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

1.1     ! maekawa     1: with Brackets;                           use Brackets;
        !             2: with Standard_Complex_Matrices;
        !             3: with Standard_Complex_Poly_Matrices;
        !             4:
        !             5: package Specialization_of_Planes is
        !             6:
        !             7: -- DESCRIPTION :
        !             8: --   Set up of the moving cycles in the Pieri homotopy algorithm.
        !             9: --   The U-matrix generates the special m-plane.
        !            10:
        !            11:   function Random_Upper_Triangular
        !            12:                ( n : natural ) return Standard_Complex_Matrices.Matrix;
        !            13:
        !            14:   -- DESCRIPTION :
        !            15:   --   Returns an n*n random upper triangular matrix that has 1's on its
        !            16:   --   anti-diagonal, to be used for the first Pieri tree.
        !            17:
        !            18:   function Random_Lower_Triangular
        !            19:                ( n : natural ) return Standard_Complex_Matrices.Matrix;
        !            20:
        !            21:   -- DESCRIPTION :
        !            22:   --   Returns an n*n random lower triangular matrix that has 1's on its
        !            23:   --   diagonal, to be used for the second Pieri tree.
        !            24:
        !            25:   function U_Matrix ( F : Standard_Complex_Matrices.Matrix; b : Bracket )
        !            26:                     return Standard_Complex_Matrices.Matrix;
        !            27:
        !            28:   -- DESCRIPTION :
        !            29:   --   Determines the matrix U in the moving cycles for the Pieri tree.
        !            30:
        !            31:   -- ON ENTRY :
        !            32:   --   F         general triangular matrix, output of either
        !            33:   --             Random_Upper_Triangular or Random_Lower_Triangular;
        !            34:   --   b         bracket of first jumping-branching node down the tree.
        !            35:
        !            36:   function Special_Plane ( m : natural; b : Bracket )
        !            37:                          return Standard_Complex_Matrices.Matrix;
        !            38:
        !            39:   -- DESCRIPTION :
        !            40:   --   Generates the special m-plane that every child of the node with
        !            41:   --   the pivots in the bracket b intersects.
        !            42:   --   The plane on return is spanned by the standard basis vectors
        !            43:   --   except those that are indexed by the entries in the bracket b.
        !            44:
        !            45:   function Special_Bottom_Plane ( m : natural; b : Bracket )
        !            46:                                 return Standard_Complex_Matrices.Matrix;
        !            47:
        !            48:   -- DESCRIPTION :
        !            49:   --   Same as special m-plane, but with random numbers above the diagonal.
        !            50:
        !            51:   function Special_Top_Plane ( m : natural; b : Bracket )
        !            52:                              return Standard_Complex_Matrices.Matrix;
        !            53:
        !            54:   -- DESCRIPTION :
        !            55:   --   Same as special m-plane, but with random numbers below the diagonal.
        !            56:
        !            57:   function Special_Plane
        !            58:                 ( n,m,k : natural; b : Bracket;
        !            59:                   special : in Standard_Complex_Matrices.Matrix )
        !            60:                 return Standard_Complex_Matrices.Matrix;
        !            61:
        !            62:   -- DESCRIPTION :
        !            63:   --   Returns a special (m+1-k)-plane, by random combinations from the
        !            64:   --   n-dimensional basis vectors of special indexed by the pivots in b.
        !            65:   --   The basis vectors have random numbers above the diagonal.
        !            66:   --   Note that here not the complement of the indices in b is used!
        !            67:
        !            68:   function Moving_U_Matrix
        !            69:                ( n : natural; U,L : Standard_Complex_Matrices.Matrix )
        !            70:                return Standard_Complex_Poly_Matrices.Matrix;
        !            71:
        !            72:   -- DESCRIPTION :
        !            73:   --   Determines the moving U-matrix for the Pieri tree, when i=0.
        !            74:   --   Returns a polynomial matrix in the continuation parameter t,
        !            75:   --   which is the last variable in the polynomials on return.
        !            76:
        !            77:   -- ON ENTRY :
        !            78:   --   n         number of variables of the polynomials in the matrix;
        !            79:   --   U         output of U_Matrix function listed above, start m-plane;
        !            80:   --   L         target m-plane that will be folded in during the deformation.
        !            81:
        !            82:   function Moving_U_Matrix
        !            83:                ( U : Standard_Complex_Matrices.Matrix;
        !            84:                  i,r : natural; b : bracket )
        !            85:                return Standard_Complex_Poly_Matrices.Matrix;
        !            86:
        !            87:   -- DESCRIPTION :
        !            88:   --   Determines the moving U-matrix for the Pieri tree, when i>0.
        !            89:   --   Returns a polynomial matrix in the continuation parameter t.
        !            90:
        !            91:   -- ON ENTRY :
        !            92:   --   U         output of U_Matrix function listed above;
        !            93:   --   i         counts the number of nodes till 1st jumping node down;
        !            94:   --   b         bracket of first jumping-branching node down the tree.
        !            95:
        !            96:   function Lower_Section
        !            97:                ( M : Standard_Complex_Poly_Matrices.Matrix;
        !            98:                  row : natural ) return Standard_Complex_Poly_Matrices.Matrix;
        !            99:
        !           100:   -- DESCRIPTION :
        !           101:   --   The columns in M that have nonzero entries in the rows strictly
        !           102:   --   larger than the given row index will be removed.  This corresponds
        !           103:   --   to intersecting the column space of M with <e_1,..,e_row>.
        !           104:
        !           105:   function Upper_Section
        !           106:                ( M : Standard_Complex_Poly_Matrices.Matrix;
        !           107:                  row : natural ) return Standard_Complex_Poly_Matrices.Matrix;
        !           108:
        !           109:   -- DESCRIPTION :
        !           110:   --   The columns in M that have nonzero entries in the rows strictly
        !           111:   --   lower than the given row index will be removed.  This corresponds
        !           112:   --   to intersecting the column space of M with <e_row,..,e_n>.
        !           113:
        !           114: end Specialization_of_Planes;