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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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  1 Category of Matrices

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  1.1 Constructors

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  1.1-1 MatrixCategory

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  MatrixCategory( F )  attribute

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  Returns:  a category

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  The  argument is a homalg field F. The output is the matrix category over F.

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  Objects  in  this  category  are  non-negative  integers.  Morphisms  from a

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  non-negative  integer  m to a non-negative integer n are given by m \times n

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  matrices.

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  1.1-2 VectorSpaceMorphism

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  VectorSpaceMorphism( S, M, R )  operation

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  Returns:  a morphism in \mathrm{Hom}(S,R)

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  The  arguments  are  an  object  S in the category of matrices over a homalg

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  field  F,  a homalg matrix M over F, and another object R in the category of

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  matrices  over F. The output is the morphism S \rightarrow R in the category

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  of matrices over F whose underlying matrix is given by M.

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  1.1-3 VectorSpaceObject

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  VectorSpaceObject( d, F )  operation

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  Returns:  an object

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  The  arguments are a non-negative integer d and a homalg field F. The output

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  is an object in the category of matrices over F of dimension d.

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  1.2 GAP Categories

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  1.2-1 IsVectorSpaceMorphism

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  IsVectorSpaceMorphism( object )  filter

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  Returns:  true or false

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  The GAP category of morphisms in the category of matrices of a field F.

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  1.2-2 IsVectorSpaceObject

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  IsVectorSpaceObject( object )  filter

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  Returns:  true or false

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  The GAP category of objects in the category of matrices of a field F.

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  1.3 Attributes

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  1.3-1 UnderlyingFieldForHomalg

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  UnderlyingFieldForHomalg( alpha )  attribute

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  Returns:  a homalg field

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  The argument is a morphism \alpha in the matrix category over a homalg field

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  F. The output is the field F.

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  1.3-2 UnderlyingMatrix

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  UnderlyingMatrix( alpha )  attribute

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  Returns:  a homalg matrix

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  The  argument  is  a morphism \alpha in a matrix category. The output is its

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  underlying matrix M.

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  1.3-3 UnderlyingFieldForHomalg

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  UnderlyingFieldForHomalg( A )  attribute

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  Returns:  a homalg field

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  The  argument  is  an object A in the matrix category over a homalg field F.

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  The output is the field F.

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  1.3-4 Dimension

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  Dimension( A )  attribute

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  Returns:  a non-negative integer

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  The  argument  is  an  object  A  in  a  matrix  category. The output is the

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  dimension of A.

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