1 Category of Matrices
  
  
  1.1 Constructors
  
  1.1-1 MatrixCategory
  
  MatrixCategory( F )  attribute
  Returns:  a category
  
  The  argument is a homalg field F. The output is the matrix category over F.
  Objects  in  this  category  are  non-negative  integers.  Morphisms  from a
  non-negative  integer  m to a non-negative integer n are given by m \times n
  matrices.
  
  1.1-2 VectorSpaceMorphism
  
  VectorSpaceMorphism( S, M, R )  operation
  Returns:  a morphism in \mathrm{Hom}(S,R)
  
  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.
  
  1.1-3 VectorSpaceObject
  
  VectorSpaceObject( d, F )  operation
  Returns:  an object
  
  The  arguments are a non-negative integer d and a homalg field F. The output
  is an object in the category of matrices over F of dimension d.
  
  
  1.2 GAP Categories
  
  1.2-1 IsVectorSpaceMorphism
  
  IsVectorSpaceMorphism( object )  filter
  Returns:  true or false
  
  The GAP category of morphisms in the category of matrices of a field F.
  
  1.2-2 IsVectorSpaceObject
  
  IsVectorSpaceObject( object )  filter
  Returns:  true or false
  
  The GAP category of objects in the category of matrices of a field F.
  
  
  1.3 Attributes
  
  1.3-1 UnderlyingFieldForHomalg
  
  UnderlyingFieldForHomalg( alpha )  attribute
  Returns:  a homalg field
  
  The argument is a morphism \alpha in the matrix category over a homalg field
  F. The output is the field F.
  
  1.3-2 UnderlyingMatrix
  
  UnderlyingMatrix( alpha )  attribute
  Returns:  a homalg matrix
  
  The  argument  is  a morphism \alpha in a matrix category. The output is its
  underlying matrix M.
  
  1.3-3 UnderlyingFieldForHomalg
  
  UnderlyingFieldForHomalg( A )  attribute
  Returns:  a homalg field
  
  The  argument  is  an object A in the matrix category over a homalg field F.
  The output is the field F.
  
  1.3-4 Dimension
  
  Dimension( A )  attribute
  Returns:  a non-negative integer
  
  The  argument  is  an  object  A  in  a  matrix  category. The output is the
  dimension of A.