[15,6]=-BigInt(279050827135618188106138704976571118076242172562777)//BigInt(26980717750745660055932121988692169249262917386240)+BigInt(59017804198407615229179283246229064921710388893173)//BigInt(17987145167163773370621414659128112832841944924160)*6^(1//2) + A[15,7]=-BigInt(279050827135618188106138704976571118076242172562777)//BigInt(26980717750745660055932121988692169249262917386240)-BigInt(59017804198407615229179283246229064921710388893173)//BigInt(17987145167163773370621414659128112832841944924160)*6^(1//2) + A[15,8]=BigInt(68240477823918559060550996013166770535743446467404475965020846786328901)//BigInt(69628625900822775316247857716283393138506964199995817446989013471723520) + A[15,9]=BigInt(48531604865335743440838806675493568975092395234916265724406574203650554879)//BigInt(7529075569049450724715447951105730327391304314424323559158913160761835520) + A[15,10]=BigInt(7315898198049114373691779027237206235234893868747090317226910860963581499)//BigInt(432400219379131684183655517400956805867024783959757582533074834771793600) + A[15,11]=-BigInt(87035912584683752124645187592152267644073875904388006117245587111831)//BigInt(41468532532723053663401983927439573730970639521941633396843682248800) + A[15,12]=BigInt(793006054328041651061360131256412474400253089909554005378332728214806108995212138291759017448087224471716436232175864384424753159293287828190208)//BigInt(600635305507048430170531323174007915813446499853348186301444535722932552444071789775577508083955280258070844780520371987041149053341617704219325) + A[15,13]=BigInt(19013238692887784267164981427867630356262081870600946422701364458)//BigInt(146516308633144198110735805762400905606463733191840985648075179899) + A[15,14]=BigInt(368176545506575596342007241113258886329861009608750000000)//BigInt(7515329389098801941975451526298754679007062667248055263091) + A[16,1]=-BigInt(36388658330162124762200023703074655379362961851837455245313588466117)//BigInt(299291302137383314536268908335335078201218487321808786511993451315200) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-5017294099975580158862668031284197043053591531405121//432874134925719951608236287739966681862399087083520-115700422823857939498444446575144266776173664871303//199788062273409208434570594341523083936491886346240*6^(1//2) - A[16,7]=-5017294099975580158862668031284197043053591531405121//432874134925719951608236287739966681862399087083520+115700422823857939498444446575144266776173664871303//199788062273409208434570594341523083936491886346240*6^(1//2) - A[16,8]=-91869384706617020415871523809581333688744319256441669606452442156503951243//10053990532496870785611049673131231012151168225596329651077879646797168640 - A[16,9]=52862999381403119807509472978743982056878734540171187101666495333163485251//2399905281474961058988767393522446655063434938667458594324573249770618880 - A[16,10]=11964965861294434337427534231330501089458731146841410298258149571218167//1974017923973741961134058915802491373563600428420464580517659076868800 - A[16,11]=37167680872257703003686692191635149388479305578570534942584948859//3913390524272247558198063815920084715858046504866006220243936800 - A[16,12]=-29443955867054347753341026121045589578978185460220369427665634428174791788280117223531690217195051250854008448256016995751289856//6138364406531943832091734698181735919618182422997726728173639255839442923939727454711783369110119257425239678616468261908910975 - A[16,13]=407816748385172686498153181346812432791118177175769818363629863//626162397882386095196201629768303759628250075752997120162580989 + A[16,6]=-BigInt(5017294099975580158862668031284197043053591531405121)//BigInt(432874134925719951608236287739966681862399087083520)-BigInt(115700422823857939498444446575144266776173664871303)//BigInt(199788062273409208434570594341523083936491886346240)*6^(1//2) + A[16,7]=-BigInt(5017294099975580158862668031284197043053591531405121)//BigInt(432874134925719951608236287739966681862399087083520)+BigInt(115700422823857939498444446575144266776173664871303)//BigInt(199788062273409208434570594341523083936491886346240)*6^(1//2) + A[16,8]=-BigInt(91869384706617020415871523809581333688744319256441669606452442156503951243)//BigInt(10053990532496870785611049673131231012151168225596329651077879646797168640) + A[16,9]=BigInt(52862999381403119807509472978743982056878734540171187101666495333163485251)//BigInt(2399905281474961058988767393522446655063434938667458594324573249770618880) + A[16,10]=BigInt(11964965861294434337427534231330501089458731146841410298258149571218167)//BigInt(1974017923973741961134058915802491373563600428420464580517659076868800) + A[16,11]=BigInt(37167680872257703003686692191635149388479305578570534942584948859)//BigInt(3913390524272247558198063815920084715858046504866006220243936800) + A[16,12]=-BigInt(29443955867054347753341026121045589578978185460220369427665634428174791788280117223531690217195051250854008448256016995751289856)//BigInt(6138364406531943832091734698181735919618182422997726728173639255839442923939727454711783369110119257425239678616468261908910975) + A[16,13]=BigInt(407816748385172686498153181346812432791118177175769818363629863)//BigInt(626162397882386095196201629768303759628250075752997120162580989) A[16,14]=0 A[16,15]=0 α[1]=30703843389361946002220520407//1036329015084155723633962896000 @@ -4791,11 +4791,11 @@ function constructSharp9(T::Type = Float64) α[6]=0 α[7]=0 α[8]=1516681888913470906364013671875//19423768214582439936604117641536 - α[9]=1929922737998470573359614532470703125//9295447834009061726737853188569292704 - α[10]=27072397368129209968072433152000000000//159540891067276798629433718421290211669 - α[11]=3416676287738448149119878197304164096817920457//22521752441211566270536786917243920830369456000 - α[12]=909034900749411645631439991260524977916886591502548355130330148829066896764151555292038222333366816993556860935646735988456500531298304//6301978749188979317659380355882211371188146506066543226107226217493443986031316306450151922600620534579104501042337690306078523205079625 - α[13]=9160897746149204383653282352747804858423571//54934119002888850773584011583391921191449440 + α[9]=BigInt(1929922737998470573359614532470703125)//BigInt(9295447834009061726737853188569292704) + α[10]=BigInt(27072397368129209968072433152000000000)//BigInt(159540891067276798629433718421290211669) + α[11]=BigInt(3416676287738448149119878197304164096817920457)//BigInt(22521752441211566270536786917243920830369456000) + α[12]=BigInt(909034900749411645631439991260524977916886591502548355130330148829066896764151555292038222333366816993556860935646735988456500531298304)//BigInt(6301978749188979317659380355882211371188146506066543226107226217493443986031316306450151922600620534579104501042337690306078523205079625) + α[13]=BigInt(9160897746149204383653282352747804858423571)//BigInt(54934119002888850773584011583391921191449440) α[14]=3769686146953412690297035156250000//195792979665408643382362918863397227 α[15]=50782110772148063247179059//1538266148871578545201811280 α[16]=0 @@ -4809,9 +4809,9 @@ function constructSharp9(T::Type = Float64) αEEst[8]=2518169234679274570156341552734375//38284247150941989115046715871467456 αEEst[9]=13171020424136540706261627197265625//61559257178867958455217570785227104 αEEst[10]=33191111003144264098986272000000000//196721197370254992144801132455351679 - αEEst[11]=98603841096694858013088556726735239713679//574051243626833692823306576536179258032000 - αEEst[12]=5093635768538576107415789300891145054334065554846760039946162068969260804962050605021707042060987973190001839145435136//40589106364182299226269510371318864016087966429387805447847648739509460272079710913035195393529050583646417571607929125 - αEEst[13]=108010721096523379193662759959856611609133//570689193181223151553200582051397411377120 + αEEst[11]=BigInt(98603841096694858013088556726735239713679)//BigInt(574051243626833692823306576536179258032000) + αEEst[12]=BigInt(5093635768538576107415789300891145054334065554846760039946162068969260804962050605021707042060987973190001839145435136)//BigInt(40589106364182299226269510371318864016087966429387805447847648739509460272079710913035195393529050583646417571607929125) + αEEst[13]=BigInt(108010721096523379193662759959856611609133)//BigInt(570689193181223151553200582051397411377120) αEEst[14]=0 αEEst[15]=0 αEEst[16]=26859551018855966185191031//763900876650511794556001520 @@ -4834,11 +4834,11 @@ function constructTsitouras9(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//49 - c[3]=64//705-16//14805*6^(1//2) - c[4]=32//235-8//4935*6^(1//2) + c[3]=BigInt(64)//BigInt(705)-BigInt(16)//BigInt(14805)*6^(1//2) + c[4]=BigInt(32)//BigInt(235)-BigInt(8)//BigInt(4935)*6^(1//2) c[5]=3//7 - c[6]=8//21+4//63*6^(1//2) - c[7]=8//21-4//63*6^(1//2) + c[6]=BigInt(8)//BigInt(21)+BigInt(4)//BigInt(63)*6^(1//2) + c[7]=BigInt(8)//BigInt(21)-BigInt(4)//BigInt(63)*6^(1//2) c[8]=40//63 c[9]=10//21 c[10]=19//18 @@ -4849,122 +4849,122 @@ function constructTsitouras9(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//49 - A[3,1]=-165952//1491075+38896//10437525*6^(1//2) - A[3,2]=301312//1491075-7168//1491075*6^(1//2) - A[4,1]=8//235-2//4935*6^(1//2) + A[3,1]=-BigInt(165952)//BigInt(1491075)+BigInt(38896)//BigInt(10437525)*6^(1//2) + A[3,2]=BigInt(301312)//BigInt(1491075)-BigInt(7168)//BigInt(1491075)*6^(1//2) + A[4,1]=BigInt(8)//BigInt(235)-BigInt(2)//BigInt(4935)*6^(1//2) A[4,2]=0 - A[4,3]=24//235-2//1645*6^(1//2) - A[5,1]=38937//44800+171//5600*6^(1//2) + A[4,3]=BigInt(24)//BigInt(235)-BigInt(2)//BigInt(1645)*6^(1//2) + A[5,1]=BigInt(38937)//BigInt(44800)+BigInt(171)//BigInt(5600)*6^(1//2) A[5,2]=0 - A[5,3]=-149931//44800-81//700*6^(1//2) - A[5,4]=65097//22400+477//5600*6^(1//2) - A[6,1]=176//5103-29//5103*6^(1//2) + A[5,3]=-BigInt(149931)//BigInt(44800)-BigInt(81)//BigInt(700)*6^(1//2) + A[5,4]=BigInt(65097)//BigInt(22400)+BigInt(477)//BigInt(5600)*6^(1//2) + A[6,1]=BigInt(176)//BigInt(5103)-BigInt(29)//BigInt(5103)*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=364520//1674351+87715//5023053*6^(1//2) - A[6,5]=1940224//15069159+779264//15069159*6^(1//2) - A[7,1]=4336//127575+479//127575*6^(1//2) + A[6,4]=BigInt(364520)//BigInt(1674351)+BigInt(87715)//BigInt(5023053)*6^(1//2) + A[6,5]=BigInt(1940224)//BigInt(15069159)+BigInt(779264)//BigInt(15069159)*6^(1//2) + A[7,1]=BigInt(4336)//BigInt(127575)+BigInt(479)//BigInt(127575)*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=90731944//400648275-170142739//8413613775*6^(1//2) - A[7,5]=8245504//62429373-22187008//437005611*6^(1//2) - A[7,6]=-3936//340025+11464//3060225*6^(1//2) + A[7,4]=BigInt(90731944)//BigInt(400648275)-BigInt(170142739)//BigInt(8413613775)*6^(1//2) + A[7,5]=BigInt(8245504)//BigInt(62429373)-BigInt(22187008)//BigInt(437005611)*6^(1//2) + A[7,6]=-BigInt(3936)//BigInt(340025)+BigInt(11464)//BigInt(3060225)*6^(1//2) A[8,1]=40//567 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=160//567-10//567*6^(1//2) + A[8,6]=BigInt(160)//BigInt(567)-BigInt(10)//BigInt(567)*6^(1//2) A[8,7]=10//567*6^(1//2)+160//567 A[9,1]=95//1344 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=295//1344-115//2688*6^(1//2) - A[9,7]=295//1344+115//2688*6^(1//2) + A[9,6]=BigInt(295)//BigInt(1344)-BigInt(115)//BigInt(2688)*6^(1//2) + A[9,7]=BigInt(295)//BigInt(1344)+BigInt(115)//BigInt(2688)*6^(1//2) A[9,8]=-15//448 A[10,1]=52918819//138240000 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=-1453047743//103680000-4153586941//829440000*6^(1//2) - A[10,7]=-1453047743//103680000+4153586941//829440000*6^(1//2) + A[10,6]=-BigInt(1453047743)//BigInt(103680000)-BigInt(4153586941)//BigInt(829440000)*6^(1//2) + A[10,7]=-BigInt(1453047743)//BigInt(103680000)+BigInt(4153586941)//BigInt(829440000)*6^(1//2) A[10,8]=44599023//5120000 A[10,9]=518179039//25920000 - A[11,1]=258780283//8618400000+585428803//51710400000*6^(1//2) + A[11,1]=BigInt(258780283)//BigInt(8618400000)+BigInt(585428803)//BigInt(51710400000)*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=19//25 - A[11,7]=1180508473123//443296800000-136404911099//147765600000*6^(1//2) - A[11,8]=-106856621//190800000+585428803//2289600000*6^(1//2) - A[11,9]=-1260561943//591300000+585428803//886950000*6^(1//2) - A[11,10]=13167297224//792049782825-9366860848//2376149348475*6^(1//2) - A[12,1]=307213395328582867964430765847473084972824867512957518186088963//5126364212860621132939944111710304798478633358572140981841000000+119107533326819222510639750832411974467191643469020133053//29137664905764716334007503363213354847664112851105748578125*6^(1//2) + A[11,7]=BigInt(1180508473123)//BigInt(443296800000)-BigInt(136404911099)//BigInt(147765600000)*6^(1//2) + A[11,8]=-BigInt(106856621)//BigInt(190800000)+BigInt(585428803)//BigInt(2289600000)*6^(1//2) + A[11,9]=-BigInt(1260561943)//BigInt(591300000)+BigInt(585428803)//BigInt(886950000)*6^(1//2) + A[11,10]=BigInt(13167297224)//BigInt(792049782825)-BigInt(9366860848)//BigInt(2376149348475)*6^(1//2) + A[12,1]=BigInt(307213395328582867964430765847473084972824867512957518186088963)//BigInt(5126364212860621132939944111710304798478633358572140981841000000)+BigInt(119107533326819222510639750832411974467191643469020133053)//BigInt(29137664905764716334007503363213354847664112851105748578125)*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=10354821182100230493026667000379184955505622050895245676387169//146467548938874889512569831763151565670818095959204028052600000-3268463788087907168885902319404754223684763360609854606186699//41847871125392825575019951932329018763090884559772579443600000*6^(1//2) - A[12,7]=542371157260956891298011197530777699174343335570401188235055068891//715703215922030799396778727922657043395761853183510539934169000000-2557103919967567420571445567798380600417779349808054092568810687111//10019845022908431191554902190917198607540665944569147559078366000000*6^(1//2) - A[12,8]=-892225578009519154676238995901578841509244882985862325637048827//38813900468801845720831005417235164902766795429189067433939000000+20367388198886087049319397392342447633889771033202442752063//220613748572218566528913954035758258132313997301229239234375*6^(1//2) - A[12,9]=-550688605235770338034863642917595195825050633798073448796494914//835322740042020854251374821774223772966384453517335472487484375+72417380262706087286468968506106480476052519229164240896224//303864219731546327483221106502082129125640034018674235171875*6^(1//2) - A[12,10]=123396895115495738434549229715587040998178289648593721222723693824//16960466422214315122555088502288155618001490986047888958907461648625-8781560217119727637264447549372070053517105489683916369731584//6169685857480653009296139869875647732994358307038155314262445125*6^(1//2) - A[12,11]=-241890129426298647138485610377551406165672225318019246672//3661688723471872237814245794078789141770452398980100701315 - A[13,1]=45077846760256141387004276823//110315894143992133591739924480+1493491403898138129099//13100021190238236835840*6^(1//2) + A[12,6]=BigInt(10354821182100230493026667000379184955505622050895245676387169)//BigInt(146467548938874889512569831763151565670818095959204028052600000)-BigInt(3268463788087907168885902319404754223684763360609854606186699)//BigInt(41847871125392825575019951932329018763090884559772579443600000)*6^(1//2) + A[12,7]=BigInt(542371157260956891298011197530777699174343335570401188235055068891)//BigInt(715703215922030799396778727922657043395761853183510539934169000000)-BigInt(2557103919967567420571445567798380600417779349808054092568810687111)//BigInt(10019845022908431191554902190917198607540665944569147559078366000000)*6^(1//2) + A[12,8]=-BigInt(892225578009519154676238995901578841509244882985862325637048827)//BigInt(38813900468801845720831005417235164902766795429189067433939000000)+BigInt(20367388198886087049319397392342447633889771033202442752063)//BigInt(220613748572218566528913954035758258132313997301229239234375)*6^(1//2) + A[12,9]=-BigInt(550688605235770338034863642917595195825050633798073448796494914)//BigInt(835322740042020854251374821774223772966384453517335472487484375)+BigInt(72417380262706087286468968506106480476052519229164240896224)//BigInt(303864219731546327483221106502082129125640034018674235171875)*6^(1//2) + A[12,10]=BigInt(123396895115495738434549229715587040998178289648593721222723693824)//BigInt(16960466422214315122555088502288155618001490986047888958907461648625)-BigInt(8781560217119727637264447549372070053517105489683916369731584)//BigInt(6169685857480653009296139869875647732994358307038155314262445125)*6^(1//2) + A[12,11]=-BigInt(241890129426298647138485610377551406165672225318019246672)//BigInt(3661688723471872237814245794078789141770452398980100701315) + A[13,1]=BigInt(45077846760256141387004276823)//BigInt(110315894143992133591739924480)+BigInt(1493491403898138129099)//BigInt(13100021190238236835840)*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=28530732123103900185//9849639992660328448-15062887306567756845//5628365710091616256*6^(1//2) - A[13,7]=530875502237315716994493//24064781139210466754560-8920823473649531766699837//1347627743795786138255360*6^(1//2) - A[13,8]=-155850251753928802974915857362119//174015086605340016477040216637440+13441422635083243161891//5220309196109974077440*6^(1//2) - A[13,9]=-493074073683718697930133408597//27602712116408194083051274240+1493491403898138129099//224694912332563742720*6^(1//2) - A[13,10]=200609996314078300148532240828075//1019933691979646265167106381709312-336035565877081079047275//8465066424794973677551616*6^(1//2) + A[13,6]=BigInt(28530732123103900185)//BigInt(9849639992660328448)-BigInt(15062887306567756845)//BigInt(5628365710091616256)*6^(1//2) + A[13,7]=BigInt(530875502237315716994493)//BigInt(24064781139210466754560)-BigInt(8920823473649531766699837)//BigInt(1347627743795786138255360)*6^(1//2) + A[13,8]=-BigInt(155850251753928802974915857362119)//BigInt(174015086605340016477040216637440)+BigInt(13441422635083243161891)//BigInt(5220309196109974077440)*6^(1//2) + A[13,9]=-BigInt(493074073683718697930133408597)//BigInt(27602712116408194083051274240)+BigInt(1493491403898138129099)//BigInt(224694912332563742720)*6^(1//2) + A[13,10]=BigInt(200609996314078300148532240828075)//BigInt(1019933691979646265167106381709312)-BigInt(336035565877081079047275)//BigInt(8465066424794973677551616)*6^(1//2) A[13,11]=-1259978731825102407292471875//947642075600343143202947072 - A[13,12]=-193916214235317468987992391599053188049367133486207120889311375//42748092349455088111344007455417233641020280098816132254793728 - A[14,1]=36716621212098036093935018687105425505961//72248275402215258274603114496000000000000+1221461237263884679751555607//9994523002806272000000000000*6^(1//2) + A[13,12]=-BigInt(193916214235317468987992391599053188049367133486207120889311375)//BigInt(42748092349455088111344007455417233641020280098816132254793728) + A[14,1]=BigInt(36716621212098036093935018687105425505961)//BigInt(72248275402215258274603114496000000000000)+1221461237263884679751555607//9994523002806272000000000000*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=8283471074731862302286097//7514678949478400000000000-15668946773152185221466849//4294102256844800000000000*6^(1//2) - A[14,7]=397408075485926915758262202639//18359970961922048000000000000-6493922587539771225254133441201//1028158373867634688000000000000*6^(1//2) - A[14,8]=2435278493903047909370803905780425755549361787//6951941874960961660657094977773568000000000000+10993151135374962117764000463//3982779843223552000000000000*6^(1//2) - A[14,9]=-558123239069103416347126929975086912148938889//34184771406932232290260692794368000000000000+1221461237263884679751555607//171428613534976000000000000*6^(1//2) - A[14,10]=306734586161727173704146823378382330889519//1406266800626214225846914661737584000000000-10993151135374962117764000463//258333325951995046312000000000*6^(1//2) - A[14,11]=-163845778835264660255510638493965671483//114196173990354810149157741209600000000 - A[14,12]=-379727098691580451304129337662817719784451899678250630685021894233169654109523405323//74980943726337976053062781324716052947047103330285761853079535691020475760640000000 + A[14,6]=BigInt(8283471074731862302286097)//BigInt(7514678949478400000000000)-BigInt(15668946773152185221466849)//BigInt(4294102256844800000000000)*6^(1//2) + A[14,7]=BigInt(397408075485926915758262202639)//BigInt(18359970961922048000000000000)-BigInt(6493922587539771225254133441201)//BigInt(1028158373867634688000000000000)*6^(1//2) + A[14,8]=BigInt(2435278493903047909370803905780425755549361787)//BigInt(6951941874960961660657094977773568000000000000)+10993151135374962117764000463//3982779843223552000000000000*6^(1//2) + A[14,9]=-BigInt(558123239069103416347126929975086912148938889)//BigInt(34184771406932232290260692794368000000000000)+1221461237263884679751555607//171428613534976000000000000*6^(1//2) + A[14,10]=BigInt(306734586161727173704146823378382330889519)//BigInt(1406266800626214225846914661737584000000000)-10993151135374962117764000463//258333325951995046312000000000*6^(1//2) + A[14,11]=-BigInt(163845778835264660255510638493965671483)//BigInt(114196173990354810149157741209600000000) + A[14,12]=-BigInt(379727098691580451304129337662817719784451899678250630685021894233169654109523405323)//BigInt(74980943726337976053062781324716052947047103330285761853079535691020475760640000000) A[14,13]=-235412270220829707518634576//10004921377982463725322265625 - A[15,1]=246936976626965995144662615055843//458607216908592948032148676000000+1082690484492446489//9760276369928000000*6^(1//2) + A[15,1]=BigInt(246936976626965995144662615055843)//BigInt(458607216908592948032148676000000)+BigInt(1082690484492446489)//BigInt(9760276369928000000)*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=-5604689614035063//3669276830800000-556441805223969//131045601100000*6^(1//2) - A[15,7]=613864878280672501731//35859318285004000000-1204548796910252147313//251015227995028000000*6^(1//2) - A[15,8]=2797434125723089631989036145593862912367//1454544479209361363081818944324206000000+9744214360432018401//3889433440648000000*6^(1//2) - A[15,9]=-78495184115962971170097375833699424291//6993857040773733071103139785566500000+1082690484492446489//167410755405250000*6^(1//2) - A[15,10]=38933993403647216169460437449231039304//187659712667940353060087104196403689875-155907429766912294416//4036458217999922598625*6^(1//2) + A[15,6]=-BigInt(5604689614035063)//BigInt(3669276830800000)-BigInt(556441805223969)//BigInt(131045601100000)*6^(1//2) + A[15,7]=BigInt(613864878280672501731)//BigInt(35859318285004000000)-BigInt(1204548796910252147313)//BigInt(251015227995028000000)*6^(1//2) + A[15,8]=BigInt(2797434125723089631989036145593862912367)//BigInt(1454544479209361363081818944324206000000)+9744214360432018401//3889433440648000000*6^(1//2) + A[15,9]=-BigInt(78495184115962971170097375833699424291)//BigInt(6993857040773733071103139785566500000)+1082690484492446489//167410755405250000*6^(1//2) + A[15,10]=BigInt(38933993403647216169460437449231039304)//BigInt(187659712667940353060087104196403689875)-155907429766912294416//4036458217999922598625*6^(1//2) A[15,11]=-4116079644901049270506242987//3129604261871291193409631155 - A[15,12]=-869293931367062297302433741250572190497190440843976042585249416347005728190566119731//185354770907948507678541561399002564941703939116570719233261621774655604595976403844 + A[15,12]=-BigInt(869293931367062297302433741250572190497190440843976042585249416347005728190566119731)//BigInt(185354770907948507678541561399002564941703939116570719233261621774655604595976403844) A[15,13]=37424319425692041216//5567956245138066768875 A[15,14]=-26637096887808000000//690666426738105277187 - A[16,1]=29766990313562078086727231879295211//61911974282660047984340071260000000+13591007763158148317//146404145548920000000*6^(1//2) + A[16,1]=BigInt(29766990313562078086727231879295211)//BigInt(61911974282660047984340071260000000)+BigInt(13591007763158148317)//BigInt(146404145548920000000)*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-583353427111301443//293542146464000000-40076566638916409//10483648088000000*6^(1//2) - A[16,7]=19531933359906438277223//1434372731400160000000-9404496119706140958251//2510152279950280000000*6^(1//2) - A[16,8]=117813280551292383465368402104818510183261//58181779168374454523272757772968240000000+40773023289474444951//19447167203240000000*6^(1//2) - A[16,9]=-2325450203082696961260142930045971433803//279754281630949322844125591422660000000+13591007763158148317//2511161331078750000*6^(1//2) - A[16,10]=2829276993010365332321333380796499415893//15951075576774930010107403856694313639375-652368372631591119216//20182291089999612993125*6^(1//2) + A[16,6]=-BigInt(583353427111301443)//BigInt(293542146464000000)-BigInt(40076566638916409)//BigInt(10483648088000000)*6^(1//2) + A[16,7]=BigInt(19531933359906438277223)//BigInt(1434372731400160000000)-BigInt(9404496119706140958251)//BigInt(2510152279950280000000)*6^(1//2) + A[16,8]=BigInt(117813280551292383465368402104818510183261)//BigInt(58181779168374454523272757772968240000000)+40773023289474444951//19447167203240000000*6^(1//2) + A[16,9]=-BigInt(2325450203082696961260142930045971433803)//BigInt(279754281630949322844125591422660000000)+13591007763158148317//2511161331078750000*6^(1//2) + A[16,10]=BigInt(2829276993010365332321333380796499415893)//BigInt(15951075576774930010107403856694313639375)-652368372631591119216//20182291089999612993125*6^(1//2) A[16,11]=-64853022020814701128056854079867//63343190260274933754610934577200 - A[16,12]=-5501801061234219240967503472431237166019376078542725490351730718419538863636177307419649//1398104557705668743632427777409619346988852569336419139359459089957402274666793446137600 + A[16,12]=-BigInt(5501801061234219240967503472431237166019376078542725490351730718419538863636177307419649)//BigInt(1398104557705668743632427777409619346988852569336419139359459089957402274666793446137600) A[16,13]=-6425519161642982676103168//293904570399612854395066875 A[16,14]=-51926882941360640000//2663999074561263212007 A[16,15]=0 @@ -4979,7 +4979,7 @@ function constructTsitouras9(T::Type = Float64) α[9]=14586697891849999254003//29700462390576849520000 α[10]=102209317997264953344//225042304099487188475 α[11]=1883570537693211021//1872275755054959100 - α[12]=17109990417889849939560223376925306674323804078983341334325755071278367152457480027//71381427125808828146076534703173195056090466069876919551824450642795947233961810560 + α[12]=BigInt(17109990417889849939560223376925306674323804078983341334325755071278367152457480027)//BigInt(71381427125808828146076534703173195056090466069876919551824450642795947233961810560) α[13]=-10678264099993989152768//2396652442219114419375 α[14]=1212545712242913280000000//130535954653501897388343 α[15]=-5462519910419447//852178998090420 @@ -4995,7 +4995,7 @@ function constructTsitouras9(T::Type = Float64) αEEst[9]=444432599960137218801//1132275692309381360000 αEEst[10]=-439332801641475586992//417935707613333350025 αEEst[11]=-217759597939752597//869270886275516725 - αEEst[12]=17659727425367474410466504999969566436559834034377723810849746362072595341//71629450771664553932203312665447432781082741824305141429680586700646203520 + αEEst[12]=BigInt(17659727425367474410466504999969566436559834034377723810849746362072595341)//BigInt(71629450771664553932203312665447432781082741824305141429680586700646203520) αEEst[13]=982070268140959301632//143578256907135886875 αEEst[14]=-3885243675284052992000000//242423915785074952292637 αEEst[15]=10 @@ -5021,11 +5021,11 @@ function constructTsitouras92(T::Type = Float64) αEEst = zeros(T,16) c[2]=1//46 - c[3]=96755252944//718444993695-11256225944//718444993695*6^(1//2) - c[4]=48377626472//239481664565-5628112972//239481664565*6^(1//2) + c[3]=BigInt(96755252944)//BigInt(718444993695)-BigInt(11256225944)//BigInt(718444993695)*6^(1//2) + c[4]=BigInt(48377626472)//BigInt(239481664565)-BigInt(5628112972)//BigInt(239481664565)*6^(1//2) c[5]=71//136 - c[6]=276//715-46//715*6^(1//2) - c[7]=276//715+46//715*6^(1//2) + c[6]=BigInt(276)//BigInt(715)-BigInt(46)//BigInt(715)*6^(1//2) + c[7]=BigInt(276)//BigInt(715)+BigInt(46)//BigInt(715)*6^(1//2) c[8]=92//143 c[9]=69//143 c[10]=3//44 @@ -5036,123 +5036,123 @@ function constructTsitouras92(T::Type = Float64) c[15]=1 c[16]=1 A[2,1]=1//46 - A[3,1]=-163287951175938724532816//516163208965408589753025+42011574289334042817176//516163208965408589753025*6^(1//2) - A[3,2]=232801278267248934720896//516163208965408589753025-50098553466700618240256//516163208965408589753025*6^(1//2) - A[4,1]=12094406618//239481664565-1407028243//239481664565*6^(1//2) + A[3,1]=-BigInt(163287951175938724532816)//BigInt(516163208965408589753025)+BigInt(42011574289334042817176)//BigInt(516163208965408589753025)*6^(1//2) + A[3,2]=BigInt(232801278267248934720896)//BigInt(516163208965408589753025)-BigInt(50098553466700618240256)//BigInt(516163208965408589753025)*6^(1//2) + A[4,1]=BigInt(12094406618)//BigInt(239481664565)-BigInt(1407028243)//BigInt(239481664565)*6^(1//2) A[4,2]=0 - A[4,3]=36283219854//239481664565-4221084729//239481664565*6^(1//2) - A[5,1]=450479172821804238979159483//489985471732935255816699904+65404175703680378526395577//244992735866467627908349952*6^(1//2) + A[4,3]=BigInt(36283219854)//BigInt(239481664565)-BigInt(4221084729)//BigInt(239481664565)*6^(1//2) + A[5,1]=BigInt(450479172821804238979159483)//BigInt(489985471732935255816699904)+BigInt(65404175703680378526395577)//BigInt(244992735866467627908349952)*6^(1//2) A[5,2]=0 - A[5,3]=-1663285823745576633021875313//489985471732935255816699904-258991054585998425691922779//244992735866467627908349952*6^(1//2) - A[5,4]=734303944921586208649981787//244992735866467627908349952+96793439441159023582763601//122496367933233813954174976*6^(1//2) - A[6,1]=188634486760257//2753187875656075-40451003556679//5506375751312150*6^(1//2) + A[5,3]=-BigInt(1663285823745576633021875313)//BigInt(489985471732935255816699904)-BigInt(258991054585998425691922779)//BigInt(244992735866467627908349952)*6^(1//2) + A[5,4]=BigInt(734303944921586208649981787)//BigInt(244992735866467627908349952)+BigInt(96793439441159023582763601)//BigInt(122496367933233813954174976)*6^(1//2) + A[6,1]=BigInt(188634486760257)//BigInt(2753187875656075)-BigInt(40451003556679)//BigInt(5506375751312150)*6^(1//2) A[6,2]=0 A[6,3]=0 - A[6,4]=890541395040155939974909749//3404930508779360011084250045-235414842445143790083329443//6809861017558720022168500090*6^(1//2) - A[6,5]=127509164130554343284736//2278805333809176804299525-51090254569210884816896//2278805333809176804299525*6^(1//2) - A[7,1]=523150756520001//5294592068569375+372205675002861//137659393782803750*6^(1//2) + A[6,4]=BigInt(890541395040155939974909749)//BigInt(3404930508779360011084250045)-BigInt(235414842445143790083329443)//BigInt(6809861017558720022168500090)*6^(1//2) + A[6,5]=BigInt(127509164130554343284736)//BigInt(2278805333809176804299525)-BigInt(51090254569210884816896)//BigInt(2278805333809176804299525)*6^(1//2) + A[7,1]=BigInt(523150756520001)//BigInt(5294592068569375)+BigInt(372205675002861)//BigInt(137659393782803750)*6^(1//2) A[7,2]=0 A[7,3]=0 - A[7,4]=121832502441158811994748302664452173//6319431229672072722127362725145820625-12054008141355156662680357922224203047//164305211971473890775311430853791336250*6^(1//2) - A[7,5]=-7345188891123909155979140554752//52428978281511938535235507146875+71382195182457889488943971467264//681576717659655200958061592909375*6^(1//2) - A[7,6]=84211752143498940768//206389046233053165625+567839841668979868//18762640566641196875*6^(1//2) + A[7,4]=BigInt(121832502441158811994748302664452173)//BigInt(6319431229672072722127362725145820625)-BigInt(12054008141355156662680357922224203047)//BigInt(164305211971473890775311430853791336250)*6^(1//2) + A[7,5]=-BigInt(7345188891123909155979140554752)//BigInt(52428978281511938535235507146875)+BigInt(71382195182457889488943971467264)//BigInt(681576717659655200958061592909375)*6^(1//2) + A[7,6]=BigInt(84211752143498940768)//BigInt(206389046233053165625)+BigInt(567839841668979868)//BigInt(18762640566641196875)*6^(1//2) A[8,1]=92//1287 A[8,2]=0 A[8,3]=0 A[8,4]=0 A[8,5]=0 - A[8,6]=368//1287+23//1287*6^(1//2) - A[8,7]=368//1287-23//1287*6^(1//2) + A[8,6]=BigInt(368)//BigInt(1287)+BigInt(23)//BigInt(1287)*6^(1//2) + A[8,7]=BigInt(368)//BigInt(1287)-BigInt(23)//BigInt(1287)*6^(1//2) A[9,1]=1311//18304 A[9,2]=0 A[9,3]=0 A[9,4]=0 A[9,5]=0 - A[9,6]=4071//18304+1587//36608*6^(1//2) - A[9,7]=4071//18304-1587//36608*6^(1//2) + A[9,6]=BigInt(4071)//BigInt(18304)+BigInt(1587)//BigInt(36608)*6^(1//2) + A[9,7]=BigInt(4071)//BigInt(18304)-BigInt(1587)//BigInt(36608)*6^(1//2) A[9,8]=-621//18304 A[10,1]=2451872601//50434064384 A[10,2]=0 A[10,3]=0 A[10,4]=0 A[10,5]=0 - A[10,6]=84329349//1146228736-1383050643//100868128768*6^(1//2) - A[10,7]=84329349//1146228736+1383050643//100868128768*6^(1//2) + A[10,6]=BigInt(84329349)//BigInt(1146228736)-BigInt(1383050643)//BigInt(100868128768)*6^(1//2) + A[10,7]=BigInt(84329349)//BigInt(1146228736)+BigInt(1383050643)//BigInt(100868128768)*6^(1//2) A[10,8]=-1098320769//50434064384 A[10,9]=-333490521//3152129024 - A[11,1]=-11290810941252792923651//1669469461414577748900000-76218489460616423924209//10016816768487466493400000*6^(1//2) + A[11,1]=-BigInt(11290810941252792923651)//BigInt(1669469461414577748900000)-BigInt(76218489460616423924209)//BigInt(10016816768487466493400000)*6^(1//2) A[11,2]=0 A[11,3]=0 A[11,4]=0 A[11,5]=0 A[11,6]=1//30 - A[11,7]=-44608220078798131601386867//1778327431680661626219300000-302663621648107819403033939//5334982295041984878657900000*6^(1//2) - A[11,8]=4768550623191902657077//335320789258483564950000+76218489460616423924209//9388982099237539818600000*6^(1//2) - A[11,9]=76371166597983496297729//1268154687036073482337500+76218489460616423924209//1902232030554110223506250*6^(1//2) - A[11,10]=12837092726068800321242176//73489499260117750229428125+224387232972054752032871296//13889515360162254793361915625*6^(1//2) - A[12,1]=-355843792738780589211336013211266011894384892859307606673616682840321037292934264483298005378753134077//6114980501338466999761271314291724602877525435623381536957589416556451501095664913528943447961301150000+1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761//62508689569237662664226328990537629273859148897483455711122025147021504233422352449406977468048856200000*6^(1//2) + A[11,7]=-BigInt(44608220078798131601386867)//BigInt(1778327431680661626219300000)-BigInt(302663621648107819403033939)//BigInt(5334982295041984878657900000)*6^(1//2) + A[11,8]=BigInt(4768550623191902657077)//BigInt(335320789258483564950000)+BigInt(76218489460616423924209)//BigInt(9388982099237539818600000)*6^(1//2) + A[11,9]=BigInt(76371166597983496297729)//BigInt(1268154687036073482337500)+BigInt(76218489460616423924209)//BigInt(1902232030554110223506250)*6^(1//2) + A[11,10]=BigInt(12837092726068800321242176)//BigInt(73489499260117750229428125)+BigInt(224387232972054752032871296)//BigInt(13889515360162254793361915625)*6^(1//2) + A[12,1]=-BigInt(355843792738780589211336013211266011894384892859307606673616682840321037292934264483298005378753134077)//BigInt(6114980501338466999761271314291724602877525435623381536957589416556451501095664913528943447961301150000)+BigInt(1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761)//BigInt(62508689569237662664226328990537629273859148897483455711122025147021504233422352449406977468048856200000)*6^(1//2) A[12,2]=0 A[12,3]=0 A[12,4]=0 A[12,5]=0 - A[12,6]=-17594918026040863488775323023688367263938903884097169692619657825340943285779242173824532021369934883//34620197299885474706340736056297763905521990158606221624621429312196525421587764433517710597688597280-1718800244468971293911190106580576895962584281439946985382458420029691073118839588510586218092229//134447368154895047403264994393389374390376660810121249027656036163870001637234036635020235330829504*6^(1//2) - A[12,7]=-138207307502597872414466248711907117101238289950946956575872497287994333538943652935288845283125425999567221//449445892634106961164222874370868126852218761612180707797390011848931329871568905581758203549930436500950000+373422609934822782117113512174693455251869921393106586844571126171756173532479385325874622983683540733325899//1797783570536427844656891497483472507408875046448722831189560047395725319486275622327032814199721746003800000*6^(1//2) - A[12,8]=12632445836279619113294210780168171565726892406599945732333835965116776912265868042131556830549327654393//112996477298237313277639902405971868302745384545450862247028276227308103806571175581620305423011393900000-6303547312203088429495101153246145287920801370707526715790327134571780988988474483681572268319398771221//225992954596474626555279804811943736605490769090901724494056552454616207613142351163240610846022787800000*6^(1//2) - A[12,9]=1115379785277627713874987636432084522404410826010464628546537384975239192450316138834225701046102632948257//3347520639960280405850082108776916598468832017158981794068212683234002575269671076605501548156712544287500-1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761//11870640567235036900177596130414597866910751833897098560525576890900718352020110200728728894172739518750*6^(1//2) - A[12,10]=11195395793619792818419572687595618271094922253700867106612850891912759357989068567623193453186950145251776//37146762745465379216384266737567863919875050348378042013698628944987922182903823702648363618722076517534375-687320121745403419867910288709505619542179230939368838936545299414049008577113662220686991034529999350912//12382254248488459738794755579189287973291683449459347337899542981662640727634607900882787872907358839178125*6^(1//2) - A[12,11]=73825104187474768875967421005730375156586805528272061538441201406502469378399602291332635087412//92871272539029599143289144740668914525146202470165909630170359355065425993729905138177287271317 - A[13,1]=-64719070744144335733962214412431202035561004419937320357188840883//101209800434111984325751891003355158288493635359529771992774000000+3559372342256314491923633965576963561357143961289//36357243706101884581258626118802982597639184500000*6^(1//2) + A[12,6]=-BigInt(17594918026040863488775323023688367263938903884097169692619657825340943285779242173824532021369934883)//BigInt(34620197299885474706340736056297763905521990158606221624621429312196525421587764433517710597688597280)-BigInt(1718800244468971293911190106580576895962584281439946985382458420029691073118839588510586218092229)//BigInt(134447368154895047403264994393389374390376660810121249027656036163870001637234036635020235330829504)*6^(1//2) + A[12,7]=-BigInt(138207307502597872414466248711907117101238289950946956575872497287994333538943652935288845283125425999567221)//BigInt(449445892634106961164222874370868126852218761612180707797390011848931329871568905581758203549930436500950000)+BigInt(373422609934822782117113512174693455251869921393106586844571126171756173532479385325874622983683540733325899)//BigInt(1797783570536427844656891497483472507408875046448722831189560047395725319486275622327032814199721746003800000)*6^(1//2) + A[12,8]=BigInt(12632445836279619113294210780168171565726892406599945732333835965116776912265868042131556830549327654393)//BigInt(112996477298237313277639902405971868302745384545450862247028276227308103806571175581620305423011393900000)-BigInt(6303547312203088429495101153246145287920801370707526715790327134571780988988474483681572268319398771221)//BigInt(225992954596474626555279804811943736605490769090901724494056552454616207613142351163240610846022787800000)*6^(1//2) + A[12,9]=BigInt(1115379785277627713874987636432084522404410826010464628546537384975239192450316138834225701046102632948257)//BigInt(3347520639960280405850082108776916598468832017158981794068212683234002575269671076605501548156712544287500)-BigInt(1634253006867467370609841039730482111683170725738988407797492220074165441589604495769296514008733014761)//BigInt(11870640567235036900177596130414597866910751833897098560525576890900718352020110200728728894172739518750)*6^(1//2) + A[12,10]=BigInt(11195395793619792818419572687595618271094922253700867106612850891912759357989068567623193453186950145251776)//BigInt(37146762745465379216384266737567863919875050348378042013698628944987922182903823702648363618722076517534375)-BigInt(687320121745403419867910288709505619542179230939368838936545299414049008577113662220686991034529999350912)//BigInt(12382254248488459738794755579189287973291683449459347337899542981662640727634607900882787872907358839178125)*6^(1//2) + A[12,11]=BigInt(73825104187474768875967421005730375156586805528272061538441201406502469378399602291332635087412)//BigInt(92871272539029599143289144740668914525146202470165909630170359355065425993729905138177287271317) + A[13,1]=-BigInt(64719070744144335733962214412431202035561004419937320357188840883)//BigInt(101209800434111984325751891003355158288493635359529771992774000000)+BigInt(3559372342256314491923633965576963561357143961289)//BigInt(36357243706101884581258626118802982597639184500000)*6^(1//2) A[13,2]=0 A[13,3]=0 A[13,4]=0 A[13,5]=0 - A[13,6]=-66005588850553492194962577164587068367312330247//19603612723583140697294028442079849957408380800-13176568020345600854085799476910283462657777//76130534848866565814734091037203300805469440*6^(1//2) - A[13,7]=-9318570701703691930191534222789494006237103047579881711//3562968864769188061196125478115789029665196590638000000+6434757944786940764537553522803508307647498263055753667//7125937729538376122392250956231578059330393181276000000*6^(1//2) - A[13,8]=-3761276943318114593157887595063197569838926771255702620302334773297//1464216542935037622889021617525045499738187320641028236799386000000-3559372342256314491923633965576963561357143961289//34078442106289230846820763513066043517445275500000*6^(1//2) - A[13,9]=438696881717332693164574683605145782902979477404432064959580227217//190320793597985643524049406938231176153947641989529318077977593750-3559372342256314491923633965576963561357143961289//6904380415341463658460171786984220252917056671875*6^(1//2) - A[13,10]=39393077397330623465044422844130393549390670768068628724675776122752//24104666116749847055078895726017945791587677982957405550119962671875-911199319617616509932450295187702671707428854089984//4383797390367410875150919593877143523760184037765625*6^(1//2) - A[13,11]=1455014345065512890761705230599774567929341275785651//437274533681980646175086038705021590800143506216585 - A[13,12]=43491235157516875762138510242422928845963515012067399050743561004230490804423974878600834753885909//15650073716933473532700213239415706508578020603344410725067680963543589421556571669667160279586515 - A[14,1]=1113523038973067377822299106095464437335258246585030516055024186482995053//1172081821952666268571554825436238158838606320428900711229598548800375000-9656355719858106181793772673915704646989403181//42650123991481333817759653132492492758879187500*6^(1//2) + A[13,6]=-BigInt(66005588850553492194962577164587068367312330247)//BigInt(19603612723583140697294028442079849957408380800)-BigInt(13176568020345600854085799476910283462657777)//BigInt(76130534848866565814734091037203300805469440)*6^(1//2) + A[13,7]=-BigInt(9318570701703691930191534222789494006237103047579881711)//BigInt(3562968864769188061196125478115789029665196590638000000)+BigInt(6434757944786940764537553522803508307647498263055753667)//BigInt(7125937729538376122392250956231578059330393181276000000)*6^(1//2) + A[13,8]=-BigInt(3761276943318114593157887595063197569838926771255702620302334773297)//BigInt(1464216542935037622889021617525045499738187320641028236799386000000)-BigInt(3559372342256314491923633965576963561357143961289)//BigInt(34078442106289230846820763513066043517445275500000)*6^(1//2) + A[13,9]=BigInt(438696881717332693164574683605145782902979477404432064959580227217)//BigInt(190320793597985643524049406938231176153947641989529318077977593750)-BigInt(3559372342256314491923633965576963561357143961289)//BigInt(6904380415341463658460171786984220252917056671875)*6^(1//2) + A[13,10]=BigInt(39393077397330623465044422844130393549390670768068628724675776122752)//BigInt(24104666116749847055078895726017945791587677982957405550119962671875)-BigInt(911199319617616509932450295187702671707428854089984)//BigInt(4383797390367410875150919593877143523760184037765625)*6^(1//2) + A[13,11]=BigInt(1455014345065512890761705230599774567929341275785651)//BigInt(437274533681980646175086038705021590800143506216585) + A[13,12]=BigInt(43491235157516875762138510242422928845963515012067399050743561004230490804423974878600834753885909)//BigInt(15650073716933473532700213239415706508578020603344410725067680963543589421556571669667160279586515) + A[14,1]=BigInt(1113523038973067377822299106095464437335258246585030516055024186482995053)//BigInt(1172081821952666268571554825436238158838606320428900711229598548800375000)-BigInt(9656355719858106181793772673915704646989403181)//BigInt(42650123991481333817759653132492492758879187500)*6^(1//2) A[14,2]=0 A[14,3]=0 A[14,4]=0 A[14,5]=0 - A[14,6]=65156558806314041332627176859309009839731119//11498348446055040912040697694327646399463400+2893908603034923903437694020377944093049//44653780373029285095303680366320956891120*6^(1//2) - A[14,7]=8209640140354849710164186531509948506760631106345347//2089832016538282470163966831380108687881472614625000-7326425889801057568096943993446608268878122947239059//4179664033076564940327933662760217375762945229250000*6^(1//2) - A[14,8]=358387301461393123075253933751833574944722054371964074460462507967392441417//600381220734980367702253537950121782364502552531871330639897526611625875000+9656355719858106181793772673915704646989403181//39976896846716122011518307352108347913593312500*6^(1//2) - A[14,9]=-642851404125311605101723817200220613720981758568362376903035228606467992291//274647144865445671171423994203344292862210985060954852952360191727428234375+77250845758864849454350181391325637175915225448//64795380679365872530827165335902056306758765625*6^(1//2) - A[14,10]=-369969589301763518639761285997824520507173970793320519753635225871563412913152//180850870268987312974476662632186804296491491034759756207691410652763681078125+454852979828196233587213868032125351691788847437824//946232027174365750372191179393662736769436409578125*6^(1//2) - A[14,11]=-7715303458281199041757411869319392732268755939408305903151657039//1483062857858019956599354292891821472831958379628421680653323310 - A[14,12]=-945432908618140420875128019003679821034774098061354410087876969999388668430388640158852256997513450369741874915618358283//1183336256073681379271114843949311985569932050547818490887959987766109714104308279282406274069868573023638087923030436570 - A[14,13]=1056911827593717127690972016166243945915857152155//7359790814129537930306952068888958882079118176267 - A[15,1]=71647807109611556622880429107737597894249449144677487291739567//4608441750702552040544087416037317498817362012884252849000000-751354288295256883750046307992744439//260856700304180835921321781903000000*6^(1//2) + A[14,6]=BigInt(65156558806314041332627176859309009839731119)//BigInt(11498348446055040912040697694327646399463400)+BigInt(2893908603034923903437694020377944093049)//BigInt(44653780373029285095303680366320956891120)*6^(1//2) + A[14,7]=BigInt(8209640140354849710164186531509948506760631106345347)//BigInt(2089832016538282470163966831380108687881472614625000)-BigInt(7326425889801057568096943993446608268878122947239059)//BigInt(4179664033076564940327933662760217375762945229250000)*6^(1//2) + A[14,8]=BigInt(358387301461393123075253933751833574944722054371964074460462507967392441417)//BigInt(600381220734980367702253537950121782364502552531871330639897526611625875000)+BigInt(9656355719858106181793772673915704646989403181)//BigInt(39976896846716122011518307352108347913593312500)*6^(1//2) + A[14,9]=-BigInt(642851404125311605101723817200220613720981758568362376903035228606467992291)//BigInt(274647144865445671171423994203344292862210985060954852952360191727428234375)+BigInt(77250845758864849454350181391325637175915225448)//BigInt(64795380679365872530827165335902056306758765625)*6^(1//2) + A[14,10]=-BigInt(369969589301763518639761285997824520507173970793320519753635225871563412913152)//BigInt(180850870268987312974476662632186804296491491034759756207691410652763681078125)+BigInt(454852979828196233587213868032125351691788847437824)//BigInt(946232027174365750372191179393662736769436409578125)*6^(1//2) + A[14,11]=-BigInt(7715303458281199041757411869319392732268755939408305903151657039)//BigInt(1483062857858019956599354292891821472831958379628421680653323310) + A[14,12]=-BigInt(945432908618140420875128019003679821034774098061354410087876969999388668430388640158852256997513450369741874915618358283)//BigInt(1183336256073681379271114843949311985569932050547818490887959987766109714104308279282406274069868573023638087923030436570) + A[14,13]=BigInt(1056911827593717127690972016166243945915857152155)//BigInt(7359790814129537930306952068888958882079118176267) + A[15,1]=BigInt(71647807109611556622880429107737597894249449144677487291739567)//BigInt(4608441750702552040544087416037317498817362012884252849000000)-751354288295256883750046307992744439//260856700304180835921321781903000000*6^(1//2) A[15,2]=0 A[15,3]=0 A[15,4]=0 A[15,5]=0 - A[15,6]=538527061627015039205734500467757677//6645826087749591758241674935867200+55735563892040165710948254310427//25809033350483851488317184216960*6^(1//2) - A[15,7]=10166737271161511304691200043681679377006693//172554720727113306507896188662956931000000-8156608278080671316516960851836659322130571//345109441454226613015792377325913862000000*6^(1//2) - A[15,8]=13730153329629135442521913725273883916343982389395960187482153016633//175471617700441378138284361033681728617635976027122756488121000000+20286565783971935861251250315804099853//6601681107698115001393451249699000000*6^(1//2) - A[15,9]=-653480004921889631988496090206918830045333930618354572374567471359//12778455326756234342932466086484629156552273764794479235501062500+751354288295256883750046307992744439//49537690682765110667751011467156250*6^(1//2) - A[15,10]=-1892005381291509192972446465852606492709607810610330309174017655027008//53004882228844808583820366645125601151772763811007845509116404390625+2211987024741236265760136330730639628416//361709036854355745656111465938134640625*6^(1//2) - A[15,11]=-754694656733111129471952033526995126769302954114714957//10457763407796883263416278675753537185966936455426905 - A[15,12]=-3809310391558597134511116925648017476134448177941143033030907811018093065572169647629059619278510306257177668207871699977487//49657222601249321414413002320858790760827862034335478005117886015451993139010886447467038877038198587307390592603767686355 - A[15,13]=1329021384022690762809893094055902242790//314695772164147033634887576401647768207 + A[15,6]=BigInt(538527061627015039205734500467757677)//BigInt(6645826087749591758241674935867200)+BigInt(55735563892040165710948254310427)//BigInt(25809033350483851488317184216960)*6^(1//2) + A[15,7]=BigInt(10166737271161511304691200043681679377006693)//BigInt(172554720727113306507896188662956931000000)-BigInt(8156608278080671316516960851836659322130571)//BigInt(345109441454226613015792377325913862000000)*6^(1//2) + A[15,8]=BigInt(13730153329629135442521913725273883916343982389395960187482153016633)//BigInt(175471617700441378138284361033681728617635976027122756488121000000)+BigInt(20286565783971935861251250315804099853)//BigInt(6601681107698115001393451249699000000)*6^(1//2) + A[15,9]=-BigInt(653480004921889631988496090206918830045333930618354572374567471359)//BigInt(12778455326756234342932466086484629156552273764794479235501062500)+751354288295256883750046307992744439//49537690682765110667751011467156250*6^(1//2) + A[15,10]=-BigInt(1892005381291509192972446465852606492709607810610330309174017655027008)//BigInt(53004882228844808583820366645125601151772763811007845509116404390625)+BigInt(2211987024741236265760136330730639628416)//BigInt(361709036854355745656111465938134640625)*6^(1//2) + A[15,11]=-BigInt(754694656733111129471952033526995126769302954114714957)//BigInt(10457763407796883263416278675753537185966936455426905) + A[15,12]=-BigInt(3809310391558597134511116925648017476134448177941143033030907811018093065572169647629059619278510306257177668207871699977487)//BigInt(49657222601249321414413002320858790760827862034335478005117886015451993139010886447467038877038198587307390592603767686355) + A[15,13]=BigInt(1329021384022690762809893094055902242790)//BigInt(314695772164147033634887576401647768207) A[15,14]=-6893352883273198849981789770//5486160832491820655265629723 - A[16,1]=-2570623236993305537882133348905686861198442251997239696046711165213//1788444074612646395894349444415762174941041849960120845639920000000+17049571162138593122630888759407239103637//41413609740291749510869046094920280000000*6^(1//2) + A[16,1]=-BigInt(2570623236993305537882133348905686861198442251997239696046711165213)//BigInt(1788444074612646395894349444415762174941041849960120845639920000000)+BigInt(17049571162138593122630888759407239103637)//BigInt(41413609740291749510869046094920280000000)*6^(1//2) A[16,2]=0 A[16,3]=0 A[16,4]=0 A[16,5]=0 - A[16,6]=-104754859887173191244557803812288138363//11164987827419314153846013892256896000+3784288812661530935801759817347107//43359176028812870500372869484492800*6^(1//2) - A[16,7]=-12625417179938563922326639910886861363642731119//2029243515750852484532859178676373508560000000+4034430827439578769139663757402876281578669781//1352829010500568323021906119117582339040000000*6^(1//2) - A[16,8]=-121185791557797038984865049921261438811435078875133421073861312913308541//761448556714003333948396687643999840432514259811137574414811792240000000-17049571162138593122630888759407239103637//38817884913264916208193493348230120000000*6^(1//2) - A[16,9]=7831706161943944732903576802308126564075661689777008313099672046941217//1912115178728933570934305539114995143003765478134474309438025195000000-17049571162138593122630888759407239103637//7864603772795788969612150580525726250000*6^(1//2) - A[16,10]=1231862339518930958878836935481237970791679023430521469669885456183927336//350627295943808408781971725357505851618976832609816898042805015043984375-6274242187667002269128167063461863990138416//7178115836374689772545532041542281943203125*6^(1//2) - A[16,11]=23975119191644794266115435124846718653445865470965352804548709//2618162142480251258794523717542364435163988588525025359875200 - A[16,12]=54918621392363748304153623111076473105288800876284517914641326502791860135537567319289496873218100975783896487633335215553248687//42045763520929825428011777325117555313008167341712535936493416447003511630663297772799291157965783507844913762569462175390505600 - A[16,13]=-35648602464057004250287591332213307928385//140983705929537871068429634227938200156736 + A[16,6]=-BigInt(104754859887173191244557803812288138363)//BigInt(11164987827419314153846013892256896000)+3784288812661530935801759817347107//43359176028812870500372869484492800*6^(1//2) + A[16,7]=-BigInt(12625417179938563922326639910886861363642731119)//BigInt(2029243515750852484532859178676373508560000000)+BigInt(4034430827439578769139663757402876281578669781)//BigInt(1352829010500568323021906119117582339040000000)*6^(1//2) + A[16,8]=-BigInt(121185791557797038984865049921261438811435078875133421073861312913308541)//BigInt(761448556714003333948396687643999840432514259811137574414811792240000000)-BigInt(17049571162138593122630888759407239103637)//BigInt(38817884913264916208193493348230120000000)*6^(1//2) + A[16,9]=BigInt(7831706161943944732903576802308126564075661689777008313099672046941217)//BigInt(1912115178728933570934305539114995143003765478134474309438025195000000)-BigInt(17049571162138593122630888759407239103637)//BigInt(7864603772795788969612150580525726250000)*6^(1//2) + A[16,10]=BigInt(1231862339518930958878836935481237970791679023430521469669885456183927336)//BigInt(350627295943808408781971725357505851618976832609816898042805015043984375)-BigInt(6274242187667002269128167063461863990138416)//BigInt(7178115836374689772545532041542281943203125)*6^(1//2) + A[16,11]=BigInt(23975119191644794266115435124846718653445865470965352804548709)//BigInt(2618162142480251258794523717542364435163988588525025359875200) + A[16,12]=BigInt(54918621392363748304153623111076473105288800876284517914641326502791860135537567319289496873218100975783896487633335215553248687)//BigInt(42045763520929825428011777325117555313008167341712535936493416447003511630663297772799291157965783507844913762569462175390505600) + A[16,13]=-BigInt(35648602464057004250287591332213307928385)//BigInt(140983705929537871068429634227938200156736) A[16,14]=180996536632507119654644161465573//475057638807131734180761408974016 A[16,15]=0 α[1]=385924436255198461459913//25885297292164750617319296 @@ -5163,10 +5163,10 @@ function constructTsitouras92(T::Type = Float64) α[6]=0 α[7]=0 α[8]=-81508791888782942071778080019859673//399395400777999552787672219983509760 - α[9]=935936315524449978576662571821361001//4086801409502444670525951816974611200 + α[9]=BigInt(935936315524449978576662571821361001)//BigInt(4086801409502444670525951816974611200) α[10]=2172547024243858864854526674870272//16972283408414027681310867548214525 - α[11]=1193746724713997342094811077921918673563219//5333839543124606397779553737025343484595200 - α[12]=78998885900843720607956191287550920802893766832745691186069543513026890766039702331356142187984337094261434894685526783//199728353759405693383344357357050366806065734043901244628659238274456345277244226082448918708806038102409307770530790400 + α[11]=BigInt(1193746724713997342094811077921918673563219)//BigInt(5333839543124606397779553737025343484595200) + α[12]=BigInt(78998885900843720607956191287550920802893766832745691186069543513026890766039702331356142187984337094261434894685526783)//BigInt(199728353759405693383344357357050366806065734043901244628659238274456345277244226082448918708806038102409307770530790400) α[13]=11409994679937666036993318622713183//210646829819316523523317257829664000 α[14]=10048608923923592706010638721995991//79176273134521955696793568162336000 α[15]=-491671864801784912209409//935818304406566046193728000 @@ -5178,11 +5178,11 @@ function constructTsitouras92(T::Type = Float64) αEEst[5]=0 αEEst[6]=0 αEEst[7]=0 - αEEst[8]=29177952541973984236460298638317525091//1395926082130949417341226925726678720 + αEEst[8]=BigInt(29177952541973984236460298638317525091)//BigInt(1395926082130949417341226925726678720) αEEst[9]=-481359954433374971820713358519126547//262512559006778653160811139234495296 αEEst[10]=-325585565780649471399541319800832//3935361974048520890008015792480311 - αEEst[11]=828906176711503347732519444777342468824091//1234749218911637779745721368343853865102720 - αEEst[12]=-19819005742497004038604841557068415948625832456498098356731269808855703554130425034149167680385863035602494067//944246035063763492934067294951661726695697507391691339725080641234241699449384342323015093676255343392536960 + αEEst[11]=BigInt(828906176711503347732519444777342468824091)//BigInt(1234749218911637779745721368343853865102720) + αEEst[12]=-BigInt(19819005742497004038604841557068415948625832456498098356731269808855703554130425034149167680385863035602494067)//BigInt(944246035063763492934067294951661726695697507391691339725080641234241699449384342323015093676255343392536960) αEEst[13]=96762135771288342741313072067956263//15762193817514374346399946534150720 αEEst[14]=-250908066606160220133619476267717281//58399326977497401115669462861805760 αEEst[15]=33//92 @@ -7852,13 +7852,13 @@ function constructDormandPrince8(T::Type = Float64) 3//80 0 0 3//16 3//20 0 0 0 0 0 0 0 0 215595617//4500000000 0 0 202047683//1800000000 -28693883//1125000000 23124283//1800000000 0 0 0 0 0 0 0 14873762658037143//879168438156250000 0 0 3467633544794897//8940695981250000 1474287494383247//40978189914062500 26709270507070017//135600555715625000 -14591655588284//84484570233063 0 0 0 0 0 0 - 7586331039021946882049083502441337664277676907617750536566352//109794461601491217860220353338581031394059220336451160078730445 0 0 -236057339412812449835946465344221735535939129430991059693568//372184615598275314780407977418918750488336340123563254504171 -3299739166368883603096250588167927276977533790499480498577408//20470153857905142312922438758040531276858498706795978997729405 4695919603694846215470554638065271273971468502369170235542016//33868800019443053645017125945121606294438606951244256159879561 291851811898394201384602939640627532330843113837053004434432000000//310174233778061645620360730197195350622945922304711702829528117367 6992959981041103840944260661352231159203510904000000//33042342481018810238716485165383193327572243242031481 0 0 0 0 0 - 99299034813490800741867453179778547//540971123539151162906952826011200000 0 0 -2493835259080554724582//1010153717930905426875 -48550347897506146536052//166675363458599395434375 -24871192635697392099560348960246//939492072180864357472739828818125 478776089216929482237673925052922000//168119099731629344552415590032785027 6560308981643238155096750//23314158982833116227901307 1586281686644478270321241459439899956623408540189275177//12818966182821619734532382093543907143647820508227904000 0 0 0 0 - -102116003386322998978127600084904875522141269364791505043913504184525097818434721165778087547359160299919872547571820573487921693//84016717385376362440519288454722754561118206109968455863629915569413007015484884082989277327146750610032897620427741658059440288 0 0 338590872606752219742507143357021902717271169524361004010718467428498066558752974165816979255870352236800//20308212073515087965058545521329962060416948491603802421256875704911573108931922671691153944392874968051 68189290605616416787948548385820859588684790288743680764422049661712817412461535969920258787664375619072//74463444269555322538548000244876527554862144469213942211275210918009101399417049796200897796107208216187 -1734282043732424474072631498514610096486835338935534079058145376760622893524503274680375038942168945756187943481380463560951840//286345537377499805912462279621622489249909215975695809863482134802066603511244489020404711919081949534640172065152437496912477 -3399549280223124443696423490103003766707892326374755946138975000967466690241111348721006509128775254952212682658842765965521154240000000//212424385105117691648087703103838079790425456287912424851546922389328485500145214289225448961304538830766072442444722564103495915888123 14452808190943733856347403293564049428070036006455540637351575894308889412108389906599600485253194980566957563315340127500000//973298753951638431793701721528200883789914680313298926814615071301495341142665245758696799918623095581715765886887649741383 -847205714160239289113307424793539077951658318917591980262304042838612275700008766016957700930195545053374220841398660187944621107065829310608865394026418258355//63358704383980726998416112830322706485300332630289060627019459285960825979588560697460438306253611095891491565590971432387489415884103732012574255897878321824 115188988949323598098458035263894669359112068207548636038131244599058496172710646622536373145562218909633738697549245770000//22435701423704647109276644681016984863989966659062291511947760084943925084166270812354794844590216383205333034660617626349 0 0 0 - 21969012306961489525323859125985377266525845354279828748//84868015648089839210997460517819380601933600521692915045 0 0 -2291872762438069505504//480025046760766258851 -3829018311866050387904//8800459190614048078935 -607977714773374460437401016185253441418120832060126402968//199370728929424959394190105343852509479613745231838418799 5302029233035772894614097632213626682295966947853615180783170000000//950538766256052885387161080614691196420735587733978871061913292363 102968047255116137164987219663037502898143843145000000//16726911019578511096352500731821705820659977305290973 -111383789341965407321602142444917514115800834690201329379027449761759895100011973929185171163615//22003454775272439861723739055800175619777853128055268766511800511549546753240522083740083243539 44737471541467333111555512048686345065750//20391511842264262870398286145868618178341 596546910748352988538198147432444829112451075399436970876618894337461087953328002664759407401623072330633057948252//4431076125983762085449284205348478790535717302043416234911901479328512794465980800998816354448181196721636373483787 0 0 - 1066221205855832326088695778460159015192405644968016897066521076847764032613686056268693633//1296431693610525557488309197474904206216262654240544950471874305723890174339356551609704000 0 0 -1335791413506612664643690684478806471077526746614666064//114574907798601779179110271814903983120429559544320175 -1591415543044168099882026495959288688569084060473110176//2100539976307699284950354983273239690541208591645869875 33975758488532631832742416857645572913178866704247539610423012370193845167470455176890924//47586856225469573819304596274208152402640120925455970356063642741972959597009066064956075 12176653428667113090492984656207574633063967759246601254930448409444470870786024235115138527800000//1008353786145118968620988891518234034224047994442049071310258686840184337101721351612973016221399 -339784374935367314296824613776444883113869450234942131172912300100535979345925250000//159698690787587746004588725210359673189662237866695585709500421500486548151424426361 4955095692700499418628052380948016677978733013841365878109775677669056866398110949788869771135857671298802131693154421086808143//2489789885462873158531234022579722982784822257458164105126884288597324542930882581099522281388970940826324647386340365850671680 -563115171027780776675066866318087406247194110301648522108648094708415//2403532595444498372383116767918060257292523183751650851596520916634577 147332487580158450887955957061658718012538967463083369806963200702426559434915876714751833908862217396388157664714990174448521780809//837599084085749358149340415048050308970085851893614803629073546048735327947816070400330404870816820234727495143522673498826476267825 0 0] - α = [ 212810988215683677989664967567559//5097575504458999984164528930580800;0;0;0;0;-570667999368605802515460802224128//10291145812277763122885317774476825;3970894643399159150754126826496000000000000//16592904867230933191457493387696939021741363;177094288219480472437690862000000000000//251729356670100506734814442705774463449;-66822609448295850920212176513645119787713273203022994500406050793972052314809461629969645683//87952305220338336969447643899150816363456821562985998778022435070001091778042097545895594560;314652731163869955629145958568800000//476340207420551356675670184044905167;177014954088789647707522848990757432519504314686067075784476503038212450536095365316360385634933688213244039743969578872631174179769//1119019983628991838522384101261104859676427163726922121733732080377576616485631933067985100908132443862205090961383250990215178108200;-454665916000392064556420344242099//1909482158429176288068071462671400;1//4] - αEEst = [7136040226482108704342809557217//241464102842794736092004001974880;0;0;0;0;-15349154422148033115423212285265536//18524062462099973621193571994058285;45434521806506196832804182374790400000000//145978635195580057402851847985603569106229;365696286946774693155766999232150000000//148214481030059176862554298041717674741;-836336669851503831866889530158468123932231502753408325817124013619515886965077571//328368994730082689886153304749497093954319862912916225944630536728837081959128864;294694385044387823293019951454286000//204145803180236295718144364590673643;1759482754698187564675489259591170188433054767657805212470918093603353527288272972728828708146708084742711724049636//22155380629918810427246421026742393952678586510217081174559507396642563972329904004994081772240905983608181867418935;2//45;0] + BigInt(7586331039021946882049083502441337664277676907617750536566352)//BigInt(109794461601491217860220353338581031394059220336451160078730445) 0 0 -BigInt(236057339412812449835946465344221735535939129430991059693568)//BigInt(372184615598275314780407977418918750488336340123563254504171) -BigInt(3299739166368883603096250588167927276977533790499480498577408)//BigInt(20470153857905142312922438758040531276858498706795978997729405) BigInt(4695919603694846215470554638065271273971468502369170235542016)//BigInt(33868800019443053645017125945121606294438606951244256159879561) BigInt(291851811898394201384602939640627532330843113837053004434432000000)//BigInt(310174233778061645620360730197195350622945922304711702829528117367) BigInt(6992959981041103840944260661352231159203510904000000)//BigInt(33042342481018810238716485165383193327572243242031481) 0 0 0 0 0 + 99299034813490800741867453179778547//540971123539151162906952826011200000 0 0 -2493835259080554724582//1010153717930905426875 -48550347897506146536052//166675363458599395434375 -24871192635697392099560348960246//939492072180864357472739828818125 478776089216929482237673925052922000//168119099731629344552415590032785027 6560308981643238155096750//23314158982833116227901307 BigInt(1586281686644478270321241459439899956623408540189275177)//BigInt(12818966182821619734532382093543907143647820508227904000) 0 0 0 0 + -BigInt(102116003386322998978127600084904875522141269364791505043913504184525097818434721165778087547359160299919872547571820573487921693)//BigInt(84016717385376362440519288454722754561118206109968455863629915569413007015484884082989277327146750610032897620427741658059440288) 0 0 BigInt(338590872606752219742507143357021902717271169524361004010718467428498066558752974165816979255870352236800)//BigInt(20308212073515087965058545521329962060416948491603802421256875704911573108931922671691153944392874968051) BigInt(68189290605616416787948548385820859588684790288743680764422049661712817412461535969920258787664375619072)//BigInt(74463444269555322538548000244876527554862144469213942211275210918009101399417049796200897796107208216187) -BigInt(1734282043732424474072631498514610096486835338935534079058145376760622893524503274680375038942168945756187943481380463560951840)//BigInt(286345537377499805912462279621622489249909215975695809863482134802066603511244489020404711919081949534640172065152437496912477) -BigInt(3399549280223124443696423490103003766707892326374755946138975000967466690241111348721006509128775254952212682658842765965521154240000000)//BigInt(212424385105117691648087703103838079790425456287912424851546922389328485500145214289225448961304538830766072442444722564103495915888123) BigInt(14452808190943733856347403293564049428070036006455540637351575894308889412108389906599600485253194980566957563315340127500000)//BigInt(973298753951638431793701721528200883789914680313298926814615071301495341142665245758696799918623095581715765886887649741383) -BigInt(847205714160239289113307424793539077951658318917591980262304042838612275700008766016957700930195545053374220841398660187944621107065829310608865394026418258355)//BigInt(63358704383980726998416112830322706485300332630289060627019459285960825979588560697460438306253611095891491565590971432387489415884103732012574255897878321824) BigInt(115188988949323598098458035263894669359112068207548636038131244599058496172710646622536373145562218909633738697549245770000)//BigInt(22435701423704647109276644681016984863989966659062291511947760084943925084166270812354794844590216383205333034660617626349) 0 0 0 + BigInt(21969012306961489525323859125985377266525845354279828748)//BigInt(84868015648089839210997460517819380601933600521692915045) 0 0 -2291872762438069505504//480025046760766258851 -3829018311866050387904//8800459190614048078935 -BigInt(607977714773374460437401016185253441418120832060126402968)//BigInt(199370728929424959394190105343852509479613745231838418799) BigInt(5302029233035772894614097632213626682295966947853615180783170000000)//BigInt(950538766256052885387161080614691196420735587733978871061913292363) BigInt(102968047255116137164987219663037502898143843145000000)//BigInt(16726911019578511096352500731821705820659977305290973) -BigInt(111383789341965407321602142444917514115800834690201329379027449761759895100011973929185171163615)//BigInt(22003454775272439861723739055800175619777853128055268766511800511549546753240522083740083243539) BigInt(44737471541467333111555512048686345065750)//BigInt(20391511842264262870398286145868618178341) BigInt(596546910748352988538198147432444829112451075399436970876618894337461087953328002664759407401623072330633057948252)//BigInt(4431076125983762085449284205348478790535717302043416234911901479328512794465980800998816354448181196721636373483787) 0 0 + BigInt(1066221205855832326088695778460159015192405644968016897066521076847764032613686056268693633)//BigInt(1296431693610525557488309197474904206216262654240544950471874305723890174339356551609704000) 0 0 -BigInt(1335791413506612664643690684478806471077526746614666064)//BigInt(114574907798601779179110271814903983120429559544320175) -BigInt(1591415543044168099882026495959288688569084060473110176)//BigInt(2100539976307699284950354983273239690541208591645869875) BigInt(33975758488532631832742416857645572913178866704247539610423012370193845167470455176890924)//BigInt(47586856225469573819304596274208152402640120925455970356063642741972959597009066064956075) BigInt(12176653428667113090492984656207574633063967759246601254930448409444470870786024235115138527800000)//BigInt(1008353786145118968620988891518234034224047994442049071310258686840184337101721351612973016221399) -BigInt(339784374935367314296824613776444883113869450234942131172912300100535979345925250000)//BigInt(159698690787587746004588725210359673189662237866695585709500421500486548151424426361) BigInt(4955095692700499418628052380948016677978733013841365878109775677669056866398110949788869771135857671298802131693154421086808143)//BigInt(2489789885462873158531234022579722982784822257458164105126884288597324542930882581099522281388970940826324647386340365850671680) -BigInt(563115171027780776675066866318087406247194110301648522108648094708415)//BigInt(2403532595444498372383116767918060257292523183751650851596520916634577) BigInt(147332487580158450887955957061658718012538967463083369806963200702426559434915876714751833908862217396388157664714990174448521780809)//BigInt(837599084085749358149340415048050308970085851893614803629073546048735327947816070400330404870816820234727495143522673498826476267825) 0 0] + α = [ 212810988215683677989664967567559//5097575504458999984164528930580800;0;0;0;0;-570667999368605802515460802224128//10291145812277763122885317774476825;BigInt(3970894643399159150754126826496000000000000)//BigInt(16592904867230933191457493387696939021741363);BigInt(177094288219480472437690862000000000000)//BigInt(251729356670100506734814442705774463449);-BigInt(66822609448295850920212176513645119787713273203022994500406050793972052314809461629969645683)//BigInt(87952305220338336969447643899150816363456821562985998778022435070001091778042097545895594560);314652731163869955629145958568800000//476340207420551356675670184044905167;BigInt(177014954088789647707522848990757432519504314686067075784476503038212450536095365316360385634933688213244039743969578872631174179769)//BigInt(1119019983628991838522384101261104859676427163726922121733732080377576616485631933067985100908132443862205090961383250990215178108200);-454665916000392064556420344242099//1909482158429176288068071462671400;1//4] + αEEst = [7136040226482108704342809557217//241464102842794736092004001974880;0;0;0;0;-15349154422148033115423212285265536//18524062462099973621193571994058285;BigInt(45434521806506196832804182374790400000000)//BigInt(145978635195580057402851847985603569106229);BigInt(365696286946774693155766999232150000000)//BigInt(148214481030059176862554298041717674741);-BigInt(836336669851503831866889530158468123932231502753408325817124013619515886965077571)//BigInt(328368994730082689886153304749497093954319862912916225944630536728837081959128864);294694385044387823293019951454286000//204145803180236295718144364590673643;BigInt(1759482754698187564675489259591170188433054767657805212470918093603353527288272972728828708146708084742711724049636)//BigInt(22155380629918810427246421026742393952678586510217081174559507396642563972329904004994081772240905983608181867418935);2//45;0] c = [0;1//18;1//12;1//8;5//16;3//8;59//400;93//200;5490023248//9719169821;13//20;30992876149296355//33518267164510641;1;1] A = map(T,A) α = map(T,α)