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# SPDX-License-Identifier: GPL-2.0-or-later
# MatricesForHomalg: Matrices for the homalg project
#
# Declarations
#
####################################
#
# categories:
#
####################################
# two new GAP-categories:
## this is introduced to allow internal matrices
## to remain mutable, although Eval is an attribute
DeclareCategory( "IsInternalMatrixHull",
IsAdditiveElementWithInverse and
IsExtLElement and
IsComponentObjectRep ); ## CAUTION: never let such matrix hulls be multiplicative elements!!
## <#GAPDoc Label="IsHomalgMatrix">
## <ManSection>
## <Filt Type="Category" Arg="A" Name="IsHomalgMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; matrices.
## <Listing Type="Code"><![CDATA[
DeclareCategory( "IsHomalgMatrix",
IsMatrixObj and
IsAttributeStoringRep );
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
####################################
#
# properties:
#
####################################
DeclareOperation( "SetIsMutableMatrix",
[ IsHomalgMatrix, IsBool ] );
## <#GAPDoc Label="IsInitialMatrix">
## <ManSection>
## <Filt Arg="A" Name="IsInitialMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareFilter( "IsInitialMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsInitialIdentityMatrix">
## <ManSection>
## <Filt Arg="A" Name="IsInitialIdentityMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareFilter( "IsInitialIdentityMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsVoidMatrix">
## <ManSection>
## <Filt Arg="A" Name="IsVoidMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareFilter( "IsVoidMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsZero:matrix">
## <ManSection>
## <Prop Arg="A" Name="IsZero" Label="for matrices"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; matrix <A>A</A> is a zero matrix, taking possible ring relations into account.<P/>
## (for the installed standard method see <Ref Meth="IsZeroMatrix" Label="homalgTable entry"/>)
## <Example><![CDATA[
## gap> zz := HomalgRingOfIntegers( );
## Z
## gap> A := HomalgMatrix( "[ 2 ]", zz );
## <A 1 x 1 matrix over an internal ring>
## gap> Z2 := zz / 2;
## Z/( 2 )
## gap> A := Z2 * A;
## <A 1 x 1 matrix over a residue class ring>
## gap> Display( A );
## [ [ 2 ] ]
##
## modulo [ 2 ]
## gap> IsZero( A );
## true
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="IsOne:matrix">
## <ManSection>
## <Prop Arg="A" Name="IsOne"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; matrix <A>A</A> is an identity matrix, taking possible ring relations into account.<P/>
## (for the installed standard method see <Ref Meth="IsIdentityMatrix" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
## <#GAPDoc Label="IsPermutationMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsPermutationMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsPermutationMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsSpecialSubidentityMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsSpecialSubidentityMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsSpecialSubidentityMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsSubidentityMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsSubidentityMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsSubidentityMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsLeftRegular">
## <ManSection>
## <Prop Arg="A" Name="IsLeftRegular"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsLeftRegular",
IsHomalgMatrix );
## <#GAPDoc Label="IsRightRegular">
## <ManSection>
## <Prop Arg="A" Name="IsRightRegular"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsRightRegular",
IsHomalgMatrix );
