(* ---------------------------------------------------------------------------- * $Id: SACUPFAC.md,v 1.2 1992/02/12 17:35:06 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: SACUPFAC.md,v $ * Revision 1.2 1992/02/12 17:35:06 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:15:48 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE SACUPFAC; (* SAC Univariate Polynomial Factorization Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: SACUPFAC.md,v 1.2 1992/02/12 17:35:06 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau";PROCEDURE IPFLC(RL,M,I,A,L,D: LIST): LIST; (*Integral polynomial factor list combine. A is a non-constant primitive r-variate integral polynomial. M is a positive integer. I is a list (d sub 1, ...,d sub r - 1) of non-negative beta-digits. L is a list of monic factors of A modulo M, ((x sub 1)**(d sub 1), ... ,(x sub rl- 1)**(d sub r - 1)) such that if B is an integral factor of A, then H sub M,I (B) is an associate of some product of elements of L. D is either 0, or a characteristic set for the possible degrees of integral factors of A. LP is a list of the primitive irreducible integral factors of A. *)PROCEDURE IUPFAC(A: LIST;VARSL,CL,L: LIST); (*Integral univariate polynomial factorization. A is a non-zero integral univariate polynomial. s=sign(A), c=cont(A). L is a list ((e1,A1), ...,(ek,Ak)), k ge 0, where each ei is a positive integer, e1 le e2 le ... le ek, each A i is an ir- reducible positive integral univariate polynomial, and A = s * c * the product of A i ** ei, 1 le i le k.*)PROCEDURE IUPFDS(A: LIST;VARPL,F,C: LIST); (*Integral univariate polynomial factor degree set. A is a non-zero square-free integral polynomial. C is the intersection of the degree sets of factorizations over Z sub p for as many as NPFDS primes p (fewer only if SMPRM is exhausted or A is proved irredu- cible). C is represented as a characteristic set. p is the least examined prime in P which gave the smallest number of factors, and F is the distinct degree factorization of A over Z sub p, unless A is shown to be irreducible, in which case p=0, F=().*)PROCEDURE IUPQH(PL,AB,BB,SB,TB,M,C: LIST;VARA,B: LIST); (*Integral univariate polynomial quadratic Hensel lemma. AB, BB, SB, TB are univariate polynomials over Z sub p, p a prime beta-integer, with AB*SB+BB*TB=1, and deg(TB) lt deg(AB). C is a univariate integral polynomial with H sub p of C=AB*BB. M, a positive integer, is equal to p**j for some positive integer j. A and B are univariate polynomials over Z sub M, with H sub p of A=AB, H sub p of B=BB, ldcf(A)=ldcf(AB),deg(A)=deg(AB), and H sub M of C=A*B.*)PROCEDURE IUPQHL(PL,F,M,C: LIST): LIST; (*Integral univariate polynomial quadratic Hensel lemma, list. C is an integral univariate polynomial. F is a list (f sub 1, ...,f sub r) of monic polynomials in Z sub p (x) with H sub p of C similar to the product of the f sub i, and gcd(f sub i,f sub j)=1 for 1 le i lt j le r, p a beta-prime not dividing ldcf(C). M is a positive power of p. FP is a list (fp sub 1, ...,fp sub r) of monic polynomials in Z sub M (x) with H sub M of C similar to the product of the fp sub i, H sub p of fp sub i=f sub i and deg(fp sub i)=deg(f sub i), for 1 le i le r.*)PROCEDURE IUSFPF(A: LIST): LIST; (*Integral univariate squarefree polynomial factorization. A is an integral univariate squarefree polynomial which is positive, primitive and of positive degree. L is a list (A1, ...,Ak) of the positive irreducible factors of A.*)ENDSACUPFAC. (* -EOF- *)