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15 Rings as categories
 15.1 Random methods

15 Rings as categories

15.1 Random methods

15.1-1 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).

15.1-2 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).

15.1-3 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.

15.1-4 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.

15.1-5 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.

15.1-6 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.

15.1-7 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.

15.1-8 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.

15.1-9 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.

15.1-10 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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