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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
## ResidueClassRingBasic.gi MatricesForHomalg package Mohamed Barakat
##
## Copyright 2007-2009 Mohamed Barakat, Universität des Saarlandes
##
## Implementation stuff for homalg residue class rings.
##
#############################################################################
####################################
#
# global variables:
#
####################################
##
InstallValue( CommonHomalgTableForResidueClassRingsBasic,
rec(
## Must only then be provided by the RingPackage in case the default
## "service" function does not match the Ring
## <#GAPDoc Label="BasisOfRowModule:ResidueClassRing">
## <ManSection>
## <Func Arg="M" Name="BasisOfRowModule" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
BasisOfRowModule :=
function( M )
local Mrel;
Mrel := UnionOfRows( M );
Mrel := HomalgResidueClassMatrix(
BasisOfRowModule( Mrel ), HomalgRing( M ) );
return GetRidOfObsoleteRows( Mrel );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfColumnModule:ResidueClassRing">
## <ManSection>
## <Func Arg="M" Name="BasisOfColumnModule" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
BasisOfColumnModule :=
function( M )
local Mrel;
Mrel := UnionOfColumns( M );
Mrel := HomalgResidueClassMatrix(
BasisOfColumnModule( Mrel ), HomalgRing( M ) );
return GetRidOfObsoleteColumns( Mrel );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfRowsCoeff:ResidueClassRing">
## <ManSection>
## <Func Arg="M, T" Name="BasisOfRowsCoeff" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
BasisOfRowsCoeff :=
function( M, T )
local Mrel, TT, bas, nz;
Mrel := UnionOfRows( M );
TT := HomalgVoidMatrix( HomalgRing( Mrel ) );
bas := BasisOfRowsCoeff( Mrel, TT );
bas := HomalgResidueClassMatrix( bas, HomalgRing( M ) );
nz := NonZeroRows( bas );
SetEval( T, CertainRows( CertainColumns( TT, [ 1 .. NrRows( M ) ] ), nz ) );
ResetFilterObj( T, IsVoidMatrix );
## the generic BasisOfRowsCoeff will assume that
## ( NrRows( B ) = 0 ) = IsZero( B )
return CertainRows( bas, nz );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfColumnsCoeff:ResidueClassRing">
## <ManSection>
## <Func Arg="M, T" Name="BasisOfColumnsCoeff" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
BasisOfColumnsCoeff :=
function( M, T )
local Mrel, TT, bas, nz;
Mrel := UnionOfColumns( M );
TT := HomalgVoidMatrix( HomalgRing( Mrel ) );
bas := BasisOfColumnsCoeff( Mrel, TT );
bas := HomalgResidueClassMatrix( bas, HomalgRing( M ) );
nz := NonZeroColumns( bas );
SetEval( T, CertainColumns( CertainRows( TT, [ 1 .. NrColumns( M ) ] ), nz ) );
ResetFilterObj( T, IsVoidMatrix );
## the generic BasisOfColumnsCoeff will assume that
## ( NrColumns( B ) = 0 ) = IsZero( B )
return CertainColumns( bas, nz );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroRows:ResidueClassRing">
## <ManSection>
## <Func Arg="A, B" Name="DecideZeroRows" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
DecideZeroRows :=
function( A, B )
local Brel;
Brel := UnionOfRows( B );
Brel := BasisOfRowModule( Brel );
return HomalgResidueClassMatrix(
DecideZeroRows( Eval( A ), Brel ), HomalgRing( A ) );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroColumns:ResidueClassRing">
## <ManSection>
## <Func Arg="A, B" Name="DecideZeroColumns" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
DecideZeroColumns :=
function( A, B )
local Brel;
Brel := UnionOfColumns( B );
Brel := BasisOfColumnModule( Brel );
return HomalgResidueClassMatrix(
DecideZeroColumns( Eval( A ), Brel ), HomalgRing( A ) );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroRowsEffectively:ResidueClassRing">
## <ManSection>
## <Func Arg="A, B, T" Name="DecideZeroRowsEffectively" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
DecideZeroRowsEffectively :=
function( A, B, T )
local Brel, TT, red;
Brel := UnionOfRows( B );
TT := HomalgVoidMatrix( HomalgRing( Brel ) );
red := DecideZeroRowsEffectively( Eval( A ), Brel, TT );
