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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/reduction_of_polynomials.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
                      2:
                      3: package Reduction_of_Polynomials is
                      4:
                      5: -- DESCRIPTION :
                      6: --   This package implements S-polynomials and R-polynomials.
                      7:
                      8:   function Spoly ( p,q : poly ) return Poly;
                      9:
                     10:   -- DESCRIPTION :
                     11:   --   Returns the S-polynomial of p and q :
                     12:   --              lcm(in(p),in(q))              lcm(in(p),in(q))
                     13:   --   S =  c_q * ----------------  p  -  c_p * ---------------- q
                     14:   --                   in(p)                          in(q)
                     15:   --   where lcm stands for the least common multiple,
                     16:   --         in(p) is the leading term of the polynomial p
                     17:   --     and the coefficients c_q and c_p are chosen such that
                     18:   --         their moduli are smaller than or equal to 1.
                     19:
                     20:   function Rpoly ( p,q : Poly ) return Poly;
                     21:
                     22:   -- DESCRIPTION :
                     23:   --   Returns the R-polynomial of the polynomials p and q :
                     24:   --            c_p   lcm(in(p),term(q))
                     25:   --   R = p -  --- * ------------------ * q
                     26:   --            c_q        term(q)
                     27:   --   such that the leading term of p vanishes.
                     28:
                     29: end Reduction_of_Polynomials;