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Extend the range of precomputed simple groups from orders up to 10^18 to orders up to about 10^27 #3861

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Jan 22, 2020
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Extend the range of precomputed simple groups from orders up to 10^18 to orders up to about 10^27 #3861

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3ef17cd
ENHANCE: Extended range of simple groups
hulpke Dec 24, 2019
734b395
Update grp/simple.gi
hulpke Jan 22, 2020
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4 changes: 2 additions & 2 deletions grp/simple.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -75,7 +75,7 @@ DeclareGlobalFunction("EpimorphismFromClassical");
##
## <Description>
## This function returns an iterator that will run over all nonabelian simple groups, starting
## at order <A>start</A> if specified, up to order <M>10^{18}</M> (or -- if specified
## at order <A>start</A> if specified, up to order <M>10^{27}</M> (or -- if specified
## -- order <A>end</A>). If the option <A>NOPSL2</A> is given, groups of type
## <M>PSL_2(q)</M> are omitted.
## <Example><![CDATA[
Expand All @@ -95,7 +95,7 @@ DeclareGlobalFunction("EpimorphismFromClassical");
## </ManSection>
## <#/GAPDoc>
DeclareGlobalFunction("SimpleGroupsIterator");

BindGlobal("SIMPLE_GROUPS_ITERATOR_RANGE",10^27);

#############################################################################
##
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27 changes: 20 additions & 7 deletions grp/simple.gi
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Expand Up @@ -703,16 +703,30 @@ local NextL2PrimePowerInt;
fi;
end);

BindGlobal("LOADSIMPLE2",function()
local a;
if not IsBound(SIMPLEGPSNONL2[248]) then
MakeReadWriteGlobal("SIMPLEGPSNONL2");
a:=ReadAsFunction(Filename(List(GAPInfo.RootPaths,Directory),
"grp/simple2.g"));
SIMPLEGPSNONL2:=Immutable(Concatenation(SIMPLEGPSNONL2,a()));
MakeReadOnlyGlobal("SIMPLEGPSNONL2");
fi;
end);

BindGlobal("NextIterator_SimGp",function(it)
local a,l,pos,g,b;
if it!.done then return fail;fi;
a:=it!.b;
if a>1259903 then
# 1259903 is the last prime power whose L2 order is <10^18
Error("List of simple groups is only available up to order 10^18");
if a>=1316848669 then
# 1316848669 is the first prime power whose L2 order is beyond the
# simple2 list
Error("List of simple groups only available up to order",
SIMPLE_GROUPS_ITERATOR_RANGE);
fi;
l:=SizeL2Q(a);
pos:=it!.pos;
if pos>=245 then LOADSIMPLE2(); fi;
if l<SIMPLEGPSNONL2[pos][1] and not it!.nopsl2 then
# next is a L2
g:=SimpleGroup("L",2,a);
Expand Down Expand Up @@ -775,8 +789,8 @@ InstallGlobalFunction(SimpleGroupsIterator,function(arg)
stack:=a[3];
a:=a[2];
until SizeL2Q(b)>=start;
pos:=First([1..Length(SIMPLEGPSNONL2)],x->SIMPLEGPSNONL2[x][1]>=start);

if start>=10^18 then LOADSIMPLE2(); fi;
pos:=First([1..Length(SIMPLEGPSNONL2)],x->SIMPLEGPSNONL2[x][1]>=start);
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Optional alternative (should be double checked ;-):

Suggested change
pos:=First([1..Length(SIMPLEGPSNONL2)],x->SIMPLEGPSNONL2[x][1]>=start);
pos:=PositionProperty(SIMPLEGPSNONL2,x->x[1]>=start);

return IteratorByFunctions(rec(
IsDoneIterator:=IsDoneIterator_SimGp,
NextIterator:=NextIterator_SimGp,
Expand Down Expand Up @@ -1165,7 +1179,7 @@ local a;
if n<168 then return 5;fi;
a:=Filtered(SIMPLEGPSNONL2,x->x[1]=n);
# we have degree data up to order 2^55
if n<=10^55 and Length(a)=0 then
if n<=2^55 and Length(a)=0 then
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# L2 case
return 2*RootInt(n,3);
elif Length(a)>0 and ForAll(a,x->Length(x)>4) then
Expand Down Expand Up @@ -1262,4 +1276,3 @@ local H,d,id,hom,field,C,dom,orbs;
return hom*RestrictedInverseGeneralMapping(d);

end);

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