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# SPDX-License-Identifier: GPL-2.0-or-later
# LinearAlgebraForCAP: Category of Matrices over a Field for CAP
#
# Implementations
#
####################################
##
## Constructors
##
####################################
##
InstallMethod( AsVectorSpaceMorphism,
[ IsHomalgMatrix ],
function( homalg_matrix )
local field;
Print( "WARNING: AsVectorSpaceMorphism is deprecated and will not be supported after 2025.08.14. Use `<homalg_matrix> / <matrix_category>` instead.\n" );
field := HomalgRing( homalg_matrix );
return VectorSpaceMorphism(
VectorSpaceObject( NrRows( homalg_matrix ), field ),
homalg_matrix,
VectorSpaceObject( NrColumns( homalg_matrix ), field )
);
end );
##
# convenience
InstallMethod( VectorSpaceMorphism,
[ IsVectorSpaceObject, IsList, IsVectorSpaceObject ],
function( source, element_list, range )
local field, homalg_matrix;
field := UnderlyingRing( CapCategory( source ) );
homalg_matrix := HomalgMatrix( element_list, AsInteger( source ), AsInteger( range ), field );
return VectorSpaceMorphism( source, homalg_matrix, range );
end );
##
# convenience
InstallMethod( VectorSpaceMorphism,
[ IsVectorSpaceObject, IsHomalgMatrix, IsVectorSpaceObject ],
function( source, homalg_matrix, range )
return VectorSpaceMorphism( CapCategory( source ), source, homalg_matrix, range );
end );
##
InstallOtherMethodForCompilerForCAP( VectorSpaceMorphism,
[ IsMatrixCategory, IsVectorSpaceObject, IsHomalgMatrix, IsVectorSpaceObject ],
function( cat, source, homalg_matrix, range )
if not IsHomalgMatrix( homalg_matrix ) then
Error( "the morphism datum must be a homalg matrix" );
fi;
if not IsIdenticalObj( HomalgRing( homalg_matrix ), UnderlyingRing( cat ) ) then
Error( "the matrix is defined over a different ring than the category" );
fi;
if NrRows( homalg_matrix ) <> AsInteger( source ) then
Error( "the number of rows has to be equal to the dimension of the source" );
fi;
if NrColumns( homalg_matrix ) <> AsInteger( range ) then
Error( "the number of columns has to be equal to the dimension of the range" );
fi;
return AsCapCategoryMorphism( cat, source, homalg_matrix, range );
end );
####################################
##
## Attributes
##
####################################
##
InstallMethod( UnderlyingFieldForHomalg,
[ IsVectorSpaceMorphism ],
function( morphism )
return UnderlyingRing( CapCategory( morphism ) );
end );
##
InstallMethod( UnderlyingMatrix,
[ IsVectorSpaceMorphism ],
function( morphism )
return AsHomalgMatrix( morphism );
end );
####################################
##
## View
##
####################################
##
InstallMethod( DisplayString,
[ IsVectorSpaceMorphism ],
function( vector_space_morphism )
return Concatenation( StringDisplay( AsHomalgMatrix( vector_space_morphism ) ), "\n", StringMutable( vector_space_morphism ), "\n" );
end );
##
#= comment for Julia
InstallMethod( LaTeXOutput,
[ IsVectorSpaceMorphism ],
function( vector_space_morphism )
local matrix;
matrix := LaTeXOutput( AsHomalgMatrix( vector_space_morphism ) );
if ValueOption( "OnlyDatum" ) = true then
return Concatenation(
"""{\color{blue}{""",
matrix,
"""}}"""
);
else
return Concatenation(
LaTeXOutput( Source( vector_space_morphism ) ),
"""{\color{blue}{\xrightarrow{""",
matrix,
"""}}}""",
LaTeXOutput( Range( vector_space_morphism ) )
);
fi;
end );
# =#
####################################
##
## Convenience
##
####################################
##
InstallOtherMethod( \/,
[ IsHomalgMatrix, IsMatrixCategory ],
function( homalg_matrix, category )
local field;
field := HomalgRing( homalg_matrix );
return VectorSpaceMorphism(
MatrixCategoryObject( category, NrRows( homalg_matrix ) ),
homalg_matrix,
MatrixCategoryObject( category, NrColumns( homalg_matrix ) )
);
end );
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