h.pfact

来自「强大的数学工具包」· PFACT 代码 · 共 56 行

                               * * * * * * *
                               *   pfact   *
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        "factorization modulo prime"
        SYNTAX: X=pfact(p, A)

        p is an expression whose value is a prime.
        A is an expression whose value is a univariate polynomial over 
        Z or Q.
        
        pfact computes the factorization of A mod p. 
        X is the prime factor of A mod p with greatest degree.

        If A is polynomial with its factorization mod p of the form
        c * p1^e1 * ... * pN^eN, then AV[0]=c, AV[1]=p1, AV[2]=e1, ...,
        AV[2*N-1]=pN, AV[2*N]=eN. (See "?avfunc".)

        Warning: If p > 2^30, the primality of p is not tested.


        Example 1: (correct)

                pfact(3, x^2 + 2*x + 1)


        Example 2: (correct)

                pfact(3, x^2 + 1/7*x + 1/5)


        Example 3: (correct)

                pfact(1073741827, (x + 1)^20 + 1)
 

        Example 4: (incorrect)

                pfact(4, x^2)

_ERR_NR_046


        Example 5: (incorrect)

                pfact(3, x*y)
                                
_ERR_NR_100


        Example 6: (incorrect)
                
                pfact(5, x/(x + 1))
                
_ERR_NR_043