Quelle  HomalgFiltration.gd   Sprache: Shell

# SPDX-License-Identifier: GPL-2.0-or-later
# homalg: A homological algebra meta-package for computable Abelian categories
#
# Declarations
#

##  Declaration stuff for a filtration.

####################################
#
# categories:
#
####################################

# A new GAP-category:

##  <#GAPDoc Label="IsHomalgFiltration">
##  <ManSection>
##    <Filt Type="Category" Arg="filt" Name="IsHomalgFiltration"/>
##    <Returns><C>true</C> or <C>false</C></Returns>
##    <Description>
##      The &GAP; category of &homalg; filtrations.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareCategory( "IsHomalgFiltration",
        IsAttributeStoringRep );

## CAUTION: in the code the following two categories are the only ones for sets of generators,
##          i.e. IsHomalgFiltration and not IsHomalgFiltrationOfLeftObject => IsHomalgFiltrationOfRightObject

DeclareCategory( "IsHomalgFiltrationOfLeftObject",
        IsHomalgFiltration );

DeclareCategory( "IsHomalgFiltrationOfRightObject",
        IsHomalgFiltration );

DeclareCategory( "IsDescendingFiltration",
        IsHomalgFiltration );

DeclareCategory( "IsAscendingFiltration",
        IsHomalgFiltration );

####################################
#
# properties:
#
####################################

DeclareProperty( "IsGradation",
        IsHomalgFiltration );

DeclareProperty( "IsFiltration",
        IsHomalgFiltration );

DeclareProperty( "IsPurityFiltration",
        IsHomalgFiltration );

DeclareProperty( "IsCompletePurityFiltration",
        IsHomalgFiltration );

####################################
#
# attributes:
#
####################################

##  <#GAPDoc Label="SpectralSequence:filt">
##  <ManSection>
##    <Attr Arg="BC" Name="SpectralSequence" Label="for filtrations"/>
##    <Returns>a &homalg; (co)homological spectral sequence</Returns>
##    <Description>
##      The spectral sequence used to construct the filtration (if any).
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareAttribute( "SpectralSequence",
        IsHomalgFiltration );

####################################
#
# global functions and operations:
#
####################################

# constructors:

DeclareGlobalFunction( "HomalgFiltration" );

DeclareGlobalFunction( "HomalgFiltrationFromTelescope" );

DeclareGlobalFunction( "HomalgFiltrationFromTower" );

DeclareGlobalFunction( "HomalgDescendingFiltration" );

DeclareGlobalFunction( "HomalgAscendingFiltration" );

# basic operations:

DeclareOperation( "DegreesOfFiltration",
        [ IsHomalgFiltration ] );

DeclareOperation( "LowestDegree",
        [ IsHomalgFiltration ] );

DeclareOperation( "HighestDegree",
        [ IsHomalgFiltration ] );

DeclareOperation( "CertainMorphism",
        [ IsHomalgFiltration, IsInt ] );

DeclareOperation( "CertainObject",
        [ IsHomalgFiltration, IsInt ] );

DeclareOperation( "ObjectsOfFiltration",
        [ IsHomalgFiltration ] );

DeclareOperation( "LowestDegreeObject",
        [ IsHomalgFiltration ] );

DeclareOperation( "HighestDegreeObject",
        [ IsHomalgFiltration ] );

DeclareOperation( "StructureObject",
        [ IsHomalgFiltration ] );

DeclareOperation( "MorphismsOfFiltration",
        [ IsHomalgFiltration ] );

DeclareOperation( "LowestDegreeMorphism",
        [ IsHomalgFiltration ] );

DeclareOperation( "HighestDegreeMorphism",
        [ IsHomalgFiltration ] );

if IsBoundGlobal( "UnderlyingObject" ) and not IsAttribute( ValueGlobal( "UnderlyingObject" ) ) then
    DeclareOperation( "UnderlyingObject", [ IsHomalgFiltration ] );
else
    DeclareAttribute( "UnderlyingObject", IsHomalgFiltration );
fi;

DeclareOperation( "IsomorphismOfFiltration",
        [ IsHomalgFiltration ] );

DeclareOperation( "UnlockObject",
        [ IsHomalgFiltration ] );

DeclareOperation( "AssociatedSecondSpectralSequence",
        [ IsHomalgFiltration ] );

DeclareOperation( "*",
        [ IsHomalgFiltration, IsHomalgStaticMorphism ] );