## <#GAPDoc Label="IsInvertibleMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsInvertibleMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsInvertibleMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsLeftInvertibleMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsLeftInvertibleMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsLeftInvertibleMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsRightInvertibleMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsRightInvertibleMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsRightInvertibleMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsEmptyMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsEmptyMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if not IsBound(IsEmptyMatrix) then # GAP >= 4.11 already provides this property
DeclareProperty( "IsEmptyMatrix",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="IsDiagonalMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsDiagonalMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if the &homalg; matrix <A>A</A> is a diagonal matrix, taking possible ring relations into account.<P/>
## (for the installed standard method see <Ref Meth="IsDiagonalMatrix" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if not IsBound(IsDiagonalMatrix) then # GAP >= 4.11 already provides this property
DeclareProperty( "IsDiagonalMatrix",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="IsScalarMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsScalarMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsScalarMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsUpperTriangularMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsUpperTriangularMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if not IsBound(IsUpperTriangularMatrix) then # GAP >= 4.11 already provides this property
DeclareProperty( "IsUpperTriangularMatrix",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="IsLowerTriangularMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsLowerTriangularMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if not IsBound(IsLowerTriangularMatrix) then # GAP >= 4.11 already provides this property
DeclareProperty( "IsLowerTriangularMatrix",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="IsStrictUpperTriangularMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsStrictUpperTriangularMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsStrictUpperTriangularMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsStrictLowerTriangularMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsStrictLowerTriangularMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsStrictLowerTriangularMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsUpperStairCaseMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsUpperStairCaseMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsUpperStairCaseMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsLowerStairCaseMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsLowerStairCaseMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsLowerStairCaseMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsTriangularMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsTriangularMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsTriangularMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsBasisOfRowsMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsBasisOfRowsMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsBasisOfRowsMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsBasisOfColumnsMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsBasisOfColumnsMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsBasisOfColumnsMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsReducedBasisOfRowsMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsReducedBasisOfRowsMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsReducedBasisOfRowsMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsReducedBasisOfColumnsMatrix">
## <ManSection>
## <Prop Arg="A" Name="IsReducedBasisOfColumnsMatrix"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsReducedBasisOfColumnsMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="IsUnitFree">
## <ManSection>
## <Prop Arg="A" Name="IsUnitFree"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsUnitFree",
IsHomalgMatrix );
DeclareProperty( "IsPrimeModule",
IsHomalgMatrix );
####################################
#
# attributes:
#
####################################
DeclareAttribute( "Eval",