SetEval( T, CertainColumns( TT, [ 1 .. NrRows( B ) ] ) );
ResetFilterObj( T, IsVoidMatrix );
return HomalgResidueClassMatrix( red, HomalgRing( A ) );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroColumnsEffectively:ResidueClassRing">
## <ManSection>
## <Func Arg="A, B, T" Name="DecideZeroColumnsEffectively" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
DecideZeroColumnsEffectively :=
function( A, B, T )
local Brel, TT, red;
Brel := UnionOfColumns( B );
TT := HomalgVoidMatrix( HomalgRing( Brel ) );
red := DecideZeroColumnsEffectively( Eval( A ), Brel, TT );
SetEval( T, CertainRows( TT, [ 1 .. NrColumns( B ) ] ) );
ResetFilterObj( T, IsVoidMatrix );
return HomalgResidueClassMatrix( red, HomalgRing( A ) );
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="SyzygiesGeneratorsOfRows:ResidueClassRing">
## <ManSection>
## <Func Arg="M" Name="SyzygiesGeneratorsOfRows" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
SyzygiesGeneratorsOfRows :=
function( M )
local R, ring_rel, rel, S;
R := HomalgRing( M );
ring_rel := RingRelations( R );
rel := MatrixOfRelations( ring_rel );
if IsHomalgRingRelationsAsGeneratorsOfRightIdeal( ring_rel ) then
rel := Involution( rel );
fi;
rel := DiagMat( ListWithIdenticalEntries( NrColumns( M ), rel ) );
S := SyzygiesGeneratorsOfRows( Eval( M ), rel );
S := HomalgResidueClassMatrix( S, R );
S := GetRidOfObsoleteRows( S );
if IsZero( S ) then
SetIsLeftRegular( M, true );
fi;
return S;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="SyzygiesGeneratorsOfColumns:ResidueClassRing">
## <ManSection>
## <Func Arg="M" Name="SyzygiesGeneratorsOfColumns" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
SyzygiesGeneratorsOfColumns :=
function( M )
local R, ring_rel, rel, S;
R := HomalgRing( M );
ring_rel := RingRelations( R );
rel := MatrixOfRelations( ring_rel );
if IsHomalgRingRelationsAsGeneratorsOfLeftIdeal( ring_rel ) then
rel := Involution( rel );
fi;
rel := DiagMat( ListWithIdenticalEntries( NrRows( M ), rel ) );
S := SyzygiesGeneratorsOfColumns( Eval( M ), rel );
S := HomalgResidueClassMatrix( S, R );
S := GetRidOfObsoleteColumns( S );
if IsZero( S ) then
SetIsRightRegular( M, true );
fi;
return S;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="RelativeSyzygiesGeneratorsOfRows:ResidueClassRing">
## <ManSection>
## <Func Arg="M, M2" Name="RelativeSyzygiesGeneratorsOfRows" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
RelativeSyzygiesGeneratorsOfRows :=
function( M, M2 )
local M2rel, S;
M2rel := UnionOfRows( M2 );
S := SyzygiesGeneratorsOfRows( Eval( M ), M2rel );
S := HomalgResidueClassMatrix( S, HomalgRing( M ) );
S := GetRidOfObsoleteRows( S );
if IsZero( S ) then
SetIsLeftRegular( M, true );
fi;
return S;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="RelativeSyzygiesGeneratorsOfColumns:ResidueClassRing">
## <ManSection>
## <Func Arg="M, M2" Name="RelativeSyzygiesGeneratorsOfColumns" Label="ResidueClassRing"/>
## <Returns>a &homalg; matrix over the ambient ring</Returns>
## <Description>
## <Listing Type="Code"><![CDATA[
RelativeSyzygiesGeneratorsOfColumns :=
function( M, M2 )
local M2rel, S;
M2rel := UnionOfColumns( M2 );
S := SyzygiesGeneratorsOfColumns( Eval( M ), M2rel );
S := HomalgResidueClassMatrix( S, HomalgRing( M ) );
S := GetRidOfObsoleteColumns( S );
if IsZero( S ) then
SetIsRightRegular( M, true );
fi;
return S;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
X_ReducedBasisOfRowModule :=
function( M )
local Mrel;
Mrel := UnionOfRows( M );
Mrel := HomalgResidueClassMatrix( ReducedBasisOfRowModule( Mrel ), HomalgRing( M ) );
return GetRidOfObsoleteRows( Mrel );
end,
X_ReducedBasisOfColumnModule :=
function( M )
local Mrel;
Mrel := UnionOfColumns( M );
Mrel := HomalgResidueClassMatrix( ReducedBasisOfColumnModule( Mrel ), HomalgRing( M ) );
return GetRidOfObsoleteColumns( Mrel );
end,
X_ReducedSyzygiesGeneratorsOfRows :=
function( M )
end,
X_ReducedSyzygiesGeneratorsOfColumns :=
function( M )
end,
)
);