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YB_given_derived.g
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YB_given_derived.g
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LoadPackage("IO");
LoadPackage("YangBaxter");
Read("derived_v3.g");
twist_matrix := function(obj, f)
local i,j,m,n;
n := Size(obj);
m := NullMat(n,n);
for i in [1..n] do
for j in [1..n] do
if obj[i^Inverse(f)][j^Inverse(f)] <> 0 then
m[i][j] := obj[i^Inverse(f)][j^Inverse(f)]^f;
fi;
od;
od;
return m;
end;
is_isomorphism_YB := function(f, r, s)
local x, y, u, v;
for x in [1..Size(r)] do
for y in [1..Size(r)] do
u := YB_xy(r, x, y)[1];
v := YB_xy(r, x, y)[2];
if not [u^f, v^f] = YB_xy(s, x^f, y^f) then
return false;
fi;
od;
od;
return true;
end;
isomorphism_YB := function(r, s)
return true in List(SymmetricGroup(Size(r)), f->is_isomorphism_YB(f, r, s));
end;
shelfandlambda2YB := function(rack, matrix)
local x,y,m,n,rhos,lambdas,tmp;
n := Size(rack);
tmp := List(matrix, x->Inverse(PermList(x)));
lambdas := List(tmp, x->List(ListPerm(x,n),y->y));
rhos := NullMat(n,n);
for x in [1..n] do
for y in [1..n] do
rhos[y][x] := matrix[lambdas[x][y]][rack[lambdas[x][y]][x]];
od;
od;
return [lambdas, rhos];
end;
is_automorphism := function(f, rack)
local x,y;
for x in [1..Size(rack)] do
for y in [1..Size(rack)] do
if rack[x][y]^f <> rack[x^f][y^f] then
return false;
fi;
od;
od;
return true;
end;
fixed := function(rack)
return Filtered(SymmetricGroup(Size(rack)), x->twist_matrix(rack, x)=rack and is_automorphism(x,rack));
end;
create_files := function(n, racks)
local x,f,k,s,m,lines,perms,tmp1,tmp2,rack;
m := 0;
for rack in racks do
tmp1 := "";
tmp2 := "";
perms := SymmetricGroup(n);
perms := fixed(rack);
for k in perms do
Append(tmp1, Concatenation(String(List(ListPerm(k,n),y->y)),",\n"));
Append(tmp2, Concatenation(String(List(ListPerm(Inverse(k),n),y->y)),",\n"));
od;
m := m+1;
lines := [
"language ESSENCE' 1.0\n",
Concatenation("letting n be ", String(n), "\n"),
"letting perms be [", tmp1, "]\n",
"letting inverses be [\n", tmp2, "]\n",
"letting rack be \n", rack, "\n",
"find M : matrix indexed by [int(1..n), int(1..n)] of int(1..n)\n",
"such that\n",
"forAll x : int(1..n) .",
" allDiff(M[x,..]),\n",
"forAll x,y,z : int(1..n) .",
" M[M[x,rack[x,y]],M[x,z]]=M[M[y,x],M[y,z]],\n",
"forAll x,y,z : int(1..n) .",
" M[x,rack[y,z]]=rack[M[x,y],M[x,z]],"
];
Add(lines, Concatenation("forAll p : int(1..", String(Size(perms)), ") .\n\\
flatten( [ M[i,j] | i : int(1..n), j : int(1..n)] )\n\\
<=lex flatten( [ inverses[p,M[perms[p,i],perms[p,j]]] | i : int(1..n), j : int(1..n)] ),"));
Add(lines, "\ntrue\n");
f := IO_File(Concatenation("eprime/solutions/YB", String(n), "_r", String(m),".eprime"), "w");
for x in lines do
IO_WriteLine(f, x);
od;
IO_Flush(f);
IO_Close(f);
od;
return;
end;
read_file := function(n, filename)
local l, k, x, m, f, done;
l := [];
k := 0;
f := IO_File(filename, "r");
done := false;
while not done do
x := IO_ReadLine(f);
if StartsWith(x, "Created information file") then
done := true;
elif StartsWith(x, "Solution") then
m := EvalString(String(x{[46..Size(x)]}));
k := k+1;
Add(l, m);
fi;
od;
Print("I found ", k, " cubic solutions\n");
IO_Flush(f);
IO_Close(f);
return l;
end;
compute_YB := function(n,racks)
local m,l,T,k,s,f,x,t,input, output, t0, t1, mytime, rack;
t0 := NanosecondsSinceEpoch();
k := 1;
m := 0;
s := "../savilerow-1.9.1-mac/savilerow -run-solver -all-solutions -solutions-to-stdout-one-line ";
