Revision 3a654fb6556f8b24081daeae9249680d8ff68214 authored by Sebastian Gutsche on 06 October 2016, 15:26:25 UTC, committed by Sebastian Gutsche on 06 October 2016, 15:26:25 UTC
1 parent 8ba25ff
HomalgGenerators.gd
#############################################################################
##
## HomalgGenerators.gd Modules package Mohamed Barakat
##
## Copyright 2007-2008 Lehrstuhl B für Mathematik, RWTH Aachen
##
## Declaration stuff for a set of generators.
##
#############################################################################
####################################
#
# categories:
#
####################################
# three new GAP-categories:
## <#GAPDoc Label="IsHomalgGenerators">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgGenerators"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; generators.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgGenerators",
IsAttributeStoringRep );
## CAUTION: in the code the following two categories are the only ones for sets of generators,
## i.e. IsHomalgGenerators and not IsHomalgGeneratorsOfLeftModule => IsHomalgGeneratorsOfRightModule
## <#GAPDoc Label="IsHomalgGeneratorsOfLeftModule">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgGeneratorsOfLeftModule"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; generators of a left module. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgGenerators</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgGeneratorsOfLeftModule",
IsHomalgGenerators );
## <#GAPDoc Label="IsHomalgGeneratorsOfRightModule">
## <ManSection>
## <Filt Type="Category" Arg="rel" Name="IsHomalgGeneratorsOfRightModule"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; generators of a right module. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgGenerators</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgGeneratorsOfRightModule",
IsHomalgGenerators );
####################################
#
# properties:
#
####################################
## <#GAPDoc Label="IsReduced:generators">
## <ManSection>
## <Prop Arg="gen" Name="IsReduced" Label="for generators"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; set of generators <A>gen</A> is marked reduced. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsReduced",
IsHomalgGenerators );
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="ProcedureToNormalizeGenerators">
## <ManSection>
## <Attr Arg="gen" Name="ProcedureToNormalizeGenerators"/>
## <Returns>a function</Returns>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProcedureToNormalizeGenerators",
IsHomalgGenerators );
## <#GAPDoc Label="ProcedureToReadjustGenerators">
## <ManSection>
## <Attr Arg="gen" Name="ProcedureToReadjustGenerators"/>
## <Returns>a function</Returns>
## <Description>
## A function that takes the rows/columns of <A>gen</A> and returns an object (e.g. a matrix) that
## can be interpreted as a generator (this is important for modules of homomorphisms).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProcedureToReadjustGenerators",
IsHomalgGenerators );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareGlobalFunction( "HomalgGeneratorsForLeftModule" );
DeclareGlobalFunction( "HomalgGeneratorsForRightModule" );
DeclareOperation( "RingMap",
[ IsHomalgGenerators, IsHomalgRing, IsHomalgRing ] );
# basic operations:
DeclareOperation( "MatrixOfGenerators",
[ IsHomalgGenerators ] );
DeclareOperation( "HomalgRing",
[ IsHomalgGenerators ] );
DeclareOperation( "GetGenerators",
[ IsHomalgGenerators, IsInt ] );
DeclareOperation( "GetGenerators",
[ IsHomalgGenerators, IsList ] );
DeclareOperation( "GetGenerators",
[ IsHomalgGenerators ] );
DeclareOperation( "RelationsOfHullModule",
[ IsHomalgGenerators ] );
DeclareOperation( "HasNrRelations",
[ IsHomalgGenerators ] );
DeclareOperation( "NrRelations",
[ IsHomalgGenerators ] );
DeclareOperation( "MatrixOfRelations",
[ IsHomalgGenerators ] );
DeclareOperation( "HasNrGenerators",
[ IsHomalgGenerators ] );
DeclareOperation( "NrGenerators",
[ IsHomalgGenerators ] );
DeclareOperation( "CertainGenerators",
[ IsHomalgGenerators, IsList ] );
DeclareOperation( "CertainGenerator",
[ IsHomalgGenerators, IsPosInt ] );
DeclareOperation( "NewHomalgGenerators",
[ IsHomalgMatrix, IsHomalgGenerators ] );
DeclareOperation( "UnionOfRelations",
[ IsHomalgGenerators, IsHomalgRelations ] );
DeclareOperation( "BasisOfModule",
[ IsHomalgGenerators ] );
DeclareOperation( "DecideZero",
[ IsHomalgGenerators ] );
DeclareOperation( "DecideZero",
[ IsHomalgGenerators, IsHomalgRelations ] );
DeclareOperation( "SyzygiesGenerators",
[ IsHomalgGenerators, IsHomalgRelations ] );
DeclareOperation( "ReducedSyzygiesGenerators",
[ IsHomalgGenerators, IsHomalgRelations ] );
DeclareOperation( "GetRidOfZeroGenerators",
[ IsHomalgGenerators ] );
DeclareOperation( "*",
[ IsHomalgMatrix, IsHomalgGenerators ] );
DeclareOperation( "*",
[ IsHomalgGenerators, IsHomalgGenerators ] );
DeclareOperation( "*",
[ IsHomalgRelations, IsHomalgGenerators ] );
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