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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/interpolating_homotopies.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Integer_Matrices;          use Standard_Integer_Matrices;
                      2: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
                      3: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
                      4: with Partitions_of_Sets_of_Unknowns;     use Partitions_of_Sets_of_Unknowns;
                      5:
                      6: package Interpolating_Homotopies is
                      7:
                      8: -- DESCRIPTION :
                      9: --   This package contains facilities for constructing interpolating
                     10: --   homotopies, based on a given m-homogeneous structure.
                     11: --   The routines are given in the order in which they should be applied.
                     12: --   Null polynomials are ignored, making scaled interpolation possible,
                     13: --   the scaling equation, used for generating the interpolating vectors,
                     14: --   can be added afterwards.  For linear scalers, the last unknown of the
                     15: --   scaling equation should be ignored in those monomials that have degree
                     16: --   one in that unknown, to avoid singular interpolation matrices.
                     17:
                     18:   function Dense_Representation
                     19:               ( p : Poly_Sys; z : partition ) return Poly_Sys;
                     20:   function Dense_Representation
                     21:               ( p : Poly_Sys; z : partition; d : Matrix ) return Poly_Sys;
                     22:
                     23:   -- DESCRIPTION :
                     24:   --   A dense representation of an m-homogeneous structure is returned.
                     25:   --   The coefficients of the polynomials in the returned system are all one.
                     26:
                     27:   function Independent_Representation ( p : Poly_Sys ) return Poly_Sys;
                     28:
                     29:   -- DESCRIPTION :
                     30:   --   An independent representation of a polynomial system is returned.
                     31:   --   This means that the initial term of each polynomial does not occur
                     32:   --   in every other polynomial.
                     33:
                     34:   function Independent_Roots ( p : Poly_Sys ) return natural;
                     35:   function Independent_Roots ( p : Poly_Sys; i : natural ) return natural;
                     36:
                     37:   -- DESCRIPTION :
                     38:   --   Returns the number of independent roots the system p can have.
                     39:   --   When the ith unknown is given as parameter, the monomials that
                     40:   --   have degree one in x_i are not counted.
                     41:
                     42:   -- IMPORTANT NOTE : p must be an independent representation of a polynomial
                     43:   --                  system, otherwise the result might not be reliable.
                     44:
                     45:   function Interpolate ( p : Poly_Sys; b : natural; sols : Solution_List )
                     46:                        return Poly_Sys;
                     47:   function Interpolate ( p : Poly_Sys; i,b : natural; sols : Solution_List )
                     48:                        return Poly_Sys;
                     49:
                     50:   -- DESCRIPTION :
                     51:   --   This routine constructs a start system q with the same monomial
                     52:   --   structure as the system p.
                     53:
                     54:   -- ON ENTRY :
                     55:   --  p         a polynomial system;
                     56:   --  i         monomials with degree one in x_i will be ignored;
                     57:   --  b         must equal Independent_Roots(p);
                     58:   --  sols      interpolation vectors, Length_Of(sols) = b.
                     59:
                     60:   -- ON RETURN :
                     61:   --  q         system that has the given list sols as solutions.
                     62:
                     63: end Interpolating_Homotopies;