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Add more matrix generators. #822

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Apr 20, 2022
Merged

Add more matrix generators. #822

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89ba410
add higher dimension matrix generators from paper
MT-resource-bot Apr 20, 2022
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lint
MT-resource-bot Apr 20, 2022
c7f267f
lint2
MT-resource-bot Apr 20, 2022
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Apply suggestions from code review
james-d-mitchell Apr 20, 2022
b8f91bb
fixup
MT-resource-bot Apr 20, 2022
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Binary file added data/gens/fullbool-8.pickle.gz
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40 changes: 34 additions & 6 deletions gap/semigroups/semiex.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1378,9 +1378,17 @@ function(n)
"/data/gens/reflex.pickle.gz"));
fi;

if n = 6 and not IsBound(SEMIGROUPS.GENERATORS.Reflex[6]) then
Info(InfoSemigroups, 2, "reading generators; this may take some time");
Add(SEMIGROUPS.GENERATORS.Reflex,
ReadGenerators(Concatenation(SEMIGROUPS.PackageDir,
"/data/gens/reflex-6.pickle.gz")));
fi;

if not IsBound(SEMIGROUPS.GENERATORS.Reflex[n]) then
ErrorNoReturn("generators for this monoid are only known up to dimension ",
String(Length(SEMIGROUPS.GENERATORS.Reflex)));
ErrorNoReturn("Semigroups: ReflexiveBooleanMatMonoid:\n",
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"generators for this monoid are only provided up to ",
"dimension 6,");
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fi;

return Monoid(SEMIGROUPS.GENERATORS.Reflex[n]);
Expand All @@ -1389,15 +1397,26 @@ end);
InstallMethod(HallMonoid, "for a positive integer",
[IsPosInt],
function(n)
local gens, p;

if not IsBound(SEMIGROUPS.GENERATORS.Hall) then
SEMIGROUPS.GENERATORS.Hall :=
ReadGenerators(Concatenation(SEMIGROUPS.PackageDir,
"/data/gens/hall.pickle.gz"));
fi;

if n = 8 then
gens := GeneratorsOfSemigroup(FullBooleanMatMonoid(8));
p := PositionProperty(gens,
x -> ListWithIdenticalEntries(8, false)
in AsList(x));
return Monoid(gens{[1 .. p - 1]}, gens{[p + 1 .. Length(gens)]});
fi;

if not IsBound(SEMIGROUPS.GENERATORS.Hall[n]) then
ErrorNoReturn("generators for this monoid are only known up to dimension ",
String(Length(SEMIGROUPS.GENERATORS.Hall)));
ErrorNoReturn("Semigroups: HallMonoid:\n",
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"generators for this monoid are only known up to dimension ",
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"8,");
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fi;

return Monoid(SEMIGROUPS.GENERATORS.Hall[n]);
Expand All @@ -1412,14 +1431,23 @@ function(n)
"/data/gens/fullbool.pickle.gz"));
fi;

if n = 8 and not IsBound(SEMIGROUPS.GENERATORS.FullBool[8]) then
Info(InfoSemigroups, 2, "reading generators; this may take some time");
Add(SEMIGROUPS.GENERATORS.FullBool,
ReadGenerators(Concatenation(SEMIGROUPS.PackageDir,
"/data/gens/fullbool-8.pickle.gz")));
fi;

if not IsBound(SEMIGROUPS.GENERATORS.FullBool[n]) then
ErrorNoReturn("generators for this monoid are only known up to dimension ",
String(Length(SEMIGROUPS.GENERATORS.FullBool)));
ErrorNoReturn("Semigroups: FullBooleanMatMonoid:\n",
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"generators for this monoid are only known up to dimension ",
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"8,");
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fi;

return Monoid(SEMIGROUPS.GENERATORS.FullBool[n]);
end);


#############################################################################
## Tropical matrix monoids
#############################################################################
Expand Down
23 changes: 17 additions & 6 deletions tst/standard/semigroups/semiex.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -2013,10 +2013,11 @@ gap> S := ReflexiveBooleanMatMonoid(3);
<monoid of 3x3 boolean matrices with 8 generators>
gap> S := ReflexiveBooleanMatMonoid(5);
<monoid of 5x5 boolean matrices with 1414 generators>
gap> S := ReflexiveBooleanMatMonoid(6);
Error, generators for this monoid are only known up to dimension 5
gap> S := ReflexiveBooleanMatMonoid(7);
Error, Semigroups: ReflexiveBooleanMatMonoid:
generators for this monoid are only provided up to dimension 6,

# Test HallBooleanMatMonoid
# Test HallMonoid
gap> HallMonoid(1);
<trivial group of 1x1 boolean matrices with 1 generator>
gap> S := HallMonoid(3);
Expand All @@ -2026,9 +2027,14 @@ gap> Size(S);
gap> S := HallMonoid(5);
<monoid of 5x5 boolean matrices with 12 generators>
gap> S := HallMonoid(6);
Error, generators for this monoid are only known up to dimension 5
<monoid of 6x6 boolean matrices with 67 generators>
gap> S := HallMonoid(7);
<monoid of 7x7 boolean matrices with 2141 generators>
gap> S := HallMonoid(9);
Error, Semigroups: HallMonoid:
generators for this monoid are only known up to dimension 8,

# Test FullBooleanMatBooleanMatMonoid
# Test FullBooleanMatMonoid
gap> FullBooleanMatMonoid(1);
<commutative monoid of 1x1 boolean matrices with 1 generator>
gap> S := FullBooleanMatMonoid(3);
Expand All @@ -2038,7 +2044,12 @@ true
gap> S := FullBooleanMatMonoid(5);
<monoid of 5x5 boolean matrices with 13 generators>
gap> S := FullBooleanMatMonoid(6);
Error, generators for this monoid are only known up to dimension 5
<monoid of 6x6 boolean matrices with 68 generators>
gap> S := FullBooleanMatMonoid(7);
<monoid of 7x7 boolean matrices with 2142 generators>
gap> S := FullBooleanMatMonoid(9);
Error, Semigroups: FullBooleanMatMonoid:
generators for this monoid are only known up to dimension 8,

#
gap> SEMIGROUPS.StopTest();
Expand Down