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############################################################################
##
## semigroups/semiboolmat.gi
## Copyright (C) 2015-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
# This file contains methods for semigroups of boolean matrices.
#############################################################################
## 0. Random
#############################################################################
InstallMethod(SEMIGROUPS_ProcessRandomArgsCons,
[IsBooleanMatSemigroup, IsList],
{filt, params} -> SEMIGROUPS_ProcessRandomArgsCons(IsSemigroup, params));
InstallMethod(SEMIGROUPS_ProcessRandomArgsCons,
[IsBooleanMatMonoid, IsList],
{filt, params} -> SEMIGROUPS_ProcessRandomArgsCons(IsSemigroup, params));
InstallMethod(RandomSemigroupCons,
"for IsBooleanMatSemigroup and list",
[IsBooleanMatSemigroup, IsList],
function(_, params)
return Semigroup(List([1 .. params[1]], i -> RandomMatrix(IsBooleanMat,
params[2])));
end);
InstallMethod(RandomMonoidCons,
"for IsBooleanMatMonoid and list",
[IsBooleanMatMonoid, IsList],
function(_, params)
return Monoid(List([1 .. params[1]], i -> RandomMatrix(IsBooleanMat,
params[2])));
end);
InstallMethod(RandomInverseSemigroupCons, "for IsBooleanMatSemigroup and list",
[IsBooleanMatSemigroup, IsList], SEMIGROUPS.DefaultRandomInverseSemigroup);
InstallMethod(RandomInverseMonoidCons, "for IsBooleanMatMonoid and list",
[IsBooleanMatMonoid, IsList], SEMIGROUPS.DefaultRandomInverseMonoid);
#############################################################################
## 1. Isomorphisms
#############################################################################
# fallback method: via a transformation semigroup
InstallMethod(IsomorphismSemigroup,
"for IsBooleanMatSemigroup and a semigroup",
[IsBooleanMatSemigroup, IsSemigroup],
SEMIGROUPS.DefaultIsomorphismSemigroup);
InstallMethod(IsomorphismSemigroup,
"for IsBooleanMatSemigroup and a boolean mat semigroup",
[IsBooleanMatSemigroup, IsBooleanMatSemigroup],
{filter, S} -> SemigroupIsomorphismByFunctionNC(S, S, IdFunc, IdFunc));
# It seems necessary that the method below occurs after the fallback method in
# this file, in order that it be selected.
InstallMethod(IsomorphismSemigroup,
"for IsBooleanMatSemigroup and a transformation semigroup",
[IsBooleanMatSemigroup, IsTransformationSemigroup],
function(_, S)
local n, T;
n := Maximum(1, DegreeOfTransformationSemigroup(S));
T := Semigroup(List(GeneratorsOfSemigroup(S), x -> AsBooleanMat(x, n)));
UseIsomorphismRelation(S, T);
return SemigroupIsomorphismByFunctionNC(S,
T,
x -> AsBooleanMat(x, n),
AsTransformation);
end);
# If the second argument here is a transformation semigroup, then
# DefaultIsomorphismMonoid uses IsomorphismTransformationMonoid, which detects
# the MultiplicativeNeutralElement of the second argument, and reduces the
# degree accordingly.
InstallMethod(AsMonoid, "for a boolean mat semigroup",
[IsBooleanMatSemigroup],
function(S)
if MultiplicativeNeutralElement(S) = fail then
return fail; # so that we do the same as the GAP / ref manual says
fi;
return Range(IsomorphismMonoid(IsBooleanMatMonoid, S));
end);
InstallMethod(IsomorphismMonoid, "for IsBooleanMatMonoid and a semigroup",
[IsBooleanMatMonoid, IsSemigroup], SEMIGROUPS.DefaultIsomorphismMonoid);
InstallMethod(IsomorphismMonoid, "for IsBooleanMatMonoid and a monoid",
[IsBooleanMatMonoid, IsMonoid],
{filter, S} -> IsomorphismSemigroup(IsBooleanMatSemigroup, S));
InstallMethod(IsomorphismMonoid,
"for IsBooleanMatMonoid and a boolean mat monoid",
[IsBooleanMatMonoid, IsBooleanMatMonoid],
{filter, S} -> SemigroupIsomorphismByFunctionNC(S, S, IdFunc, IdFunc));
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2026-03-28
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