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4 Category of rows
 4.1 Random Methods in Category of Rows

  4.1-1 RandomObjectByList
  4.1-2 RandomObjectByInteger
  4.1-3 RandomMorphismWithFixedSourceAndRangeByList
  4.1-4 RandomMorphismWithFixedSourceAndRangeByInteger
  4.1-5 RandomMorphismWithFixedSourceByList
  4.1-6 RandomMorphismWithFixedSourceByInteger
  4.1-7 RandomMorphismWithFixedRangeByList
  4.1-8 RandomMorphismWithFixedRangeByInteger
  4.1-9 RandomMorphismByList
  4.1-10 RandomMorphismByInteger
 4.2 GAP Categories

  4.2-1 IsCategoryOfRowsObject
 4.3 Supported CAP operations

  4.3-1 CategoryOfRows of an arbitrary ring
  4.3-2 CategoryOfRows of an exterior algebra over a field
  4.3-3 CategoryOfRows of a commutative ring
  4.3-4 CategoryOfRows of a field

4 Category of rows

4.1 Random Methods in Category of Rows

4.1-1 RandomObjectByList
‣ RandomObjectByList( C, L )( operation )

Returns: an object in a category of rows

The arguments are a category C and a non-empty list L of non-negative integers. The output is an object whose rank is a random element in L.

4.1-2 RandomObjectByInteger
‣ RandomObjectByInteger( C, n )( operation )

Returns: an object in a category of rows

The arguments are a category of rows C and a non-negative integer n. The output is an object whose rank is at most n.

4.1-3 RandomMorphismWithFixedSourceAndRangeByList
‣ RandomMorphismWithFixedSourceAndRangeByList( S, R, L )( operation )

Returns: a morphism in a category of rows

The arguments are two objects S, R and a list L of integers or elements in the underlying ring. The output is a morphism from S to R whose matrix is an L-linear combination of random matrices over the underlying ring.

4.1-4 RandomMorphismWithFixedSourceAndRangeByInteger
‣ RandomMorphismWithFixedSourceAndRangeByInteger( S, R, n )( operation )

Returns: a morphism in a category of rows

The arguments are two objects S, R and an integer n. The output is a morphism from S to R defined by a random matrix over the underlying ring. Particularly, the argument n will be disregarded.

4.1-5 RandomMorphismWithFixedSourceByList
‣ RandomMorphismWithFixedSourceByList( S, L )( operation )

Returns: a morphism in a category of rows

The arguments are an object S and a list L consisting of two lists: a non-empty list of non-negative integers and a list of integers or elements in the underlying ring. The output is a morphism from S to an object R whose rank is a random element in L[1]. The matrix of the morphism is an L[2]-linear combination of random matrices over the underlying ring.

4.1-6 RandomMorphismWithFixedSourceByInteger
‣ RandomMorphismWithFixedSourceByInteger( S, n )( operation )

Returns: a morphism in a category of rows

The arguments are an object S and a non-negative integer n. The output is a morphism from S to an object R whose rank is at most n.

4.1-7 RandomMorphismWithFixedRangeByList
‣ RandomMorphismWithFixedRangeByList( R, L )( operation )

Returns: a morphism in a category of rows

The arguments are an object R and a list L consisting of two lists: a non-empty list of non-negative integers and a list of integers or elements in the underlying ring. The output is a morphism to R from an object S whose rank is a random element in L[1]. The matrix of the morphism is an L[2]-linear combination of random matrices over the underlying ring.

4.1-8 RandomMorphismWithFixedRangeByInteger
‣ RandomMorphismWithFixedRangeByInteger( R, n )( operation )

Returns: a morphism in a category of rows

The arguments are an object R and a non-negative integer n. The output is a morphism to R from an object S whose rank is at most n.

4.1-9 RandomMorphismByList
‣ RandomMorphismByList( C, L )( operation )

Returns: a morphism in a category of rows

The arguments are a category of rows C and a list L consisting of 3 lists: two non-empty lists of non-negative integers and a list of integers or elements in the underlying ring. The output is a morphism from an object S to an object R whose ranks are random elements in L[1] resp. L[2]. Its matrix is an L[3]-linear combination of random matrices over the underlying ring.

4.1-10 RandomMorphismByInteger
‣ RandomMorphismByInteger( C, n )( operation )

Returns: a morphism in a category of rows

The arguments are a category of rows C and a non-negative integer n. The output is a morphism whose source and range ranks are at most n.

4.2 GAP Categories

4.2-1 IsCategoryOfRowsObject
‣ IsCategoryOfRowsObject( object )( filter )

Returns: true or false

The GAP category of objects in the category of rows over a ring \(R\).

4.3 Supported CAP operations

4.3-1 CategoryOfRows of an arbitrary ring

The following CAP operations are supported:

4.3-2 CategoryOfRows of an exterior algebra over a field

Additional to the operations listed in “CategoryOfRows of an arbitrary ring” the following operations are supported:

4.3-3 CategoryOfRows of a commutative ring

Additional to the operations listed in “CategoryOfRows of an arbitrary ring” the following operations are supported:

4.3-4 CategoryOfRows of a field

Additional to the operations listed in “CategoryOfRows of a commutative ring” the following operations are supported:

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