(* ---------------------------------------------------------------------------- * $Id: PQSMPL.md,v 1.4 1995/12/16 11:34:34 kredel Exp $ * ---------------------------------------------------------------------------- * Copyright (c) 1993 Universitaet Passau * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * $Log: PQSMPL.md,v $ * Revision 1.4 1995/12/16 11:34:34 kredel * Changed comments to documentation rules. * * Revision 1.3 1995/11/04 18:00:26 pesch * Changed comments violating documentation rules. Should be rewritten. * * Revision 1.2 1994/11/28 21:12:07 dolzmann * Moved procedures from PQSMPL into PQBASE. * * Revision 1.1 1993/12/18 20:12:17 dolzmann * System for the simplification of boolean combinations of polynomial * equations. * * ---------------------------------------------------------------------------- *) DEFINITION MODULE PQSMPL; (* Polynomial Equation Simplification Definition Module. *) (****************************************************************************** * P O L Y N O M I A L E Q U A T I O N S I M P L I F I C A T I O N * *-----------------------------------------------------------------------------* * Author: Andreas Dolzmann * * Language: Modula II * * System: This program is written for the computer algebra system MAS by * * Heinz Kredel. * * Remark: Libraries maskern, maslisp and maslog, masdom, maspoly, ... * * are used. * * Abstract: A program for simplification of polynomial equations and * * inequations in the field of the complex numbers. * ******************************************************************************) FROM MASSTOR IMPORT LIST; FROM MASLISPU IMPORT PROCF1, PROCP1, PROCF3;CONSTrcsid = "$Id: PQSMPL.md,v 1.4 1995/12/16 11:34:34 kredel Exp $";CONSTcopyright = "Copyright (c) 1993 Universitaet Passau"; (****************************************************************************** * S I M P L I F I C A T I O N * ******************************************************************************)PROCEDURE PQSCNF(phi: LIST):LIST; (* polynomial equation simplification normal form. phi is an arbitrary quantifier-free formula. A equivalent formula in SCNF is returned. *)PROCEDURE PQSDNF(phi: LIST):LIST; (* polynomial equation simplification normal form. phi is an arbitrary quantifier-free formula. A equivalent formula in SDNF is returned. *)PROCEDURE PQCnfSimplify(nu:LIST):LIST; (* polynomial equation cnf based simplification. nu is an quantifier free formula. The formula nu is simplified. Consult the documentation for a description of the rules which are applied *)PROCEDURE PQDnfSimplify(nu:LIST):LIST; (* polynomial equation dnf based simplification. nu is an quantifier free formula. The formula nu is simplified. Consult the documentation for a description of the rules which are applied *)PROCEDURE SimplifyNf(nf: LIST):LIST; (* simplify normal form. nf is a formula in disjunctive normal form or conjunctive normal form. A simplification of nf is returned. Following rules are applied: Equal literals in clauses are contracted, atomic formulas with identical polynomials are contracted to TRUE or FALSE. Note: identical clauses are not contracted. This happens in the GetDataXXX Procedures. In this procedure equal implications are contracted. *) (****************************************************************************** * I D E A L P R O C E D U R E S * ******************************************************************************)PROCEDURE IdealMember(G,p:LIST):BOOLEAN; (* ideal membership test. G is groebner basis. Iff p in ID(g) then 1 is returned otherwise 0. *)PROCEDURE RadicalMember(G,p:LIST):BOOLEAN; (* radical membership test. G is a groebner basis. Iff p in RAD(G) then 1 is returned otherwise 0. The new variable Rw is introduced. *) (****************************************************************************** * D I P A D - P R O C E D U R E S * ******************************************************************************)PROCEDURE DIPADGB(P:LIST):LIST; (* distributive polynomial arbitrary domain groebner basis. P is a list of polynomials (over the ring of integers). A groebner basis of P is returned. This procedure is at moment only a dummy procedure. It should calculate a groebner basis in respect to the coefficient ring of the polynomials. *)PROCEDURE DIPADNF(P,S:LIST):LIST; (* distributive polynomial arbitrary domain normal form. P is a list of polynomials. The normal form of the polynomial S w.r.t. P is returned. This procedure is at moment only a dummy. Is should work on Polynomials over arbitrary fields and rings. *)PROCEDURE DILADNF(P,S:LIST):LIST; (* distributive polynomial list arbitrary domain normal form. P is a list of polynomials. S is a list of polynomials. The list of normal forms of the polynomials of S w.r.t. P is returned. This procedure is at moment only a dummy. Is should work on Polynomials over arbitrary fields and rings. *)PROCEDURE DIPADGBext(gb,pols:LIST):LIST; (* distributive polynomial arbitrary domain groebner basis extension. gb is a groebner basis, pols is a list of polynomials. A groebner basis of the ideal basis gb join pols is calculated and returned. This procedure is at moment only a dummy. *)PROCEDURE DIPADGBunion(gb1,gb2:LIST):LIST; (* distributive polynomial arbitrary domain groebner basis union. gb1 and gb2 are groebner basis. A groebner basis of the ideal basis gb1 join gb2 is calculated and returned. This procedure is at moment only a dummy. *)PROCEDURE DIPADIRSET(P:LIST):LIST; (* distributive polynomial arbitrary domain irreducible set. P is a list of polynomials. A set PP of polynomials is returned. PP is the result of reducing each element p modulo P - {p} until no further reductions are possible. *)PROCEDURE DIPADGBRED(gb: LIST):LIST; (* distributive polynomial groebner basis reduction. gb is a groebner basis of distributive polynomials over an arbitrary domain. The unique reduced and ordered groebner basis to gp is returned. *) (****************************************************************************** * O P T I O N S * ******************************************************************************)PROCEDURE PQOPT(O:LIST):LIST; (* polynomial equation options. The options of the PQ-System are set. The list O is of the following format: The first entry is the trace level of the system, the second entry determines the method for the radical member ship test, the third entry is a list of powers for the pseudo radical member ship test, the fourth entry controls the replacement of the premises of the implications, and the fifth entry controls the You can omit an entry of O by writing a -1 on the place of the entry. You need not specify all entries. The old parameters are returned. *)PROCEDURE PQOPTWR(); (* polynomial options write. The options of the PQ-System are printed in the output stream. *)PROCEDURE PQDEMO(); (* Demonstration for this package. *)PROCEDURE DLSWRITE(S:ARRAY OF CHAR;b:LIST); (* debug level SWRITE. The string S is in dependency of the debug level written to the output stream. In contrast to MAS a blank line is added. (analogous to UWRITE and UWRIT1) *)PROCEDURE SETADD(a,b:LIST):LIST; (* set add element. If the element elem is not in the set set, then {elem} join set is returned else set is returned. *)PROCEDURE rabinowitsch(p:LIST):LIST; (* rabinowitsch. p is a non zero polynomial. The polynomial 1-Zp is returned. Z denotes the variable with the exponent vector (0,...,0,1). *)ENDPQSMPL. (* -EOF- *)