(* ---------------------------------------------------------------------------- * $Id: DIPCJ.md,v 1.2 1995/12/16 12:21:52 kredel Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1995 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: DIPCJ.md,v $ * Revision 1.2 1995/12/16 12:21:52 kredel * Comments slightly changed. * * Revision 1.1 1995/10/12 14:44:45 pesch * Diplomarbeit Rainer Grosse-Gehling. * Involutive Bases. * Slightly edited. * * ---------------------------------------------------------------------------- *) DEFINITION MODULE DIPCJ; (* DIP Common Polynomial System Definition Module in the sense of Janet. *) (* Import lists and declarations. *) FROM MASSTOR IMPORT LIST; FROM MASLISPU IMPORT PROCF1;CONSTrcsid = "$Id: DIPCJ.md,v 1.2 1995/12/16 12:21:52 kredel Exp $";CONSTcopyright = "Copyright (c) 1995 Universitaet Passau";PROCEDURE ADDTDG(deg, P: LIST): LIST; (* Add total degree. Input: polynomial degree deg and polynomial P in distributive list representation. Output: polynom P with first list entry now total degree of the leading exponent vector. *)PROCEDURE ADVTDG(P: LIST;VARp, PP: LIST); (* Advance total degree. Input: polynom P in distributive list representation. The first entry of the list is the total degree of the leading exponent vector. Output: p - the first entry of the list; PP - the polynom without the first entry *)PROCEDURE DILEBBS(A: LIST); (* Distributive List Extended Bubble Sort. Sort a list of polynoms in decreasing order of the total degree of the leading exponent. The total degree must be the first entry of each polynom. Input: A is a list of polynoms. A is changed *)PROCEDURE DILBBS(A: LIST); (* Distributive List Bubble Sort. Sort a list of polynoms in decreasing order of the total degree of the leading exponent. Input: A is a list of polynoms. A is changed *)PROCEDURE DILEP2P(P: LIST): LIST; (* Distributive polynom list extended polynom to polynom. Input: P - a list of extended polynoms. Output: a list of polynoms whithout the first entry. *)PROCEDURE DILATDG(P: LIST): LIST; (* Distributive polynom list add total degree. P is a list of distributive polynomials. The result is a list of distributive polynoms with total degree of the leading term as first entry of each polynomial. *)PROCEDURE DILTDG(A: LIST): LIST; (* Distributive polynomial list total degree Input: A is a list of distributive polynomials, Output tdg: the total degree of A *)PROCEDURE DIPCLP(P: LIST): LIST; (* Distributiv Polynomial Class of Polynomial. Input: P is a polynomial, Output: t is the index of the lowest variable of the leading term of P, t=0 if P is Empty *)PROCEDURE DIPCLT(P: LIST): LIST; (* Distributiv Polynomial Class of Term. Input: P is a term, Output: t is the index of the lowest variable in P, t=0 if P is empty *)PROCEDURE DIPFIRST(P: LIST; extended: BOOLEAN;VARpp, PP: LIST); (* Distributive polynomial first polynomial, P is a list of polynomials, pp is the first polynomial and PP is the reductum of P.*)PROCEDURE DIPSSM(P: LIST; extended: BOOLEAN;VARpp, PP: LIST); (* Distributive polynomial sort and select minimal. Input: P - a list of polynoms, extended is TRUE iff the first entry of each polynimial in P is the total degree of the leading exponent vector. Output: pp - the minimal polynom w.r.t. the admissible term order. PP - sorted list of P without pp. P is changed *)PROCEDURE DILCAN(P: LIST; F: PROCF1): LIST; (* Distributive Polynomial Cancel. P is a list of distributive polynomials. F is the cancel-function. Output is a list of distributive polynomials or an empty list if all polynomials in A equal 0. The coefficients of each polynomial are canceld down by F. *)PROCEDURE DIILPP(P: LIST): LIST; (* Distributive integral polynomial list primitive part. P is a list of distributive integral polynoms. The result is the positive primitive part of each polynomial in P. The list-order is reversed. *)PROCEDURE DIRPMV(A,B: LIST): LIST; (* Distributiv Polynomial multiplication with a variable. Input: A is the polynomial, B is an exponent vector. Output: A*B *)PROCEDURE EVDIF2(U,V: LIST): LIST; (* Exponent vector difference. Input: U=(u1, ...,ur), V=(v1, ...,vr) are exponent vectors of length r. Output: W=(w1, ...,wr) is the componentwise difference of U and V. Unlike procedure EVDIV this procedure returns 0 and not (0...0) if U=V *)PROCEDURE EVMTJ(U,V: LIST): LIST; (* Exponent vector multiple test in the sense of Janet. Input: U=(u1, ...,ur), V=(v1, ...,vr) are exponent vectors of length r. Output: t=1 if U is a multiple in the sense of Janet of V, t=0 else. *)PROCEDURE DIPNML(G: LIST): LIST; (* Distributive polynomial nonmultiple variable list. Compute for a polynom G the List of nonmultiplicative variables. Input: G is a polynomial. Output: a list of non-multiplicative variables for the leading term of G. *)PROCEDURE DIPPGL2(F, V, LL: LIST): LIST; (* Distributive polynomial prolongation list. Input: F - polynomial which first entry is the total degree of the leading term; V - list of variables; LL - number of different variables in F. Output: PP - List of prolongations of F with non-multiplicative variables for F from V. *)PROCEDURE DIPPGL3(F, V, LL: LIST): LIST; (* Distributive polynom prolongation list. Input: F - polynomial; V - list of variables; LL - number of variables in F. Output: PP - List of prolongations of F with non-multiplicative variables for F from V. *)PROCEDURE DIPPGL(V: LIST): LIST; (* Distributive polynomial prolongation list. Input: V is an arbitrary domain polynomial. Output: List of prolongations of V with nonmultiplicative variables for V.*)PROCEDURE DIPVL(V: LIST): LIST; (* Distributive Polynomial List of Variables. Input: a polynomial V. Output: list of variables with class > 1. *)ENDDIPCJ. (* -EOF- *)