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File: [local] / OpenXM_contrib / PHC / Ada / Homotopy / reduction_of_polynomials.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:23 2000 UTC (23 years, 8 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Standard_Complex_Polynomials; use Standard_Complex_Polynomials; package Reduction_of_Polynomials is -- DESCRIPTION : -- This package implements S-polynomials and R-polynomials. function Spoly ( p,q : poly ) return Poly; -- DESCRIPTION : -- Returns the S-polynomial of p and q : -- lcm(in(p),in(q)) lcm(in(p),in(q)) -- S = c_q * ---------------- p - c_p * ---------------- q -- in(p) in(q) -- where lcm stands for the least common multiple, -- in(p) is the leading term of the polynomial p -- and the coefficients c_q and c_p are chosen such that -- their moduli are smaller than or equal to 1. function Rpoly ( p,q : Poly ) return Poly; -- DESCRIPTION : -- Returns the R-polynomial of the polynomials p and q : -- c_p lcm(in(p),term(q)) -- R = p - --- * ------------------ * q -- c_q term(q) -- such that the leading term of p vanishes. end Reduction_of_Polynomials;