IsHomalgMatrix );
DeclareAttribute( "EvalMatrixOperation",
IsHomalgMatrix );
DeclareAttribute( "EvalInvolution",
IsHomalgMatrix );
DeclareAttribute( "ItsInvolution",
IsHomalgMatrix );
DeclareAttribute( "EvalTransposedMatrix",
IsHomalgMatrix );
DeclareAttribute( "ItsTransposedMatrix",
IsHomalgMatrix );
DeclareAttribute( "EvalCoercedMatrix",
IsHomalgMatrix );
DeclareAttribute( "EvalCertainRows",
IsHomalgMatrix );
DeclareAttribute( "EvalCertainColumns",
IsHomalgMatrix );
DeclareAttribute( "EvalUnionOfRows",
IsHomalgMatrix );
DeclareAttribute( "EvalUnionOfColumns",
IsHomalgMatrix );
DeclareAttribute( "EvalConvertRowToMatrix",
IsHomalgMatrix );
DeclareAttribute( "EvalConvertColumnToMatrix",
IsHomalgMatrix );
DeclareAttribute( "EvalConvertMatrixToRow",
IsHomalgMatrix );
DeclareAttribute( "EvalConvertMatrixToColumn",
IsHomalgMatrix );
DeclareAttribute( "EvalDiagMat",
IsHomalgMatrix );
DeclareAttribute( "EvalKroneckerMat",
IsHomalgMatrix );
DeclareAttribute( "EvalDualKroneckerMat",
IsHomalgMatrix );
DeclareAttribute( "EvalCoefficientsWithGivenMonomials",
IsHomalgMatrix );
DeclareAttribute( "EvalMulMat",
IsHomalgMatrix );
DeclareAttribute( "EvalMulMatRight",
IsHomalgMatrix );
DeclareAttribute( "EvalAddMat",
IsHomalgMatrix );
DeclareAttribute( "EvalSubMat",
IsHomalgMatrix );
DeclareAttribute( "EvalCompose",
IsHomalgMatrix );
DeclareAttribute( "EvalSyzygiesOfRows",
IsHomalgMatrix );
DeclareAttribute( "EvalSyzygiesOfColumns",
IsHomalgMatrix );
DeclareAttribute( "EvalLeftInverse",
IsHomalgMatrix );
DeclareAttribute( "EvalRightInverse",
IsHomalgMatrix );
DeclareAttribute( "EvalInverse",
IsHomalgMatrix );
DeclareAttribute( "PreEval",
IsHomalgMatrix );
## <#GAPDoc Label="NumberRows">
## <ManSection>
## <Attr Arg="A" Name="NumberRows"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The number of rows of the matrix <A>A</A>.<P/>
## (for the installed standard method see <Ref Meth="NumberRows" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if false then
DeclareAttribute( "NumberRows",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="NumberColumns">
## <ManSection>
## <Attr Arg="A" Name="NumberColumns"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The number of columns of the matrix <A>A</A>.<P/>
## (for the installed standard method see <Ref Meth="NumberColumns" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if false then
DeclareAttribute( "NumberColumns",
IsHomalgMatrix );
fi;
DeclareSynonymAttr( "NrColumns", NumberColumns );
## <#GAPDoc Label="DeterminantMat">
## <ManSection>
## <Attr Arg="A" Name="DeterminantMat"/>
## <Returns>a ring element</Returns>
## <Description>
## The determinant of the quadratic matrix <A>A</A>.<P/>
## You can invoke it with <C>Determinant</C>( <A>A</A> ).<P/>
## (for the installed standard method see <Ref Meth="Determinant" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
if not IsBound( DeterminantMatrix ) then
DeclareAttribute( "DeterminantMat",
IsHomalgMatrix );
fi;
## <#GAPDoc Label="RowRankOfMatrix">
## <ManSection>
## <Attr Arg="A" Name="RowRankOfMatrix"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The row rank of the matrix <A>A</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "RowRankOfMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="ColumnRankOfMatrix">
## <ManSection>
## <Attr Arg="A" Name="ColumnRankOfMatrix"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## The column rank of the matrix <A>A</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ColumnRankOfMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="ZeroRows">
## <ManSection>
## <Attr Arg="A" Name="ZeroRows"/>
## <Returns>a (possibly empty) list of positive integers</Returns>
## <Description>
## The list of zero rows of the matrix <A>A</A>. <P/>
## (for the installed standard method see <Ref Meth="ZeroRows" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ZeroRows",
IsHomalgMatrix );
## <#GAPDoc Label="ZeroColumns">
## <ManSection>
## <Attr Arg="A" Name="ZeroColumns"/>
## <Returns>a (possibly empty) list of positive integers</Returns>
## <Description>
## The list of zero columns of the matrix <A>A</A>. <P/>
## (for the installed standard method see <Ref Meth="ZeroColumns" Label="homalgTable entry"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ZeroColumns",
IsHomalgMatrix );
