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############################################################################
##
## elements/boolmat.gd
## Copyright (C) 2015-2022 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
# This file contains an implementation of boolean matrices.
#############################################################################
## Specializations of declarations for MatrixOverSemiring
#############################################################################
DeclareCategory("IsBooleanMat", IsMatrixOverSemiring and
IsPlistMatrixOverSemiringPositionalRep);
DeclareCategoryCollections("IsBooleanMat");
DeclareCategoryCollections("IsBooleanMatCollection");
BindGlobal("BooleanMatType",
NewType(NewFamily("BooleanMatFamily",
IsBooleanMat,
CanEasilySortElements,
CanEasilySortElements),
IsBooleanMat));
DeclareGlobalFunction("BooleanMat");
#############################################################################
## Declarations specifically for Boolean mats
#############################################################################
DeclareOperation("AsBooleanMat", [IsMultiplicativeElement, IsPosInt]);
DeclareOperation("AsBooleanMat", [IsMultiplicativeElement]);
DeclareOperation("AsBooleanMat", [IsDigraph]);
DeclareOperation("AsDigraph", [IsBooleanMat]);
DeclareOperation("NumberBooleanMat", [IsBooleanMat]);
DeclareOperation("BooleanMatNumber", [IsPosInt, IsPosInt]);
DeclareGlobalFunction("NumberBlist");
DeclareGlobalFunction("BlistNumber");
DeclareAttribute("Successors", IsBooleanMat);
DeclareProperty("IsRowTrimBooleanMat", IsBooleanMat);
DeclareProperty("IsColTrimBooleanMat", IsBooleanMat);
DeclareProperty("IsTrimBooleanMat", IsBooleanMat);
DeclareGlobalFunction("OnBlist");
DeclareAttribute("CanonicalBooleanMat", IsBooleanMat);
DeclareOperation("CanonicalBooleanMat", [IsPermGroup, IsBooleanMat]);
DeclareOperation("CanonicalBooleanMat",
[IsPermGroup, IsPermGroup, IsBooleanMat]);
DeclareOperation("CanonicalBooleanMatNC",
[IsPermGroup, IsPermGroup, IsBooleanMat]);
DeclareProperty("IsSymmetricBooleanMat", IsBooleanMat);
DeclareProperty("IsAntiSymmetricBooleanMat", IsBooleanMat);
DeclareProperty("IsTransitiveBooleanMat", IsBooleanMat);
DeclareProperty("IsReflexiveBooleanMat", IsBooleanMat);
DeclareProperty("IsTotalBooleanMat", IsBooleanMat);
DeclareProperty("IsOntoBooleanMat", IsBooleanMat);
DeclareSynonymAttr("IsPartialOrderBooleanMat", IsReflexiveBooleanMat and
IsAntiSymmetricBooleanMat and IsTransitiveBooleanMat);
DeclareSynonymAttr("IsEquivalenceBooleanMat", IsReflexiveBooleanMat and
IsSymmetricBooleanMat and IsTransitiveBooleanMat);
DeclareProperty("IsTransformationBooleanMat", IsBooleanMat);
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