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14 Rings as categories

14.1 Random methods

14.1-1 RandomObjectByList
 ‣ RandomObjectByList( C, L ) ( operation )

Returns: an object in C

The arguments are a ring as category C and a list L consisting of one integer. The output is the unique object of C, i.e., RingAsCategoryUniqueObject(C).

14.1-2 RandomObjectByInteger
 ‣ RandomObjectByInteger( C, n ) ( operation )

Returns: an object in C

The arguments are a ring as category C and an integer n. The output is the unique object of C, i.e., RingAsCategoryUniqueObject(C).

14.1-3 RandomMorphismWithFixedSourceAndRangeByList
 ‣ RandomMorphismWithFixedSourceAndRangeByList( S, R, L ) ( operation )

Returns: a morphism in C

The arguments are two objects S, R and a list L consisting of one integer. The output is a morphism from S to R whose underlying element is a sum of L[1] random elements in the underlying ring.

14.1-4 RandomMorphismWithFixedSourceAndRangeByInteger
 ‣ RandomMorphismWithFixedSourceAndRangeByInteger( S, R, n ) ( operation )

Returns: a morphism in C

The arguments are two objects S, R and an integer n. The output is a morphism from S to R whose underlying element is a sum of n random elements in the underlying ring.

14.1-5 RandomMorphismWithFixedSourceByList
 ‣ RandomMorphismWithFixedSourceByList( S, L ) ( operation )

Returns: a morphism in C

The arguments are an object S in a ring as category C and a list L consisting of one integer. The output is an endomorphism of S whose underlying element is a sum of 1+Log2Int(L[1]) random elements in the underlying ring.

14.1-6 RandomMorphismWithFixedSourceByInteger
 ‣ RandomMorphismWithFixedSourceByInteger( S, n ) ( operation )

Returns: a morphism in C

The arguments are an object S in a ring as category C and an integer n. The output is an endomorphism of S whose underlying element is a sum of 1+Log2Int(n) random elements in the underlying ring.

14.1-7 RandomMorphismWithFixedRangeByList
 ‣ RandomMorphismWithFixedRangeByList( R, L ) ( operation )

Returns: a morphism in C

The arguments are an object R in a ring as category C and a list L consisting of one integer. The output is an endomorphism of R whose underlying element is a sum of 1+Log2Int(L[1]) random elements in the underlying ring.

14.1-8 RandomMorphismWithFixedRangeByInteger
 ‣ RandomMorphismWithFixedRangeByInteger( R, n ) ( operation )

Returns: a morphism in C

The arguments are an object R in a ring as category C and an integer n. The output is an endomorphism of R whose underlying element is a sum of 1+Log2Int(n) random elements in the underlying ring.

14.1-9 RandomMorphismByList
 ‣ RandomMorphismByList( C, L ) ( operation )

Returns: a morphism in C

The arguments are a ring as category C and a list L consisting of one integer. The output is an endomorphism of the unique object of C whose underlying element is a sum of 1+Log2Int(L[1]) random elements in the underlying ring.

14.1-10 RandomMorphismByInteger
 ‣ RandomMorphismByInteger( C, n ) ( operation )

Returns: a morphism in C

The arguments are a ring as category C and an integer n. The output is an endomorphism of the unique object of C whose underlying element is a sum of 1+Log2Int(n) random elements in the underlying ring.

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