## <#GAPDoc Label="NonZeroRows">
## <ManSection>
## <Attr Arg="A" Name="NonZeroRows"/>
## <Returns>a (possibly empty) list of positive integers</Returns>
## <Description>
## The list of nonzero rows of the matrix <A>A</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NonZeroRows",
IsHomalgMatrix );
## <#GAPDoc Label="NonZeroColumns">
## <ManSection>
## <Attr Arg="A" Name="NonZeroColumns"/>
## <Returns>a (possibly empty) list of positive integers</Returns>
## <Description>
## The list of nonzero columns of the matrix <A>A</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NonZeroColumns",
IsHomalgMatrix );
## <#GAPDoc Label="PositionOfFirstNonZeroEntryPerRow">
## <ManSection>
## <Attr Arg="A" Name="PositionOfFirstNonZeroEntryPerRow"/>
## <Returns>a list of nonnegative integers</Returns>
## <Description>
## The list of positions of the first nonzero entry per row of the
## matrix <A>A</A>, else zero.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "PositionOfFirstNonZeroEntryPerRow",
IsHomalgMatrix );
## <#GAPDoc Label="PositionOfFirstNonZeroEntryPerColumn">
## <ManSection>
## <Attr Arg="A" Name="PositionOfFirstNonZeroEntryPerColumn"/>
## <Returns>a list of nonnegative integers</Returns>
## <Description>
## The list of positions of the first nonzero entry per column of the
## matrix <A>A</A>, else zero.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "PositionOfFirstNonZeroEntryPerColumn",
IsHomalgMatrix );
##
DeclareAttribute( "AdjunctMatrix",
IsHomalgMatrix );
## <#GAPDoc Label="LeftInverse">
## <ManSection>
## <Attr Arg="M" Name="LeftInverse"/>
## <Returns>a &homalg; matrix</Returns>
## <Description>
## A left inverse <M>C</M> of the matrix <A>M</A>. If no left inverse exists then
## <C>false</C> is returned. (&see; <Ref Oper="RightDivide" Label="for pairs of matrices"/>) <P/>
## (for the installed standard method see <Ref Meth="LeftInverse" Label="for matrices"/>)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "LeftInverse",
IsHomalgMatrix );
## <#GAPDoc Label="RightInverse">
## <ManSection>
## <Attr Arg="M" Name="RightInverse"/>
## <Returns>a &homalg; matrix</Returns>
## <Description>
## A right inverse <M>C</M> of the matrix <A>M</A>. If no right inverse exists then
## <C>false</C> is returned. (&see; <Ref Oper="LeftDivide" Label="for pairs of matrices"/>) <P/>
## (for the installed standard method see <Ref Meth="RightInverse" Label="for matrices"/>)
##
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "RightInverse",
IsHomalgMatrix );
DeclareAttribute( "IndicatorMatrixOfNonZeroEntries",
IsHomalgMatrix );
## <#GAPDoc Label="CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries">
## <ManSection>
## <Attr Arg="A" Name="CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries"/>
## <Returns>a list of integers</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries",
IsHomalgMatrix );
## <#GAPDoc Label="CoefficientsOfNumeratorOfHilbertPoincareSeries">
## <ManSection>
## <Attr Arg="A" Name="CoefficientsOfNumeratorOfHilbertPoincareSeries"/>
## <Returns>a list of integers</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CoefficientsOfNumeratorOfHilbertPoincareSeries",
IsHomalgMatrix );
## <#GAPDoc Label="UnreducedNumeratorOfHilbertPoincareSeries">
## <ManSection>
## <Attr Arg="A" Name="UnreducedNumeratorOfHilbertPoincareSeries"/>
## <Returns>a univariate polynomial with rational coefficients</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "UnreducedNumeratorOfHilbertPoincareSeries",
IsHomalgMatrix );
## <#GAPDoc Label="NumeratorOfHilbertPoincareSeries">
## <ManSection>
## <Attr Arg="A" Name="NumeratorOfHilbertPoincareSeries"/>
## <Returns>a univariate polynomial with rational coefficients</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NumeratorOfHilbertPoincareSeries",
IsHomalgMatrix );
