chrem - Maple Help
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chrem

Chinese Remainder Algorithm

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

chrem(u, m)

Parameters

u

-

list [u1,..., un] of evaluations

m

-

list of moduli [m1,..., mn]

Description

• 

The list of moduli m must be pairwise relatively prime positive integers. (For the case of non-coprime moduli, see NumberTheory[ChineseRemainder].) Both lists u and m must be the same length . The list of images u need not be reduced modulo m on input. In the following,  denotes the product of the moduli.

• 

If u is a list of integers, chrem(u, m) computes the unique positive integer a such that  , and .

• 

If the global variable mod has been assigned to mods then the result  is returned in the symmetric range for the integers modulo . For example, the symmetric range for the integers modulo  is .

• 

If u is a list of polynomials, chrem is applied across the polynomials so that the output  is a polynomial satisfying  , ..., .

• 

If u is a list of lists, chrem is applied across the lists so that the output will be a list  satisfying , ...,  .

• 

For a definition, see Chinese remainder theorem.

Examples

(1)

(2)

(3)

(4)

(5)

See Also

GaussInt

GIchrem

NumberTheory[ChineseRemainder]

 


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