# the function will try each monoid for arg4 seconds before moving on to the next. The relevant function is TestCoxeterOrigami
NumberCombos:=function(m,n,lists,iteration)
local i,j,list,list2,lists2;
lists2:=[];
if iteration<m+1 then
if lists=[] then
for i in [0..n] do
Add(lists2,[i]);
od;
else
for list in lists do
for i in [0..3] do
list2:=ShallowCopy(list);
Add(list2,Random([0..n]));
Add(lists2, list2);
od;
od;
fi;
else
return lists;
fi;
j:=iteration+1;
return NumberCombos(m,n,lists2,j);
end;
CreateCoxeterInput := function(numGenerators, n, p)
local generators, inputs, a, b, c, d, i, j, k, y, z, blank, range, ranges, pos, rel, numlists, blanker, numbers;
# Generate generator names
generators := List([1..numGenerators], i -> Concatenation("g", String(i)));
# Create relations
blank := [];
for a in generators do
for b in generators do
if not a=b then
rel:=[a,,b];
Add(blank,rel);
fi;
od;
od;
for c in blank do
for d in blank do
if c[1]=d[3] and c[3]=d[1] then
pos:=Position(blank,d);
Remove(blank,pos);
fi;
od;
od;
inputs:=[];
numlists:=NumberCombos(Size(blank),n,[],1);;
numbers:=[];
for i in [1..p] do
j:=Random(numlists);
Add(numbers,j);
od;
for k in numbers do
blanker:=StructuralCopy(blank);
for z in blanker do
pos:=Position(blanker,z);
z[2]:=k[pos];
od;
Add(inputs,blanker);
od;
return inputs;
end;
# Main program to iterate through Coxeter Monoids and apply OrigamiMonoidIdemp
TestCoxeterOrigami := function(numGenerators, n, p, timeout)
local inputs, coxeterMonoid, origamiMonoid, tStart, tempFile, command, result, input, i;
inputs := CreateCoxeterInput(numGenerators, n, p);
for i in [1..Length(inputs)] do
input := inputs[i];
Print("Testing input ", input, "\n");
Print("Creating CoxeterMonoid...\n");
coxeterMonoid := CoxeterMonoid(input);
if coxeterMonoid = fail then
Print("Error: CoxeterMonoid creation failed for input ", input, "\n");
continue;
fi;
Print("CoxeterMonoid created successfully for input: ", input, "\n");
Print("Applying OrigamiMonoidIdemp...\n");
origamiMonoid := OrigamiMonoidIdemp(coxeterMonoid);
if origamiMonoid = fail then
Print("Error: Failed to apply OrigamiMonoidIdemp for input ", input, "\n");
continue;
fi;
Print("OrigamiMonoidIdemp applied successfully for input: ", input, "\n");
Print("Checking finiteness with timeout...\n");
tempFile := Concatenation("temp_finiteness_", String(i), ".g");
PrintTo(tempFile, Concatenation(
"Mapper := function(word, arg)\n",
" local i, u, v, w, prod, monoid;\n",
" w := ExtRepOfObj(word);\n",
" prod := [];\n",
" if IsMonoid(arg) then\n",
" monoid := arg;\n",
" for i in [1..(Length(w)/2)] do\n",
" u := monoid.(w[2*i-1])^(w[2*i]);\n",
" Add(prod, u);\n",
" od;\n",
" elif IsSemigroup(arg) then\n",
" monoid := arg;\n",
" for i in [1..(Length(w)/2)] do\n",
" u := monoid.(w[2*i-1])^(w[2*i]);\n",
" Add(prod, u);\n",
" od;\n",
" else\n",
" for i in [1..(Length(w)/2)] do\n",
" u := arg[(w[2*i-1])]^(w[2*i]);\n",
" Add(prod, u);\n",
" od;\n",
" fi;\n",
" v := Product(prod);\n",
" return v;\n",
"end;\n\n",
"OrigamiMonoidIdemp := function(monoid)\n",
" local gens, mgens, rels, newrels, mrels, agens, bgens, arels, brels, abgens, bagens, doublegens, doublerels, w, free, left, right, abrels, barels, M, rws, freeaddrules, creatingrules, i, j, n, generatorMap, fgens, pos, gens0, mapped, commrels;\n\n",
" if not IsFpMonoid(monoid) then\n",
" Print(\"Not a monoid. Perhaps try OrigamiSemigroup.\\n\");\n",
" return fail;\n",
" fi;\n\n",
" gens := [];\n",
" for i in [1..Size(GeneratorsOfMonoid(monoid))] do\n",
" Add(gens, monoid.(i));\n",
" od;\n",
" n := Size(gens);\n",
" rels := RelationsOfFpMonoid(monoid);\n",
" newrels := [];\n",
" for i in rels do\n",
