(* ---------------------------------------------------------------------------- * $Id: SACEXT5.md,v 1.2 1992/02/12 17:34:50 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: SACEXT5.md,v $ * Revision 1.2 1992/02/12 17:34:50 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:15:31 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE SACEXT5; (* SAC Extensions 5 Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: SACEXT5.md,v 1.2 1992/02/12 17:34:50 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau";PROCEDURE IPCSFB(RL,A: LIST): LIST; (*Integral polynomial coarsest squarefree basis. A eq (A sub 1 , ..., A sub n ), n ge 0, is a list of positive primitive integral polynomials in r variables, r ge 1, each of which is of positive degree in its main variable. B is a coarsest squarefree basis for A.*)PROCEDURE IPDSCR(RL,A: LIST): LIST; (*Integral polynomial discriminant. A is an integral polynomial in r variables, r ge 1, of degree greater than or equal to two in its main variable. B is the discriminant of A.*)PROCEDURE IPLCPP(RL,A: LIST;VARC,P: LIST); (*Integral polynomial list of contents and primitive parts. A eq (A sub 1 , ..., A sub n ), n ge 0, is a list of integral polynomials in r variables, r ge 1. C eq (C sub 1 , ..., C sub s ), 0 le s le n, is a list such that for 1 le i le n, content(a sub i ) eq c sub j for some j, 1 le j le s, if and only if content(a sub i ) has positive degree in some variable. P eq (P sub 1 , ..., P sub m ), 0 le m le n, is a list such that for 1 le i le n, PP(A sub i ) eq P sub j for some j, 1 le j le m, if and only if PP(a sub i ) has positive degree in its main variable.*)PROCEDURE IPPSC(RL,A,B: LIST): LIST; (*Integral polynomial principal subresultant coefficients. A and B are integral polynomials in r variables, r ge 1, of positive degree in the main variable. P is a list of the principal subresultant coefficients of the second kind of A and B.*)PROCEDURE IPSFBA(RL,A,B: LIST): LIST; (*Integral polynomial squarefree basis augmentation. A is a primitive positive squarefree integral polynomial in r variables, r ge 1, of positive degree in its main variable. B eq (B sub 1 , ..., B sub s ), s ge 0, is a squarefree integral polynomial basis in r variables. BS is a coarsest squarefree basis for (A,B sub 1 , ..., B sub s ).*)PROCEDURE ISPSFB(RL,A: LIST): LIST; (*Integral squarefree polynomial squarefree basis. A eq (A sub 1 , ..., A sub n ), n ge 0, is a list of positive primitive squarefree integral polynomials in r variables,r ge 1, each of which is of positive degree in its main variable. B is a coarsest squarefree basis for A.*)PROCEDURE IUPRC(A,B: LIST;VARC,R: LIST); (*Integral univariate polynomial resultant and cofactor. A and B are univariate integral polynomials of positive degree. R is the resultant of A and B. C is a univariate integral polynomial such that for some univariate integral polynomial D, AD+BC eq R.*)PROCEDURE MUPRC(PL,A,B: LIST;VARC,RL: LIST); (*Modular univariate polynomial resultant and cofactor. p is a prime beta-digit. A and B are univariate polynomials over Z sub p of positive degree. R is the resultant of A and B, an element of Z sub p. C is a univariate polynomial over Z sub p such that for some univariate polynomial D over Z sub p, AD+BC eq R.*)ENDSACEXT5. (* -EOF- *)