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

1.1       maekawa     1: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
                      2: with Standard_Complex_Poly_Matrices;
                      3: with Brackets;                           use Brackets;
                      4: with Bracket_Monomials;                  use Bracket_Monomials;
                      5: with Bracket_Systems;                    use Bracket_Systems;
                      6:
                      7: package Symbolic_Minor_Equations is
                      8:
                      9: -- DESCRIPTION :
                     10: --   This package generates the equations that arise from the intersection
                     11: --   conditions along the deformations determined by the Pieri trees.
                     12: --   The equations are symbolic: the coefficients are brackets.
                     13:
                     14: -- LOCALIZATION PATTERNS :
                     15:
                     16:   function Schubert_Pattern ( n : natural; b1,b2 : Bracket )
                     17:                             return Standard_Complex_Poly_Matrices.Matrix;
                     18:
                     19:   -- DESCRIPTON :
                     20:   --   Returns the representation of the pattern of the p-plane that satisfies
                     21:   --   the Schubert conditions as a polynomial matrix.
                     22:   --   This definition is used in the original Pieri implementation.
                     23:
                     24:   function Localization_Pattern ( n : natural; top,bottom : Bracket )
                     25:                                 return Standard_Complex_Poly_Matrices.Matrix;
                     26:
                     27:   -- DESCRIPTION :
                     28:   --   Returns the matrix of indeterminates for the top and bottom pivots.
                     29:   --   The dimension of the working space equals n.
                     30:   --   This definition is used in the second Pieri implementation.
                     31:
                     32: -- SYMBOLIC REPRESENTATIONS OF THE EQUATIONS :
                     33:
                     34:   function Maximal_Minors ( n,m : natural ) return Bracket_Monomial;
                     35:
                     36:   -- DESCRIPTION :
                     37:   --   Generates all maximal minors of an n-by-m matrix, n >= m.
                     38:   --   The collection of all these m-by-m minors is represented as the
                     39:   --   product of m-brackets.  Every bracket determines a selection of
                     40:   --   m rows from the n-by-m matrix.
                     41:
                     42:   function Minor_Equations
                     43:             ( m,d : natural; bm : Bracket_Monomial ) return Bracket_System;
                     44:
                     45:   -- DESCRIPTION :
                     46:   --   Returns the bracket polynomials that arise from expanding the
                     47:   --   above maximal m-minors into blocks of respective sizes m-d and d.
                     48:   --   Equation 0 in the result is the generic bracket representation of
                     49:   --   the Laplace expansion.
                     50:
                     51:   function Expanded_Minor ( m : Standard_Complex_Poly_Matrices.Matrix;
                     52:                             b : Bracket ) return Poly;
                     53:
                     54:   -- DESCRIPTION :
                     55:   --   The minor that selects rows from m, according to b is expanded.
                     56:
                     57:   function Extend_Zero_Lifting ( p : Poly ) return Poly;
                     58:
                     59:   -- DESCRIPTION :
                     60:   --   Extends every term with a new variable t^0.
                     61:
                     62: end Symbolic_Minor_Equations;