(* ---------------------------------------------------------------------------- * $Id: DINNGB.md,v 1.1 1995/12/16 13:23:13 kredel Exp $ * ---------------------------------------------------------------------------- * Copyright (c) 1993 Universitaet Passau * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * $Log: DINNGB.md,v $ * Revision 1.1 1995/12/16 13:23:13 kredel * Moved from the masdom directory. * * Revision 1.1 1994/03/11 15:35:17 pesch * Groebner bases for non noetherian polynomial rings. * Diplomarbeit I. Bader. * Modified. * Does not give correct results. Do not use. * Should be rewritten. * * ---------------------------------------------------------------------------- *) DEFINITION MODULE DINNGB; (* DIP Groebner bases for non noetherian polynomial rings.*) (* Import lists and declarations. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: DINNGB.md,v 1.1 1995/12/16 13:23:13 kredel Exp $";CONSTcopyright = "Copyright (c) 1993 Universitaet Passau";PROCEDURE DINNCP(EL,A,B: LIST): LIST; (* distributive polynomial non-commutative product. e is a non-negative integer. A and B are distributive polynomials in 2 variables. C is the non-commutative product of A and B with respect to Y * X = X**e Y. *)PROCEDURE EVNNCP(EL,S,T: LIST): LIST; (* exponent vector non-commutative product. S and T are exponent vectors. of length 2. C is the non-commutative product S * T with respect to the relation Y * X = X**e Y. *)PROCEDURE EVNRDT(EL,S,T:LIST):LIST; (* exponent vectors non-commutative right division test. s and t are exponent vectors. C=1 if s rdiv t otherwise, C=0. *)PROCEDURE EVNCRD(EL,S,T:LIST):LIST; (* exponent vectors non-commutative right division. s and t a are exponent vectors, if s rdiv t then the output is t//s. *)PROCEDURE EVNLDT(EL,S,T:LIST):LIST; (* exponent vectors non-commutative left division test. s and t are exponent vectors. C=1 if s ldiv t otherwise, C=0. *)PROCEDURE EVNCLD(EL,S,T:LIST):LIST; (* exponent vectors non-commutative left division. s and t a are exponent vectors. The output is s\\t if s ldiv t . *)PROCEDURE EVLLCM(EL,S,T:LIST):LIST; (* exponent vectors non-commutative least left common multiple. s and t are exponent vectors. C is the least left common multiple of s and t. *)PROCEDURE EVLRCM(EL,S,T:LIST):LIST; (* exponent vectors non-commutative least right common multiple. s and t exponent vectors. C is the least right common multiple of s and t if it exists! *)PROCEDURE EVRCMT(EL,S,T:LIST):LIST; (* exponent vectors non-commutative right multiple test. S and T are exponent vectors. C=1 if S and T have some right common multiple otherweise, C=0. *)PROCEDURE DNNLNF(EL,P,S:LIST):LIST; (* distributive polynomials non-noetherian left normal form. P is a list of non zero polynomials in distributive rational representation. S is a distributive rational polynomial. R is a polynomial such that S is left reducible to R modulo P and R is in normal form with respect to P. *)PROCEDURE DNNLIS(EL,P: LIST): LIST; (* distributive polynomials non-noetherian left irreducible set. P is a list of distributive rational polynomials, PP is the result of left reducing each p element of P modulo P-(p) until no further reductions are possible. *)PROCEDURE DNNLSP(EL,A,B:LIST):LIST; (* distributive polynomials non-noetherian left S-polynomial. A and B are polynomials in distributive rational representation in 2 variables. C is the left S-polynomial of A and B. *)PROCEDURE DNNLGB(EL,P,TF: LIST): LIST; (* distributive non-noetherian polynomials left Groebner base. P is a list of rational polynomials in distributive representation in 2 variables. PP is the left Groebner base of P. t is the trace flag. *)PROCEDURE DNNRNF(EL,P,S:LIST):LIST; (* distributive polynomials non-noetherian right normal form. P is a list of non zero polynomials in distributive rational representation. S is a distributive rational polynomial. R is a polynomial such that S is right reducible to R modulo P and R is in normal form with respect to P. *)PROCEDURE DNNRIS(EL,P: LIST): LIST; (* distributive polynomials non-noetherian right irreducible set. P is a list of distributive rational polynomials, PP is the result of right reducing each p element of P modulo P-(p) until no further reductions are possible. *)PROCEDURE DNNRSP(EL,A,B:LIST):LIST; (* distributive polynomials non-noetherian right S-polynomial. A and B are polynomials in distributive rational representation. C is the right S-polynomial of A and B if it exists! *)PROCEDURE DNNRGB(EL,P,TF: LIST): LIST; (* distributive polynomials non-noetherian right Groebner base. P is a list of rational polynomials in distributive representation in 2 variables. PP is the right Groebner base of P. t is the trace flag. *)PROCEDURE DNLCPL(EL,P: LIST;VARD,B: LIST); (* distributive polynomial non-noetherian left construct pair list. P is list of polynomials in distributive representation in 2 variables. B is the polynomials pairs list and D is the pairs list. *)PROCEDURE DNRCPL(EL,P: LIST;VARD,B: LIST); (* distributive polynomial non-noetherian right construct pair list. P is list of polynomials in distributive representation in 2 variables. B is the polynomials pairs list and D is the pairs list. *)PROCEDURE DNLUPL(EL,PL,P,D,B: LIST): LIST; (* distributive polynomial non-noetherian left update pair list. P is list of polynomials in distributive representation in 2 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 DNRUPL(EL,PL,P,D,B: LIST): LIST; (* distributive polynomial non-noetherian right update pair list. P is list of polynomials in distributive representation in 2 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 DNN2GB(EL,P,TF: LIST): LIST; (* distributive polynomials non-noetherian 2-sided Groebner base. P is a list of rational polynomials in distributive representation in 2 variables. PP is the Groebner base of P. t is the trace flag.*)PROCEDURE DNNTGB(EL,P,TF:LIST):LIST; (* distributive polynomials non-noetherian two-sided Groebner base. P is a list of rational polynomials in distributive representation in 2 variables. PP is the two-sided Groebner base of P. t is the trace flag. The non-commutative produkt is computed w.r.t Y*X=X**eY. *)PROCEDURE DNNLES(EL,P:LIST):LIST; (* distributive polynomials non-noetherian left exponents set. P is a list of polinomials in distributive representation. PP is the the list which is result of *-multiplication of each polynomial of P from the left with the main variable. The non-commutative multiplication is computed w.r.t the relation Y * X = X**e Y. *)PROCEDURE DNNRES(EL,P,DL,DP:LIST):LIST; (* distributive polynomials non-noetherian right exponents set. P is a list of polynomials in distributive representation, d and d'are non- negative integers with d' >= d. PP is the is result of *-multiplication of each polynomial of P from the right with exponents (e**i) of the first variable in the variable list, where i ranges from d to d'. The *-multiplication is computed w.r.t the relation Y * X = X**e Y. *)PROCEDURE DIPSPS(D,B:LIST):LIST; (* distibutive polynomials S-polynomials set. D is the pairs list and B is the polynomials pairs list. D and B are modified. H is the set of all non-zero S-polynomials. *)PROCEDURE DIPLMD(P:LIST):LIST; (* distributive polynomial list maximum degree. P is a non-empty list of polynomials in distributive form in r variables. d is the maximum degree of all polynomials of P w.r.t the main variable .*)PROCEDURE IPOWER(EL,AL:LIST):LIST; (* integer power. e and a are positive integers. C=e**a. *)ENDDINNGB. (* -EOF- *)