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

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;