(* ---------------------------------------------------------------------------- * $Id: DIPRN.md,v 1.2 1992/02/12 17:33:51 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: DIPRN.md,v $ * Revision 1.2 1992/02/12 17:33:51 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:13:42 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE DIPRN; (* DIP Rational Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: DIPRN.md,v 1.2 1992/02/12 17:33:51 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau";PROCEDURE DIRFIP(A: LIST): LIST; (*Distributive rational polynomial from integral polynomial. A is a distributive integral polynomial, B is the monic associate rational polynomial of A. *)PROCEDURE DIRLRD(V: LIST): LIST; (*Distributive rational polynomial list read. V is a variable list. A list of distributive rational polynomials in r variables, where r=length(V), r ge 0, is read from the input stream. Any blanks preceding A are skipped. *)PROCEDURE DIRLWR(A,V,S: LIST); (*Distributive rational polynomial list write. V is a variable list. A list of distributive rational polynomials in r variables, where r=length(V), r ge 0, is written to the output stream. *)PROCEDURE DIRPAB(A: LIST): LIST; (*Distributive rational polynomial absolute value. A is a distributive rational polynomial. B is the absolute value of A.*)PROCEDURE DIRPDF(A,B: LIST): LIST; (*Distributive rational polynomial difference. A and B are distributive rational polynomials. C=A-B.*)PROCEDURE DIRPDM(A: LIST): LIST; (*Distributive rational polynomial derivation main variable. A is a distributive polynomial. B is the derivation of A with respect to its main variable.*)PROCEDURE DIRPDR(A,IL: LIST): LIST; (*Distributive rational polynomial derivation. A is a distributive polynomial. B is the derivation of A with respect to its i-th variable, 0 le i le DIPNOV(A).*)PROCEDURE DIRPEM(A,AL: LIST): LIST; (*Distributive rational polynomial evaluation of main variable. A is a distributive rational polynomial. a is a rational number. B(x1, ...,x(r-1))=A(x1, ...,x(r-1),a). *)PROCEDURE DIRPEV(A,IL,AL: LIST): LIST; (*Distributive rational polynomial evaluation of the i-th variable. A is a distributive rational polynomial, 1 le i le DIPNOV(A), a is a rational number. B(x1, ...,x(i-1),x(i+1), ...,xr)= A(x1, ...,x(i-1),a,x(i+1), ...,xr). *)PROCEDURE DIRPEX(A,NL: LIST): LIST; (*Distributive rational polynomial exponentiation. A is a distributive rational polynomial, n is a non-negative beta- integer. B=A**n. 0**0 is by definition a polynomial in zero variables. *)PROCEDURE DIRPHD(A,IL,NL: LIST): LIST; (*Distributive rational polynomial higher derivation. A is a distributive rational polynomial. B is the n-th derivation of A with respect to its i-th variable, 0 le i le DIPNOV(A). *)PROCEDURE DIRPLS(A: LIST): LIST; (*Distributive rational polynomial list sum. A is a circular list of distributive rational polynomials. B is the sum of all polynomials in A. *)PROCEDURE DIRPMC(A: LIST): LIST; (*Distributive rational polynomial monic. A and C are distributive rational polynomials, C=A/LBC(A) if A ne 0 C=0 if A eq 0. *)PROCEDURE DIRPMN(A: LIST): LIST; (*Distributive rational polynomial maximum norm. A is a distributive rational polynomial. b is the maximum norm of A.*)PROCEDURE DIRPNG(A: LIST): LIST; (*Distributive rational polynomial negative. B= -A.*)PROCEDURE DIRPON(A: LIST): LIST; (*Distributive rational polynomial one. A is a distributive rational polynomial. If A=1 then t=1, otherwise t=0.*)PROCEDURE DIRPPR(A,B: LIST): LIST; (*Distributive rational polynomial product. A and B are distributive rational polynomials. C=A*B.*)PROCEDURE DIRPQ(A,B: LIST): LIST; (*Distributive rational polynomial quotient. A and B are distributive rational polynomials. B is a non zero divisor of A. C=B/A.