LogTo();
LogTo(Concatenation("log/solutions/YB", String(n), "_method1.log"));
create_files(n, racks);
for rack in racks do
t := [];
# if rack = List([1..n], x->[1..n]) then
# Print("I skip the trivial rack.\n");
# k := k+1;
# continue;
# fi;
output := Concatenation("output/solutionsYB", String(n), "_r", String(k),".output");
Print("Running savilerow. File: YB", String(n), "_r", String(k), ".eprime", ". Output: ", output, "\n");
Exec(Concatenation(s, "eprime/solutions/YB", String(n), "_r", String(k), ".eprime", " >", output));
for x in read_file(n, output) do
Add(t, shelfandlambda2YB(rack,x));
m := m+1;
od;
t1 := NanosecondsSinceEpoch();
mytime := Int(Float((t1-t0)/10^6));
Print("Rack:\n");
Display(rack);
Print("I constructed ", m, " cubic solutions in ", mytime, "ms (=", StringTime(mytime), ")\n");
f := IO_File(Concatenation("data/solutions/YB", String(n), "_r", String(k), ".g"), "w");
IO_WriteLine(f, Concatenation("data/solutions/YB", String(n), "_r", String(k)," := ["));
for x in t do
IO_WriteLine(f, Concatenation(String(x),","));
od;
IO_WriteLine(f, "];");
IO_Flush(f);
IO_Close(f);
k := k+1;
od;
end;
cubic_solutions:=function(n)
local racks;
racks:=read_derived_solutions(n);
compute_YB(n,racks);
end;
enumerate_YB := function(n,racks)
local m,l, T,k,s,f,x,t,input, output, t0, t1, mytime, rack;
t0 := NanosecondsSinceEpoch();
k := 1;
m := 0;
s := "../savilerow-1.9.1-mac/savilerow -run-solver -all-solutions -solutions-to-stdout-one-line ";
LogTo();
LogTo(Concatenation("log/solutions/YB", String(n), "_method1.log"));
create_files(n, racks);
for rack in racks do
t := [];
if rack = List([1..n], x->[1..n]) then
Print("I skip the trivial rack.\n");
k := k+1;
continue;
fi;
output := Concatenation("output/solutions/YB", String(n), "_r", String(k),".output");
Print("Running savilerow. File: YB", String(n), "_r", String(k), ".eprime", ". Output: ", output, "\n");
Exec(Concatenation(s, "eprime/solutions/YB", String(n), "_r", String(k), ".eprime", " >", output));
t := Size(read_file(n, output));
m := m+t;
t1 := NanosecondsSinceEpoch();
mytime := Int(Float((t1-t0)/10^6));
Print("Rack:\n");
Display(rack);
Print("I constructed ", m, " cubic solutions in ", mytime, "ms (=", StringTime(mytime), ")\n");
k := k+1;
od;
end;
first_condition:=function(lambdas,rhos,x,y,z)
return lambdas[x][lambdas[y][z]] = lambdas[lambdas[x][y]][lambdas[rhos[y][x]][z]];
end;
second_condition:=function(lambdas,rhos,x,y,z)
return lambdas[rhos[lambdas[y][z]][x]][rhos[z][y]] = rhos[lambdas[rhos[y][x]][z]][lambdas[x][y]];
end;
third_condition:=function(lambdas,rhos,x,y,z)
return rhos[y][rhos[y][x]]=rhos[rhos[z][y]][rhos[lambdas[y][z]][x]];
end;
is_solution:=function(lambdas,rhos)
local n,x,y,z;
n:=Size(lambdas);
for x in [1..n] do
for y in [1..n] do
for z in [1..n] do
if first_condition(lambdas,rhos,x,y,z) = false then
return false;
fi;
if second_condition(lambdas,rhos,x,y,z) = false then
return false;
fi;
if third_condition(lambdas,rhos,x,y,z) = false then
return false;
fi;
od;
od;
od;
return true;
end;
is_involutive:=function(lambdas,rhos)
local n,x,y;
n:=Size(lambdas);
for x in [1..n] do
for y in [1..n] do
if (lambdas[lambdas[x][y]][rhos[y][x]]=x) =false then
return false;
fi;
od;
od;
return true;
end;
is_idempotent:=function(lambdas,rhos)
local n,x,y;
n:=Size(lambdas);
for x in [1..n] do
for y in [1..n] do
if (lambdas[lambdas[x][y]][rhos[y][x]]=lambdas[x][y]) =false then
return false;
fi;
od;
od;
return true;
end;