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