(* ---------------------------------------------------------------------------- * $Id: SACEXT7.md,v 1.2 1992/02/12 17:34:53 pesch Exp $ * ---------------------------------------------------------------------------- * This file is part of MAS. * ---------------------------------------------------------------------------- * Copyright (c) 1989 - 1992 Universitaet Passau * ---------------------------------------------------------------------------- * $Log: SACEXT7.md,v $ * Revision 1.2 1992/02/12 17:34:53 pesch * Moved CONST definition to the right place * * Revision 1.1 1992/01/22 15:15:35 kredel * Initial revision * * ---------------------------------------------------------------------------- *) DEFINITION MODULE SACEXT7; (* SAC Extensions 7 Definition Module. *) FROM MASSTOR IMPORT LIST;CONSTrcsid = "$Id: SACEXT7.md,v 1.2 1992/02/12 17:34:53 pesch Exp $";CONSTcopyright = "Copyright (c) 1989 - 1992 Universitaet Passau"; (* -- depends on IPRRII :-( PROCEDURE IPRICL(A: LIST): LIST; (*Integral polynomial real root isolation, Collins-Loos algorithm. A is an integral polynomial. L is a strong isolation list for A.*) *) (* -- zuviele gotos :-( PROCEDURE IPRRII(A,AP,DL,LP: LIST): LIST; (*Integral polynomial real root isolation induction. A is a primitive positive univariate integral polynomial of positive degree. AP is the derivative of A. D is a binary rational real root bound for A. LP is a strong isolation list for AP. L is a strong isolation list for A.*) *)PROCEDURE IPRRRI(A,B,I,SL1,TL1: LIST): LIST; (*Integral polynomial relative real root isolation. A and B are univariate integral polynomials. I is a left-open, right-closed interval (a sub 1 ,a sub 2 ) where al sub 1 and al sub 2 are binary rational numbers with al sub 1 lt al sub 2. A and B have unique roots, alpha and beta respectively, in I, each of odd multiplicity and with alpha ne beta. sl sub 1 eq sign(A(al sub 1 +)) and tl sub 1 eq sign(B(al sub 1 +)). is eq (al sub 1 sup * ,al sub 2 sup * ) is al left-open, right-closed subinterval of I with al sub 1 sup * and al sub 2 sup * binary rational numbers and al sub 1 sup * lt al sub 2 sup *, such that is contains alpha but not beta.*)PROCEDURE IPSIFI(A,I: LIST): LIST; (*Integral polynomial standard isolating interval from isolating interval. I is an interval with binary rational endpoints, which is either left-open and right-closed or a one-point interval. A is a univariate integral polynomial which has a unique root alpha of odd multiplicity in I. If I is a one-point interval, then J=I. If I is left-open and right-closed, then J is either a standard left-open and right-closed subinterval of I containing alpha, or if alpha is a binary rational number, J may possibly instead be the one-point interval ( alpha , alpha ).*)PROCEDURE ISFPIR(A,I,KL: LIST): LIST; (*Integral squarefree polynomial isolating interval refinement. A is a squarefree univariate integral polynomial. I is an isolating interval for a real root alpha of A. k is a nonnegative beta -integer. J is a subinterval of I isolating alpha with length less than 10 sup -k.*)PROCEDURE IUPVOI(A,I: LIST): LIST; (*Integral univariate polynomial, variations for open interval. A is a non-zero integral univariate polynomial. I is an open interval (a,b) with a and b binary rational numbers such that a lt b. Let t(z) be the transformation mapping the right half-plane onto the circle having I as diameter. Let B(X) eq A(t(X)). then v is the number of sign variations in the coefficients of B.*)ENDSACEXT7. (* -EOF- *)