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# SPDX-License-Identifier: GPL-2.0-or-later
# LinearAlgebraForCAP: Category of Matrices over a Field for CAP
#
# Declarations
#
#! @Chapter Category of Matrices
####################################
##
#! @Section GAP Categories
##
####################################
#! @Description
#! The GAP category of morphisms in the category
#! of matrices of a field $F$.
#! @Arguments object
DeclareCategory( "IsVectorSpaceMorphism",
IsCapCategoryMorphism );
####################################
##
#! @Section Constructors
##
####################################
#! @Description
#! The arguments are an object $S$ in the category of matrices over a
#! homalg field $F$, a homalg matrix $M$ over $F$, and another object $R$
#! in the category of matrices over $F$.
#! The output is the morphism $S \rightarrow R$ in the category
#! of matrices over $F$ whose underlying matrix is given by $M$.
#! @Returns a morphism in $\mathrm{Hom}(S,R)$
#! @Arguments S, M, R
DeclareOperation( "VectorSpaceMorphism",
[ IsVectorSpaceObject, IsHomalgMatrix, IsVectorSpaceObject ] );
DeclareOperation( "VectorSpaceMorphism",
[ IsVectorSpaceObject, IsList, IsVectorSpaceObject ] );
DeclareAttribute( "AsVectorSpaceMorphism", IsHomalgMatrix );
DeclareOperation( "/",
[ IsHomalgMatrix, IsMatrixCategory ] );
####################################
##
#! @Section Attributes
##
####################################
#! @Description
#! The argument is a morphism $\alpha$ in the matrix category over a
#! homalg field $F$.
#! The output is the field $F$.
#! @Returns a homalg field
#! @Arguments alpha
DeclareAttribute( "UnderlyingFieldForHomalg",
IsVectorSpaceMorphism );
#! @Description
#! The argument is a morphism $\alpha$ in a matrix category.
#! The output is its underlying matrix $M$.
#! @Returns a homalg matrix
#! @Arguments alpha
DeclareAttribute( "UnderlyingMatrix",
IsVectorSpaceMorphism );
CapJitAddTypeSignature( "UnderlyingMatrix", [ IsVectorSpaceMorphism ], function ( input_types )
Assert( 0, IsHomalgRing( UnderlyingRing( input_types[1].category ) ) );
return rec(
filter := IsHomalgMatrix,
ring := UnderlyingRing( input_types[1].category ),
);
end );
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