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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############################################################################
##
## GaussTools.gi GaussForHomalg package Simon Goertzen
##
## Copyright 2007-2008 Lehrstuhl B für Mathematik, RWTH Aachen
##
## Homalg Table for calculating in Gauss with dense and sparse matrices
##
#############################################################################
####################################
#
# global variables:
#
####################################
# add IsSparseMatrix to the list of types of homalg internal matrix types:
if IsBound( HOMALG_MATRICES.OtherInternalMatrixTypes ) then
Add( HOMALG_MATRICES.OtherInternalMatrixTypes, IsSparseMatrix );
else
HOMALG_MATRICES.OtherInternalMatrixTypes := [ IsSparseMatrix ];
fi;
##
InstallMethod( Nrows, "for dense GAP matrices",
[ IsList ],
function( M )
return Length( M );
end
);
##
InstallValue( CommonHomalgTableForGaussTools,
# most of these functions just call the corresponding operation
# in the Gauss package, check there in case of questions
rec(
## <#GAPDoc Label="ZeroMatrix">
## <ManSection>
## <Func Arg="C" Name="ZeroMatrix"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns a sparse matrix with the same dimensions and base
## ring as the &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
ZeroMatrix :=
function( C )
local R;
R := HomalgRing( C );
return SparseZeroMatrix( NrRows( C ), NrColumns( C ), R!.ring );
end,
## <#GAPDoc Label="IdentityMatrix">
## <ManSection>
## <Func Arg="C" Name="IdentityMatrix"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns a sparse <M>n \times n</M> identity matrix with the
## same ring as the &homalg; matrix <A>C</A>, <M>n</M> being the
## number of rows of <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
IdentityMatrix :=
function( C )
local R;
R := HomalgRing( C );
return SparseIdentityMatrix( NrRows( C ), R!.ring );
end,
## <#GAPDoc Label="CopyMatrix">
## <ManSection>
## <Func Arg="C" Name="CopyMatrix"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns a sparse matrix which is a shallow copy of the
## sparse matrix stored in the <C>Eval</C> attribute of the
## &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
CopyMatrix :=
function( C )
return CopyMat( Eval( C ) );
end,
## <#GAPDoc Label="ImportMatrix">
## <ManSection>
## <Func Arg="M, R" Name="ImportMatrix"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the sparse version of the &GAP; matrix <A>M</A>
## over the ring <A>R</A>. It prevents &homalg; from calling sparse matrix
## algorithms on dense &GAP; matrices. Note that this is not a
## "standard" tool but neccessary because of the new data type.
## </Description>
## </ManSection>
## <#/GAPDoc>
ImportMatrix :=
function( M, R )
return SparseMatrix( One( R ) * M, R!.ring );
end,
## <#GAPDoc Label="Involution">
## <ManSection>
## <Func Arg="M" Name="Involution"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns a sparse matrix which is the transpose of the
## sparse matrix stored in the <C>Eval</C> attribute of the
## &homalg; matrix <A>M</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
# for a general ring (field) the involution is just the transposed matrix
Involution :=
function( M )
return TransposedSparseMat( Eval( M ) );
end,
## <#GAPDoc Label="CertainRows">
## <ManSection>
## <Func Arg="M, plist" Name="CertainRows"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the rows in <A>plist</A> of the sparse matrix stored
## in the <C>Eval</C> attribute of the &homalg; matrix <A>M</A> as
## a new matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
CertainRows :=
function( M, plist )
return CertainRows( Eval( M ), plist );
end,
## <#GAPDoc Label="CertainColumns">
## <ManSection>
## <Func Arg="M, plist" Name="CertainColumns"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the columns in <A>plist</A> of the sparse matrix stored
