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############################################################################
##
## semigroups/semipbr.gi
## Copyright (C) 2015-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
# TODO(later) IsomorphismSemigroup for IsBooleanMatSemigroup
#
# This file contains methods for semigroups of PBRs.
#############################################################################
## ?. Random
#############################################################################
InstallMethod(SEMIGROUPS_ProcessRandomArgsCons,
[IsPBRSemigroup, IsList],
{filt, params} -> SEMIGROUPS_ProcessRandomArgsCons(IsSemigroup, params));
InstallMethod(SEMIGROUPS_ProcessRandomArgsCons,
[IsPBRMonoid, IsList],
{filt, params} -> SEMIGROUPS_ProcessRandomArgsCons(IsSemigroup, params));
InstallMethod(RandomSemigroupCons, "for IsPBRSemigroup and a list",
[IsPBRSemigroup, IsList],
{filt, params} -> Semigroup(List([1 .. params[1]], i -> RandomPBR(params[2]))));
InstallMethod(RandomMonoidCons, "for IsPBRMonoid and a list",
[IsPBRMonoid, IsList],
{filt, params} -> Monoid(List([1 .. params[1]], i -> RandomPBR(params[2]))));
InstallMethod(RandomInverseSemigroupCons, "for IsPBRSemigroup and a list",
[IsPBRSemigroup, IsList], SEMIGROUPS.DefaultRandomInverseSemigroup);
InstallMethod(RandomInverseMonoidCons, "for IsPBRMonoid and a list",
[IsPBRMonoid, IsList], SEMIGROUPS.DefaultRandomInverseMonoid);
InstallMethod(SemigroupViewStringPrefix, "for a pbr semigroup",
[IsPBRSemigroup], S -> "\>pbr\< ");
InstallMethod(SemigroupViewStringSuffix, "for a pbr semigroup",
[IsPBRSemigroup],
function(S)
return Concatenation("\>degree \>",
ViewString(DegreeOfPBRSemigroup(S)),
"\<\< ");
end);
InstallMethod(DegreeOfPBRSemigroup, "for a PBR semigroup", [IsPBRSemigroup],
S -> DegreeOfPBR(Representative(S)));
# fall back method via a transformation semigroup
InstallMethod(IsomorphismSemigroup, "for IsPBRSemigroup and a semigroup",
[IsPBRSemigroup, IsSemigroup], SEMIGROUPS.DefaultIsomorphismSemigroup);
InstallMethod(IsomorphismSemigroup,
"for IsPBRSemigroup and a transformation semigroup",
[IsPBRSemigroup, IsTransformationSemigroup],
function(_, S)
local deg, T;
deg := Maximum(1, DegreeOfTransformationSemigroup(S));
T := Semigroup(List(GeneratorsOfSemigroup(S), x -> AsPBR(x, deg)));
UseIsomorphismRelation(S, T);
return SemigroupIsomorphismByFunctionNC(S,
T,
x -> AsPBR(x, deg),
AsTransformation);
end);
# The following is not a monoid isomorphism
InstallMethod(IsomorphismSemigroup,
"for IsPBRSemigroup and a bipartition semigroup",
[IsPBRSemigroup, IsBipartitionSemigroup],
function(_, S)
local T;
T := Semigroup(List(GeneratorsOfSemigroup(S), AsPBR));
UseIsomorphismRelation(S, T);
return SemigroupIsomorphismByFunctionNC(S,
T,
AsPBR,
AsBipartition);
end);
InstallMethod(IsomorphismSemigroup,
"for IsPBRSemigroup and a pbr semigroup",
[IsPBRSemigroup, IsPBRSemigroup],
{_, S} -> SemigroupIsomorphismByFunctionNC(S, S, IdFunc, IdFunc));
InstallMethod(AsMonoid, "for a PBR semigroup",
[IsPBRSemigroup],
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(IsPBRMonoid, S));
end);
InstallMethod(IsomorphismMonoid, "for IsPBRMonoid and a semigroup",
[IsPBRMonoid, IsSemigroup], SEMIGROUPS.DefaultIsomorphismMonoid);
InstallMethod(IsomorphismMonoid, "for IsPBRMonoid and a monoid",
[IsPBRMonoid, IsMonoid], SEMIGROUPS.DefaultIsomorphismMonoid);
InstallMethod(IsomorphismMonoid, "for IsPBRMonoid and a transformation monoid",
[IsPBRMonoid, IsTransformationMonoid],
function(_, S)
local deg, T;
deg := Maximum(1, DegreeOfTransformationSemigroup(S));
T := Monoid(List(GeneratorsOfSemigroup(S), x -> AsPBR(x, deg)));
UseIsomorphismRelation(S, T);
return SemigroupIsomorphismByFunctionNC(S,
T,
x -> AsPBR(x, deg),
AsTransformation);
end);
InstallMethod(IsomorphismMonoid,
"for IsPBRMonoid and a pbr monoid",
[IsPBRMonoid, IsPBRMonoid],
{filter, S} -> SemigroupIsomorphismByFunctionNC(S, S, IdFunc, IdFunc));
InstallMethod(\<, "for pbr semigroups",
[IsPBRSemigroup, IsPBRSemigroup],
function(S, T)
if DegreeOfPBRSemigroup(S) <> DegreeOfPBRSemigroup(T) then
return DegreeOfPBRSemigroup(S) < DegreeOfPBRSemigroup(T);
fi;
TryNextMethod();
end);
[ Dauer der Verarbeitung: 0.26 Sekunden
(vorverarbeitet)
]
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