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Impressum pbr.gd
Sprache: unbekannt
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############################################################################
##
## elements/pbr.gd
## Copyright (C) 2015-2022 Attila Egri-Nagy
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
# This file contains a declarations for partitioned binary relations (PBRs) as
# defined in:
#
# MARTIN, Paul; MAZORCHUK, Volodymyr.
# Partitioned Binary Relations. MATHEMATICA SCANDINAVICA, v113, n1, p. 30-52,
# https://arxiv.org/abs/1102.0862
DeclareCategory("IsPBR",
IsMultiplicativeElementWithInverse and
IsAssociativeElementWithStar);
DeclareCategoryCollections("IsPBR");
DeclareCategoryCollections("IsPBRCollection");
InstallTrueMethod(IsGeneratorsOfSemigroup, IsPBRCollection);
DeclareOperation("PBR", [IsDenseList, IsDenseList]);
DeclareGlobalFunction("PBRNC");
DeclareOperation("RandomPBR", [IsPosInt]);
DeclareOperation("RandomPBR", [IsPosInt, IsFloat]);
DeclareOperation("EmptyPBR", [IsPosInt]);
DeclareOperation("IdentityPBR", [IsPosInt]);
DeclareOperation("UniversalPBR", [IsPosInt]);
DeclareAttribute("DegreeOfPBR", IsPBR);
DeclareAttribute("DegreeOfPBRCollection", IsPBRCollection);
DeclareOperation("NumberPBR", [IsPBR]);
DeclareOperation("PBRNumber", [IsPosInt, IsPosInt]);
DeclareOperation("AsPBR", [IsMultiplicativeElement, IsPosInt]);
DeclareOperation("AsPBR", [IsMultiplicativeElement]);
DeclareProperty("IsEmptyPBR", IsPBR);
DeclareProperty("IsIdentityPBR", IsPBR);
DeclareProperty("IsUniversalPBR", IsPBR);
DeclareProperty("IsBipartitionPBR", IsPBR);
DeclareProperty("IsTransformationPBR", IsPBR);
DeclareProperty("IsPartialPermPBR", IsPBR);
DeclareProperty("IsPermPBR", IsPBR);
DeclareProperty("IsBlockBijectionPBR", IsPBR);
DeclareProperty("IsDualTransformationPBR", IsPBR);
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2026-03-28
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