Return to sagbi_homotopies.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Schubert

Annotation of OpenXM_contrib/PHC/Ada/Schubert/sagbi_homotopies.ads, Revision 1.1.1.1

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;