## <#GAPDoc Label="HilbertPoincareSeries">
## <ManSection>
## <Attr Arg="A" Name="HilbertPoincareSeries"/>
## <Returns>a univariate rational function with rational coefficients</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "HilbertPoincareSeries",
IsHomalgMatrix );
## <#GAPDoc Label="HilbertPolynomial">
## <ManSection>
## <Attr Arg="A" Name="HilbertPolynomial"/>
## <Returns>a univariate polynomial with rational coefficients</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "HilbertPolynomial",
IsHomalgMatrix );
## <#GAPDoc Label="AffineDimension">
## <ManSection>
## <Attr Arg="A" Name="AffineDimension"/>
## <Returns>an integer</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "AffineDimension",
IsHomalgMatrix );
## <#GAPDoc Label="AffineDegree">
## <ManSection>
## <Attr Arg="A" Name="AffineDegree"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "AffineDegree",
IsHomalgMatrix );
## <#GAPDoc Label="ProjectiveDegree">
## <ManSection>
## <Attr Arg="A" Name="ProjectiveDegree"/>
## <Returns>a nonnegative integer</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProjectiveDegree",
IsHomalgMatrix );
## <#GAPDoc Label="ConstantTermOfHilbertPolynomial">
## <ManSection>
## <Attr Arg="A" Name="ConstantTermOfHilbertPolynomialn"/>
## <Returns>an integer</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix (row convention).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ConstantTermOfHilbertPolynomial",
IsHomalgMatrix );
## <#GAPDoc Label="MatrixOfSymbols">
## <ManSection>
## <Attr Arg="A" Name="MatrixOfSymbols"/>
## <Returns>an integer</Returns>
## <Description>
## <A>A</A> is a &homalg; matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "MatrixOfSymbols",
IsHomalgMatrix );
DeclareAttribute( "MaximalDegreePartOfColumnMatrix",
IsHomalgMatrix );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareGlobalFunction( "homalgInternalMatrixHull" );
DeclareGlobalFunction( "HomalgMatrix" );
DeclareGlobalFunction( "HomalgMatrixListList" );
DeclareGlobalFunction( "HomalgRowVector" );
DeclareGlobalFunction( "HomalgColumnVector" );
DeclareGlobalFunction( "HomalgMatrixWithAttributes" );
DeclareGlobalFunction( "HomalgZeroMatrix" );
DeclareGlobalFunction( "HomalgIdentityMatrix" );
DeclareGlobalFunction( "HomalgInitialMatrix" );
DeclareGlobalFunction( "HomalgInitialIdentityMatrix" );
DeclareGlobalFunction( "HomalgVoidMatrix" );
DeclareGlobalFunction( "HomalgDiagonalMatrix" );
DeclareGlobalFunction( "HomalgScalarMatrix" );
DeclareGlobalFunction( "StringToHomalgColumnMatrix" );
DeclareGlobalFunction( "ListToListList" );
DeclareOperation( "CreateHomalgMatrixFromString",
[ IsString, IsHomalgRing ] );
DeclareOperation( "CreateHomalgMatrixFromString",
[ IsString, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "CreateHomalgBlockDiagonalMatrixFromStringList",
[ IsList, IsList, IsList, IsHomalgRing ] );
DeclareOperation( "CreateHomalgMatrixFromSparseString",
[ IsString, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "CreateHomalgMatrixFromList",
[ IsList, IsHomalgRing ] );
DeclareOperation( "CreateHomalgMatrixFromList",
[ IsList, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "SaveHomalgMatrixToFile",
[ IsString, IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "SaveHomalgMatrixToFile",
[ IsString, IsHomalgMatrix ] );
DeclareOperation( "LoadHomalgMatrixFromFile",
[ IsString, IsHomalgRing ] );
DeclareOperation( "LoadHomalgMatrixFromFile",
[ IsString, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaListListString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaListListString",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaListString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaListString",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaSparseString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrixViaSparseString",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrix",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "ConvertHomalgMatrix",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
#DeclareOperation( "*",
# [ IsHomalgRing, IsHomalgMatrix ] );
#DeclareOperation( "*",
# [ IsHomalgMatrix, IsHomalgRing ] );
# basic operations:
DeclareOperation( "HomalgRing",
[ IsHomalgMatrix ] );