*)PROCEDURE DIRPQR(A,B: LIST;VARQ,R: LIST); (*Distributive rational polynomial quotient and remainder. A and B are distributive rational polynomials with B ne 0. Q and R are unique distributive rational polynomials such that either B divides A, so Q=A/B and R=0 or B does not divide A, so A=B*Q+R with deg(R) lt deg(B). *)PROCEDURE DIRPRA(RL,KL,LL,EL: LIST): LIST; (*Distributive rational polynomial random. k, l and e are positive beta-digits. e is the maximal permitted exponent of A in any variable. A is a random distributive rational polynomial in r variables max norm of A lt 2**k and maximal l base coefficients. *)PROCEDURE DIRPRD(V: LIST): LIST; (*Distributive rational polynomial read. V is a variable list. A distributive rational polynomial A in r variables, where r=length(V), r ge 0, is read from the input stream. Any blanks preceding A are skipped. modified version, orginal version by G. E. Collins. *)PROCEDURE DIRPRP(A,BL: LIST): LIST; (*Distributive rational polynomial rational number product. Is a distributive rational polynomial, b is a rational number. C=A*b.*)PROCEDURE DIRPRQ(A,BL: LIST): LIST; (*Distributive rational polynomial rational number quotient. A is a distributive rational polynomial, b is a nonzero rational number. C=A/b.*)PROCEDURE DIRPSG(A: LIST): LIST; (*Distributive rational polynomial sign. A is a distributive rational polynomial. s is the sign of the leading base coefficient of A.*)PROCEDURE DIRPSM(A,B: LIST): LIST; (*Distributive rational polynomial sum. A and B are distributive rational polynomials. C=A+B. *)PROCEDURE DIRPSN(A: LIST): LIST; (*Distributive rational polynomial sum norm. A is a distributive rational polynomial. b is the sum norm of A.*)PROCEDURE DIRPSO(A: LIST): LIST; (*Distributive rational polynomial sort. A is a list of rational coefficients and exponent vectors, A is sorted into inverse lexicographical order, two terms with equal exponent vectors are added. *)PROCEDURE DIRPSU(A,IL,B: LIST): LIST; (*Distributive rational polynomial substitution. A and B are distributive rational polynomials, 1 le i le r=DIPNOV(A). E(x1, ...,x(i-1),x(i+1), ...,xr)=A(x1, ...,x(i-1), B(x1, ...,x(i-1),x(i+1), ...,xr),x(i+1), ...,xr). *)PROCEDURE DIRPSV(A,B: LIST): LIST; (*Distributive rational polynomial substitution for main variable. A and B are distributive rational polynomials. t=DIPNOV(A)-1. C(x1, ...,xt)=A(x1, ...,xt,B(x1, ...,xt)). *)PROCEDURE DIRPTM(A,HL: LIST): LIST; (*Distributive rational polynomial translation main variable. A is a distributive rational polynomial, h is a rational number. B(x1, ...xr)=A(x1, ...,x(r-1),x(r)+h). r=DIPNOV(A). *)PROCEDURE DIRPTR(A,HL,IL: LIST): LIST; (*Distributive rational polynomial translation. A is a distributive rational polynomial, h is a rational number, the i-th variable is translated. 1 le i le r=DIPNOV(A). B(x1, ...,xr)=A(x1, ...,x(i)+h, ...,xr).*)PROCEDURE DIRPWR(A,V,S: LIST); (*Distributive rational polynomial write. A is a distributive rational poynomial in r variables, r ge 0. V is a variable list for A. If S ge 0 then the coefficients are written by RNDWR else by RNWRIT. A is written in the output stream. Modified version, original version by G. E. Collins. *)PROCEDURE DIRPWV(A: LIST); (*Distributive rational polynomial write with standard variable list. A is a distributive rational poynomial. The standard variable list is used. A is written in the output stream.*)PROCEDURE DIRRAS(RL,KL,LL,EL,QL: LIST): LIST; (*Distributive rational polynomial, random sparse exponent vector. k, l and e are positive beta-digits. e is the maximal permitted exponent of A in any variable. A is a random distributive rational polynomial in r variables max norm of A lt 2**k and maximal l base coefficients. *)ENDDIPRN. (* -EOF- *)