" if not i[1] = i[2] then\n",
" Add(newrels, i);\n",
" fi;\n",
" od;\n",
" rels := newrels;\n\n",
" agens := [];\n",
" bgens := [];\n",
" for i in [1..Length(gens)] do\n",
" Add(agens, Concatenation(\"a\", String(i)));\n",
" Add(bgens, Concatenation(\"b\", String(i)));\n",
" od;\n",
" mgens := Concatenation(agens, bgens);\n",
" free := FreeMonoid(mgens);\n",
" generatorMap := rec();\n",
" fgens := GeneratorsOfMonoid(free);\n",
" agens := [];\n",
" for i in [1..n] do\n",
" Add(agens, free.(i));\n",
" od;\n",
" bgens := [];\n",
" for i in [n+1..Size(GeneratorsOfMonoid(free))] do\n",
" Add(bgens, free.(i));\n",
" od;\n\n",
" arels := [];\n",
" for i in rels do\n",
" left := Mapper(i[1], agens);\n",
" right := Mapper(i[2], agens);\n",
" Add(arels, [left, right]);\n",
" od;\n\n",
" brels := [];\n",
" for i in rels do\n",
" left := Mapper(i[1], bgens);\n",
" right := Mapper(i[2], bgens);\n",
" Add(brels, [left, right]);\n",
" od;\n",
" mrels := [];\n",
" UniteSet(mrels, arels);\n",
" UniteSet(mrels, brels);\n\n",
" doublerels := [];\n",
" doublegens := [];\n",
" abgens := [];\n",
" bagens := [];\n",
" for i in agens do\n",
" pos := Position(agens, i);\n",
" w := i * bgens[pos];\n",
" Add(abgens, w);\n",
" od;\n",
" for i in bgens do\n",
" pos := Position(bgens, i);\n",
" w := i * agens[pos];\n",
" Add(bagens, w);\n",
" od;\n",
" UniteSet(doublegens, abgens);\n",
" UniteSet(doublegens, bagens);\n",
" for i in mrels do\n",
" left := Mapper(i[1], doublegens);\n",
" right := Mapper(i[2], doublegens);\n",
" Add(doublerels, [left, right]);\n",
" od;\n\n",
" commrels := [];\n",
" for i in agens do\n",
" for j in bgens do\n",
" if not Position(agens, i) = Position(bgens, j) then\n",
" left := j * i;\n",
" right := i * j;\n",
" Add(commrels, [left, right]);\n",
" fi;\n",
" od;\n",
" od;\n\n",
" rels := [];\n",
" arels := Set(arels);\n",
" brels := Set(brels);\n",
" doublerels := Set(doublerels);\n",
" commrels := Set(commrels);\n",
" UniteSet(rels, arels);\n",
" UniteSet(rels, brels);\n",
" UniteSet(rels, doublerels);\n",
" UniteSet(rels, commrels);\n\n",
" M := free / rels;\n",
" return M;\n",
"end;\n\n",
"CoxeterMonoid := function(D)\n",
" local gens, rels, i, j, k, fm, f, n;\n",
" gens := [];\n",
" rels := [];\n",
" for i in D do\n",
" Add(gens, i[1]);\n",
" Add(gens, i[3]);\n",
" od;\n",
" gens := Set(gens);\n",
" fm := FreeMonoid(gens);\n",
" for i in D do\n",
" j := Position(gens, i[1]);\n",
" k := Position(gens, i[3]);\n",
" n := Int((i[2])/2);\n",
" if n = i[2]/2 then\n",
" Add(rels, [(fm.(k) * fm.(j))^(n), (fm.(j) * fm.(k))^(n)]);\n",
" else\n",
" Add(rels, [(fm.(k) * fm.(j))^(n) * fm.(k), (fm.(j) * fm.(k))^(n) * fm.(j)]);\n",
" fi;\n",
" Add(rels, [fm.(j)^2, fm.(j)]);\n",
" Add(rels, [fm.(k)^2, fm.(k)]);\n",
" od;\n",
" rels := Set(rels);\n",
" f := fm / rels;\n",
" return f;\n",
"end;\n\n",
"coxeterMonoid := CoxeterMonoid(", String(input), ");\n",
"if coxeterMonoid = fail then\n",
" Print(\"Failed to create CoxeterMonoid.\\n\");\n",
" #return;\n",
"fi;\n\n",
"origamiMonoid := OrigamiMonoidIdemp(coxeterMonoid);\n",
"if origamiMonoid = fail then\n",
" Print(\"Failed to create OrigamiMonoidIdemp.\\n\");\n",
" #return;\n",
"else\n",
" if IsFinite(origamiMonoid) then\n",
" Print(\"Finite\\n\");\n",
" Print(\Size(origamiMonoid)\);\n",
" else\n",
" Print(Size(origamiMonoid), \"\\n\");\n",
" fi;\n",
"fi;\n",
"#return;"
));
command := Concatenation("timeout ", String(timeout), "s gap -q --nointeract -r ", tempFile);
Exec(command);
Print("\n\n");
Exec(Concatenation("rm ",String(tempFile)));
od;
Print("Finished testing all inputs.\n");
end;
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