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