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Annotation of OpenXM_contrib/PHC/Ada/Homotopy/homogenization.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             2: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             3:
        !             4: package Homogenization is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package provides routines for constructing additional
        !             8: --   equations to a system for projective transformations.
        !             9: --   There is also a routine that isolates the homogeneous part
        !            10: --   of a given polynomial system.
        !            11:
        !            12:   function Homogeneous_Part ( p : Poly ) return Poly;
        !            13:   function Homogeneous_Part ( p : Poly_Sys ) return Poly_Sys;
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   These functions isolate all terms having a degree equal to
        !            17:   --   the degree of the polynomial.
        !            18:
        !            19:   function Add_Equations ( s1 : Poly_Sys; s2 : Poly_Sys ) return Poly_Sys;
        !            20:
        !            21:   -- DESCRIPTION :
        !            22:   --   The resulting polynomial system is the concatenation of s1 and s2.
        !            23:
        !            24:   function Add_Equation ( s : Poly_Sys; p : Poly ) return Poly_Sys;
        !            25:
        !            26:   -- DESCRIPTION :
        !            27:   --   the resulting polynomial system is the concatenation
        !            28:   --   of the system s and the polynomial p
        !            29:
        !            30:   function Add_Random_Hyperplanes
        !            31:                ( s : Poly_Sys; m : natural; re : boolean ) return Poly_Sys;
        !            32:
        !            33:   -- DESCRIPTION :
        !            34:   --   To the polynomial system s, m hyperplanes are added with
        !            35:   --   randomly choosen coefficients;
        !            36:   --   if re = true
        !            37:   --    then the coefficients will be floating point numbers;
        !            38:   --    else the coefficients will be complex numbers.
        !            39:
        !            40:   function Add_Standard_Hyperplanes
        !            41:                ( s : Poly_Sys; m : natural ) return Poly_Sys;
        !            42:
        !            43:   -- DESCRIPTION :
        !            44:   --   If n = Number_Of_Unknowns(s(i)), for i in s'range,
        !            45:   --    then m hyperplanes of the form
        !            46:   --           x_(j+n) - 1 = 0 will be added, for j in 1..m,
        !            47:   --         to the system s.
        !            48:
        !            49: end Homogenization;