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Annotation of OpenXM_contrib/PHC/Ada/Schubert/sagbi_homotopies.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Complex_Vectors;
        !             2: with Standard_Natural_Matrices;
        !             3: with Standard_Floating_Matrices;
        !             4: with Standard_Complex_Matrices;
        !             5: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             6:
        !             7: package SAGBI_Homotopies is
        !             8:
        !             9: -- DESCRIPTION :
        !            10: --   Provides basic routines to set up the polynomials in the SAGBI homotopy.
        !            11: --   Due to hexadecimal expansions, n and d are both limited to 16.
        !            12: --   In practice, since the #roots grow so rapidly, this is no limitation.
        !            13:
        !            14:   function Lifted_Localized_Laplace_Expansion ( n,d : natural ) return Poly;
        !            15:
        !            16:   -- DESCRIPTION :
        !            17:   --   Constructs the generic equation in the SAGBI homotopy.
        !            18:   --   The coefficients are brackets in hexadecimal expansion.
        !            19:   --   These brackets represents the selected rows for the maximal minors.
        !            20:   --   The localization chooses the lower-right upper block of the d-plane
        !            21:   --   as the identity matrix.
        !            22:
        !            23:   function Lifted_Localized_Laplace_Expansion
        !            24:              ( locmap : Standard_Natural_Matrices.Matrix ) return Poly;
        !            25:
        !            26:   -- DESCRIPTION :
        !            27:   --   The generic equation in the SAGBI homotopy is constructed using
        !            28:   --   the localizaton map in locmap.  Zeros and ones indicate the
        !            29:   --   position of the identity matrix, while free elements are twos.
        !            30:
        !            31:   function Intersection_Coefficients
        !            32:               ( m : Standard_Floating_Matrices.Matrix;
        !            33:                 c : Standard_Complex_Vectors.Vector )
        !            34:               return Standard_Complex_Vectors.Vector;
        !            35:   function Intersection_Coefficients
        !            36:               ( m : Standard_Complex_Matrices.Matrix;
        !            37:                 c : Standard_Complex_Vectors.Vector )
        !            38:               return Standard_Complex_Vectors.Vector;
        !            39:
        !            40:   -- DESCRIPTION :
        !            41:   --   Given a matrix m and the hexadecimal expansion of the coefficients
        !            42:   --   in c, the vector of maximal minors of m is returned.
        !            43:
        !            44:   function Intersection_Condition
        !            45:               ( m : Standard_Floating_Matrices.Matrix; p : Poly ) return Poly;
        !            46:   function Intersection_Condition
        !            47:               ( m : Standard_Complex_Matrices.Matrix; p : Poly ) return Poly;
        !            48:
        !            49:   -- DESCRIPTION :
        !            50:   --   Generates the particular equations in the SAGBI homotopy, with
        !            51:   --   as input a matrix m and the lifted localized Laplace expansion p.
        !            52:   --   The matrix contains in its columns the generating points of the
        !            53:   --   plane of intersection.
        !            54:
        !            55:   -- REQUIRED : The dimensions of the matrix m are n times n-d.
        !            56:
        !            57: end SAGBI_Homotopies;