DeclareOperation( "LeftInverseLazy",
[ IsHomalgMatrix ] );
DeclareOperation( "RightInverseLazy",
[ IsHomalgMatrix ] );
DeclareOperation( "GetRidOfObsoleteRows",
[ IsHomalgMatrix ] );
DeclareOperation( "GetRidOfObsoleteColumns",
[ IsHomalgMatrix ] );
DeclareOperation( "BlindlyCopyMatrixProperties",
[ IsHomalgMatrix, IsHomalgMatrix ] );
DeclareOperation( "SetConvertHomalgMatrixViaSparseString",
[ IsHomalgMatrix, IsBool ] );
DeclareOperation( "SetConvertHomalgMatrixViaFile",
[ IsHomalgMatrix, IsBool ] );
DeclareOperation( "SetMatElm",
[ IsHomalgMatrix, IsInt, IsInt, IsString, IsHomalgRing ] );
DeclareOperation( "SetMatElm",
[ IsHomalgMatrix, IsInt, IsInt, IsRingElement, IsHomalgRing ] );
DeclareOperation( "AddToMatElm",
[ IsHomalgMatrix, IsInt, IsInt, IsRingElement ] );
DeclareOperation( "AddToMatElm",
[ IsHomalgMatrix, IsInt, IsInt, IsRingElement, IsHomalgRing ] );
DeclareOperation( "MatElmAsString",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "MatElmAsString",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "MatElm",
[ IsHomalgMatrix, IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "GetListOfMatrixAsString",
[ IsList ] );
DeclareOperation( "GetListListOfStringsOfMatrix",
[ IsList, IsHomalgRing ] );
DeclareOperation( "GetListListOfStringsOfHomalgMatrix",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "GetListOfHomalgMatrixAsString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "GetListOfHomalgMatrixAsString",
[ IsHomalgMatrix ] );
DeclareOperation( "GetListListOfHomalgMatrixAsString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "GetListListOfHomalgMatrixAsString",
[ IsHomalgMatrix ] );
DeclareOperation( "GetSparseListOfHomalgMatrixAsString",
[ IsHomalgMatrix, IsHomalgRing ] );
DeclareOperation( "GetSparseListOfHomalgMatrixAsString",
[ IsHomalgMatrix ] );
DeclareOperation( "EntriesOfHomalgMatrixAsListList",
[ IsHomalgMatrix ] );
DeclareOperation( "EntriesOfHomalgMatrix",
[ IsHomalgMatrix ] );
DeclareOperation( "EntriesOfHomalgRowVector",
[ IsHomalgMatrix ] );
DeclareOperation( "EntriesOfHomalgColumnVector",
[ IsHomalgMatrix ] );
DeclareOperation( "AreComparableMatrices",
[ IsHomalgMatrix, IsHomalgMatrix ] );
DeclareOperation( "GetUnitPosition",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "GetUnitPosition",
[ IsHomalgMatrix ] );
DeclareOperation( "GetCleanRowsPositions",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "GetCleanRowsPositions",
[ IsHomalgMatrix ] );
DeclareOperation( "GetColumnIndependentUnitPositions",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "GetColumnIndependentUnitPositions",
[ IsHomalgMatrix ] );
DeclareOperation( "GetRowIndependentUnitPositions",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "GetRowIndependentUnitPositions",
[ IsHomalgMatrix ] );
DeclareOperation( "DivideEntryByUnit",
[ IsHomalgMatrix, IsInt, IsInt, IsRingElement ] );
DeclareOperation( "DivideRowByUnit",
[ IsHomalgMatrix, IsInt, IsRingElement, IsInt ] );
DeclareOperation( "DivideColumnByUnit",
[ IsHomalgMatrix, IsInt, IsRingElement, IsInt ] );
DeclareOperation( "CopyRowToIdentityMatrix",
[ IsHomalgMatrix, IsInt, IsList, IsInt ] );
DeclareOperation( "CopyColumnToIdentityMatrix",
[ IsHomalgMatrix, IsInt, IsList, IsInt ] );
DeclareOperation( "SetColumnToZero",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "ConvertRowToMatrix",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "ConvertColumnToMatrix",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "ConvertMatrixToRow",
[ IsHomalgMatrix ] );
DeclareOperation( "ConvertMatrixToColumn",
[ IsHomalgMatrix ] );
DeclareOperation( "ConvertRowToTransposedMatrix",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "ConvertColumnToTransposedMatrix",
[ IsHomalgMatrix, IsInt, IsInt ] );
DeclareOperation( "ConvertTransposedMatrixToRow",
[ IsHomalgMatrix ] );
DeclareOperation( "ConvertTransposedMatrixToColumn",
[ IsHomalgMatrix ] );
DeclareOperation( "Involution",
[ IsHomalgMatrix ] );
DeclareOperation( "TransposedMatrix",
[ IsHomalgMatrix ] );
# convenience
DeclareOperation( "CoercedMatrix",
[ IsHomalgRing, IsHomalgMatrix ] );
