(* ---------------------------------------------------------------------------- * $Id: GSYMFUIN.md,v 1.1 1995/11/05 15:57:24 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1995 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: GSYMFUIN.md,v $ * Revision 1.1 1995/11/05 15:57:24 pesch * Diplomarbeit Manfred Goebel, Reduktion G-symmetrischer Polynome fuer * beliebige Permutationsgruppen G, slightly edited. * * ---------------------------------------------------------------------------- *) DEFINITION MODULE GSYMFUIN; (* G-Symmetric Integral Polynomial System Definition Module. *) FROM MASSTOR IMPORT LIST; FROM MASELEM IMPORT GAMMAINT; CONST rcsid = "$Id: GSYMFUIN.md,v 1.1 1995/11/05 15:57:24 pesch Exp $"; CONST copyright = "Copyright (c) 1994 Universitaet Passau"; PROCEDURE GSYINF(); (*G-Symmetric Polynomial System Information. *) PROCEDURE GSYPGR(M: GAMMAINT): LIST; (*G-Symmetric Permutation Group Read. Input of producing elements for a permutation group with M variables. *) PROCEDURE GSYPGW(PG: LIST); (*G-Symmetric Permutation Group Write. Output of producing elements for the permutation group PG. *) PROCEDURE GINORP(PG, MO: LIST): LIST; (*G-Symmetric Integral Orbit Polynomial. The PG-symmetric orbit polynomial of the monomial MO is computed with respect to the permutation group PG. *) PROCEDURE GSYORD(PG: LIST): GAMMAINT; (*G-Symmetric Permutation Group Order. The order of the permutation group PG is computed. *) PROCEDURE GSYNSP(PG: LIST); (*G-Symmetric Number of Special Polynomials. The number of special polynomials is computed. *) PROCEDURE GSYSPG(N: GAMMAINT): LIST; (*Symmetric Permutation Group. The symmetric permutation group is computed for N variables. *) PROCEDURE GINOPL(PG, ML: LIST): LIST; (*G-Symmetric Integral Orbit Polynomial List. The PG-symmetric orbit polynomial list is calculated from the monomial list ML and the permutation group PG. *) PROCEDURE GINCUT(PG, POL: LIST; VAR POL_1, POL_2: LIST); (*G-Symmetric Integral Polynomial Cut. The Polynomial POL is splitted up into the G-symmetric polynomial POL_1 and the remainder polynomial POL_2 with respect to the permutation group PG and the termorder. *) PROCEDURE GINCHK(PG, BASE, POL: LIST): LIST; (*G-Symmetric Integral Polynomial Check. The original polynomial is computed from the polynomial POL and the PG-symmetric base polynomials BASE with respect to the permutation group PG. *) PROCEDURE GINCHKBAS(VAR BASE, POL: LIST); (*G-Symmetric Integral Base Check. The procedure removes not used base orbit polynomials from BASE and make an update of POL. *) PROCEDURE GSYTWG(TERM1, TERM2: LIST): GAMMAINT; (*G-Symmetric Term Weight. The weigth between TERM1 and TERM2 is computed w.r.t. the default term order. The result is 1, if wg(TERM1) > wg(TERM2), and 0, if wg(TERM1) = wg(TERM2); otherwise the result is -1. *) PROCEDURE GSYMLT(N: GAMMAINT): GAMMAINT; (*G-Symmetric Multilinear Terms. The result of the preocedure ist a list off all multilinear terms in N variables. *) PROCEDURE GSYADD(TERM: LIST): LIST; (*G-Symmetric Term Adder. The result of the procedure is the next highest descend term after TERM. *) PROCEDURE GINRED(PG, POL: LIST; VAR BASE, BASE_POL, REM_POL: LIST); (*G-Symmetric Integral Polynomial Reduction. The PG-symmetric polynomial BASE_POL, which is the PG-symmetric polynomial reconstruction with respect to the base polynomials BASE, and the remainder polynomial REM_POL are computed from the polynomial POL with respect to the permutation group PG. *) PROCEDURE GINBAS(PG: LIST): LIST; (*G-Symmetric Integral Base Construction. The PG-symmetric base polynomials for the permutation group PG are computed. *) END GSYMFUIN. (* -EOF- *)