(* ---------------------------------------------------------------------------- * $Id: DIPRNGB.md,v 1.2 1992/02/12 17:34:23 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: DIPRNGB.md,v $ * Revision 1.2 1992/02/12 17:34:23 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:14:41 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE DIPRNGB; (* DIP Rational Groebner Bases Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: DIPRNGB.md,v 1.2 1992/02/12 17:34:23 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau";PROCEDURE DIGBC3(B,PLI,PLJ,EL: LIST): LIST; (*Distributive polynomial groebner basis criterion 3. B is a non empty list of reduction sets. pi and pj are distributive polynomials. e is the least common multiple of the leading exponent vectors of pi and pj. s=1 if the reduction of pi and pj is necessary s=0 else. *)PROCEDURE DIGBC4(PLI,PLJ,EL: LIST): LIST; (*Distributive polynomial groebner basis criterion 4. pi and pj are polynomials in distributive representation. e is the least common multiple of the leading exponent vectors of pi and pj. s=1 if the reduction of pi and pj is necessary s=0 else. *)PROCEDURE DIGBMI(P: LIST): LIST; (*Distributive minimal ordered groebner basis. P is a list of non zero rational polynomials in distributive representation in r variables. PP is the minimal normed and ordered groebner basis. *)PROCEDURE DILCPL(P: LIST;VARD,B: LIST); (*Distributive polynomial list construct pair list. P is list of polynomials in distributive representation in r variables. B is the polynomials pairs list and D is the pairs list. *)PROCEDURE DILUPL(PL,P,D,B: LIST): LIST; (*Distributive polynomial list update pair list. P is list of polynomials in distributive representation in r variables. B is the polynomials pairs list and D is the pairs list. p is a non zero polynomial in distributive representation. D, P and B are modified. DP is the updated pairs list. *)PROCEDURE DIRGBA(PL,P,TF: LIST): LIST; (*Distributive rational polynomial groebner basis augmentation. P is a groebner basis of polynomials in distributive representation in r variables. p is a polynomial. PP is the groebner basis of (P,p). t is the trace flag.*)PROCEDURE DIRGBR(P,TF: LIST): LIST; (*Distributive rational polynomial groebner basis recursion. P is a list of rational polynomials in distributive representation in r variables. PP is the groebner basis of P. t is the trace flag.*)PROCEDURE DIRLIS(P: LIST): LIST; (*Distributive rational polynomial list irreducible set. P is a list of distributive rational polynomials, PP is the result of reducing each p element of P modulo P-(p) until no further reductions are possible. *)PROCEDURE DIRPGB(P,TF: LIST): LIST; (*Distributive rational polynomials groebner basis. P is a list of rational polynomials in distributive representation in r variables. PP is the groebner basis of P. t is the trace flag.*)PROCEDURE DIRPNF(P,S: LIST): LIST; (*Distributive rational polynomial normal form. P is a list of non zero polynomials in distributive rational representation in r variables. S is a distributive rational polynomial. R is a polynomial such that S is reducible to R modulo P and R is in normalform with respect to P. *)PROCEDURE DIRPSP(A,B: LIST): LIST; (*Distributive rational polynomial S polynomial. A and B are rational polynomials in distributive representation. C is the S polynomial of A and B. *)PROCEDURE EVPLM(L1,L2: LIST): LIST; (*Exponent vector pair-list merge. L1 and L2 are pair-lists of exponent vectors in non decreasing order. L is the merge of L1 and L2. L1 and L2 are modified to produce L. *)PROCEDURE EVPLSO(A: LIST): LIST; (*Exponent vector pair-list sort. A is a list of pair-lists. B is the result of sorting A into non-decreasing order. Pairs of elements of A are merged. The list A is modified to produce B. *)ENDDIPRNGB. (* -EOF- *)