DeclareOperation( "CoercedMatrix",
[ IsHomalgRing, IsHomalgRing, IsHomalgMatrix ] );
DeclareOperation( "CertainRows",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "CertainColumns",
[ IsHomalgMatrix, IsList ] );
## UnionOfRows[Eager][Op]
DeclareGlobalFunction( "UnionOfRows" );
DeclareOperation( "UnionOfRowsOp",
[ IsHomalgRing, IsInt, IsList ] );
DeclareGlobalFunction( "UnionOfRowsEager" );
DeclareOperation( "UnionOfRowsEagerOp",
[ IsList, IsHomalgMatrix ] );
## UnionOfColumns[Eager][Op]
DeclareGlobalFunction( "UnionOfColumns" );
DeclareOperation( "UnionOfColumnsOp",
[ IsHomalgRing, IsInt, IsList ] );
DeclareGlobalFunction( "UnionOfColumnsEager" );
DeclareOperation( "UnionOfColumnsEagerOp",
[ IsList, IsHomalgMatrix ] );
DeclareOperation( "DiagMat",
[ IsHomalgRing, IsList ] );
DeclareOperation( "KroneckerMat",
[ IsHomalgMatrix, IsHomalgMatrix ] );
DeclareOperation( "DualKroneckerMat",
[ IsHomalgMatrix, IsHomalgMatrix ] );
DeclareOperation( "*", ## this must remain, since an element in IsInternalMatrixHull
[ IsInternalMatrixHull, IsInternalMatrixHull ] ); ## is not a priori IsMultiplicativeElement
DeclareOperation( "DiagonalEntries",
[ IsHomalgMatrix ] );
DeclareOperation( "Minors",
[ IsInt, IsHomalgMatrix ] );
DeclareOperation( "MaximalMinors",
[ IsHomalgMatrix ] );
DeclareOperation( "Numerator",
[ IsHomalgMatrix ] );
DeclareOperation( "Denominator",
[ IsHomalgMatrix ] );
DeclareOperation( "CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "CoefficientsOfNumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "UnreducedNumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList, IsRingElement ] );
DeclareOperation( "UnreducedNumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "UnreducedNumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsRingElement ] );
DeclareOperation( "NumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList, IsRingElement ] );
DeclareOperation( "NumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "NumeratorOfHilbertPoincareSeries",
[ IsHomalgMatrix, IsRingElement ] );
DeclareOperation( "HilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList, IsRingElement ] );
DeclareOperation( "HilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList, IsString ] );
DeclareOperation( "HilbertPoincareSeries",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "HilbertPoincareSeries",
[ IsHomalgMatrix, IsRingElement ] );
DeclareOperation( "HilbertPoincareSeries",
[ IsHomalgMatrix, IsString ] );
DeclareOperation( "HilbertPolynomial",
[ IsHomalgMatrix, IsList, IsList, IsRingElement ] );
DeclareOperation( "HilbertPolynomial",
[ IsHomalgMatrix, IsList, IsList, IsString ] );
DeclareOperation( "HilbertPolynomial",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "HilbertPolynomial",
[ IsHomalgMatrix, IsRingElement ] );
DeclareOperation( "HilbertPolynomial",
[ IsHomalgMatrix, IsString ] );
DeclareOperation( "AffineDimension",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "AffineDegree",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "ProjectiveDegree",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "ConstantTermOfHilbertPolynomial",
[ IsHomalgMatrix, IsList, IsList ] );
DeclareOperation( "NoetherNormalization",
[ IsHomalgMatrix ] );
DeclareOperation( "Iterator",
[ IsHomalgMatrix ] );
DeclareOperation( "Select",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "ClearDenominatorsRowWise",
[ IsHomalgMatrix ] );
DeclareOperation( "RandomMatrix",
[ IsInt, IsInt, IsHomalgRing ] );
DeclareOperation( "CoefficientsWithGivenMonomials",
[ IsHomalgMatrix, IsHomalgMatrix ] );
DeclareOperation( "CoefficientsWithGivenMonomials",
[ IsHomalgMatrix, IsList ] );
DeclareOperation( "CoefficientsWithGivenMonomials",
[ IsHomalgRingElement, IsHomalgMatrix ] );
DeclareOperation( "CoefficientsWithGivenMonomials",
[ IsHomalgRingElement, IsList ] );
DeclareOperation( "LaTeXOutput",
[ IsHomalgMatrix ] );
####################################
#
# synonyms:
#
####################################
[ Dauer der Verarbeitung: 0.24 Sekunden
(vorverarbeitet)
]
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