## in the <C>Eval</C> attribute of the &homalg; matrix <A>M</A> as
## a new matrix.
## </Description>
## </ManSection>
## <#/GAPDoc>
CertainColumns :=
function( M, plist )
return CertainColumns( Eval( M ), plist );
end,
## <#GAPDoc Label="UnionOfRows">
## <ManSection>
## <Func Arg="A, B" Name="UnionOfRows"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the sparse matrix created by concatenating the rows of
## the sparse matrices stored in the <C>Eval</C> attributes of the &homalg;
## matrices <A>A</A> and <A>B</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
UnionOfRows :=
function( A, B )
return UnionOfRows( Eval( A ), Eval( B ) );
end,
## <#GAPDoc Label="UnionOfColumns">
## <ManSection>
## <Func Arg="A, B" Name="UnionOfColumns"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the sparse matrix created by concatenating the columns of
## the sparse matrices stored in the <C>Eval</C> attributes of the &homalg;
## matrices <A>A</A> and <A>B</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
UnionOfColumns :=
function( A, B )
return UnionOfColumns( Eval( A ), Eval( B ) );
end,
## <#GAPDoc Label="DiagMat">
## <ManSection>
## <Func Arg="e" Name="DiagMat"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This method takes a list <A>e</A> of &homalg; matrices and returns
## the sparse block matrix of the matrices stored in the <C>Eval</C>
## attributes of the matrices in <A>e</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
DiagMat :=
function( e )
return SparseDiagMat( List( e, Eval ) );
end,
## <#GAPDoc Label="KroneckerMat">
## <ManSection>
## <Func Arg="A, B" Name="KroneckerMat"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the sparse Kronecker matrix of the matrices stored in the
## <C>Eval</C> attributes of the &homalg; matrices <A>A</A> and <A>B</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
KroneckerMat :=
function( A, B )
return SparseKroneckerProduct( Eval( A ), Eval( B ) );
end,
## <#GAPDoc Label="Compose">
## <ManSection>
## <Func Arg="A, B" Name="Compose"/>
## <Returns>a sparse matrix</Returns>
## <Description>
## This returns the matrix product of the sparse matrices stored in the
## <C>Eval</C> attributes of the &homalg; matrices <A>A</A> and <A>B</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
Compose :=
function( A, B )
return Eval( A ) * Eval( B );
end,
## <#GAPDoc Label="NrRows">
## <ManSection>
## <Func Arg="C" Name="NrRows"/>
## <Returns>an integer</Returns>
## <Description>
## This returns the number of rows of the sparse matrix stored in the
## <C>Eval</C> attribute of the &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
NrRows :=
function( C )
return Nrows( Eval( C ) );
end,
## <#GAPDoc Label="NrColumns">
## <ManSection>
## <Func Arg="C" Name="NrColumns"/>
## <Returns>an integer</Returns>
## <Description>
## This returns the number of columns of the sparse matrix stored in the
## <C>Eval</C> attribute of the &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
NrColumns :=
function( C )
return Ncols( Eval( C ) );
end,
## <#GAPDoc Label="IsZeroMatrix">
## <ManSection>
## <Func Arg="C" Name="IsZeroMatrix"/>
## <Returns><B>true</B> or <B>false</B></Returns>
## <Description>
## This returns <B>true</B> if the sparse matrix stored in the <C>Eval</C>
## attribute of the &homalg; matrix <A>C</A> is a zero matrix,
## and <B>false</B> otherwise.
## </Description>
## </ManSection>
## <#/GAPDoc>
IsZeroMatrix :=
function( M )
return IsSparseZeroMatrix( Eval( M ) );
end,
## <#GAPDoc Label="IsIdentityMatrix">
## <ManSection>
## <Func Arg="C" Name="IsIdentityMatrix"/>
## <Returns><B>true</B> or <B>false</B></Returns>
## <Description>
## This returns <B>true</B> if the sparse matrix stored in the <C>Eval</C>
## attribute of the &homalg; matrix <A>C</A> is an identity matrix,
## and <B>false</B> otherwise.
## </Description>
## </ManSection>
## <#/GAPDoc>
IsIdentityMatrix :=
function( M )
return IsSparseIdentityMatrix( Eval( M ) );
end,
## <#GAPDoc Label="IsDiagonalMatrix">
## <ManSection>
## <Func Arg="C" Name="IsDiagonalMatrix"/>
## <Returns><B>true</B> or <B>false</B></Returns>
## <Description>
## This returns <B>true</B> if the sparse matrix stored in the <C>Eval</C>
## attribute of the &homalg; matrix <A>C</A> is a diagonal matrix,
## and <B>false</B> otherwise.
## </Description>
## </ManSection>
## <#/GAPDoc>
IsDiagonalMatrix :=
function( M )
return IsSparseDiagonalMatrix( Eval( M ) );
end,
## <#GAPDoc Label="ZeroRows">
## <ManSection>
## <Func Arg="C" Name="ZeroRows"/>
## <Returns>a list</Returns>
## <Description>
## This returns the list of zero rows of the sparse matrix stored in
## the <C>Eval</C> attribute of the &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
ZeroRows :=
function( C )
return SparseZeroRows( Eval( C ) );
end,
## <#GAPDoc Label="ZeroColumns">
## <ManSection>
## <Func Arg="C" Name="ZeroColumns"/>
## <Returns>a list</Returns>
## <Description>
## This returns the list of zero columns of the sparse matrix stored in
## the <C>Eval</C> attribute of the &homalg; matrix <A>C</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
ZeroColumns :=
function( C )
return SparseZeroColumns( Eval( C ) );
end,
)
);