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

1.1     ! maekawa     1: with Brackets;                           use Brackets;
        !             2: with Bracket_Monomials;                  use Bracket_Monomials;
        !             3: with Standard_Natural_Matrices;          use Standard_Natural_Matrices;
        !             4: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             5: with Bracket_Polynomials;                use Bracket_Polynomials;
        !             6:
        !             7: package Bracket_Expansions is
        !             8:
        !             9: -- DESCRIPTION :
        !            10: --   This package provides operations to expand bracket polynomials as
        !            11: --   complex multivariate polynomials in the matrix indeterminates xij.
        !            12:
        !            13:   function Expand ( n,d : natural; b : Bracket ) return Poly;
        !            14:   function Expand ( n,d : natural; b : Bracket_Monomial ) return Poly;
        !            15:   function Expand ( n,d : natural; b : Bracket_Term ) return Poly;
        !            16:   function Expand ( n,d : natural; b : Bracket_Polynomial ) return Poly;
        !            17:
        !            18:   -- DESCRIPTION :
        !            19:   --   On return is the expanded bracket polynomial in the xij's,
        !            20:   --   where i runs over 1..n and j over 1..d.
        !            21:
        !            22:   function Localized_Expand ( n,d : natural; b : Bracket ) return Poly;
        !            23:
        !            24:   -- DESCRIPTION :
        !            25:   --   For i >= n-d+1, the variable xij is either 1 or 0, depending on
        !            26:   --   whether i=j+n-d or not, for i in 1..n and j in 1..d.
        !            27:   --   This is the standard map to localize a d-plane, a better one
        !            28:   --   is generated below.
        !            29:
        !            30:   function Localization_Map ( n,d : natural ) return Matrix;
        !            31:
        !            32:   -- DESCRIPTION :
        !            33:   --   Returns a localization map for a matrix representing a d-plane
        !            34:   --   in affine n-space.  The elements of the identity matrix are as
        !            35:   --   usual represented by zeros and ones.  Every row will have at least
        !            36:   --   one free element whose entry is marked by two.
        !            37:
        !            38:   -- REQUIRED : n > d+1.
        !            39:
        !            40:   function Expand ( locmap : Matrix; b : Bracket ) return Poly;
        !            41:
        !            42:   -- DESCRIPTION :
        !            43:   --   Expands a d-by-d minor of the matrix, selecting the rows with
        !            44:   --   entries in b, respecting the localization map in locmap.
        !            45:   --   The format of locmap must be as the output of Localization_Map.
        !            46:   --   The polynomial on return has as many variables as the number of
        !            47:   --   entries in the matrix locmap.
        !            48:   --   The number of variables can be reduced by the procedure below.
        !            49:
        !            50:   procedure Reduce_Variables ( locmap : in Matrix; p : in out Poly );
        !            51:
        !            52:   -- DESCRIPTION :
        !            53:   --   Reduces the #variables in the polynomial, removing all variables that
        !            54:   --   correspond to zeros in the localization map.
        !            55:
        !            56: end Bracket_Expansions;