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

1.1     ! maekawa     1: with Standard_Complex_Numbers;           use Standard_Complex_Numbers;
        !             2: with Standard_Complex_Vectors;
        !             3: with Standard_Floating_Matrices;
        !             4: with Standard_Complex_Matrices;
        !             5: with Standard_Complex_Poly_Matrices;
        !             6: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             7: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             8: with Bracket_Monomials;                  use Bracket_Monomials;
        !             9: with Bracket_Polynomials;                use Bracket_Polynomials;
        !            10: with Bracket_Systems;                    use Bracket_Systems;
        !            11:
        !            12: package Numeric_Minor_Equations is
        !            13:
        !            14: -- DESCRIPTION :
        !            15: --   This package evaluates the symbolic equations in the Pieri homotopies.
        !            16:
        !            17: -- EXPANDING ACCORDING A BRACKET MONOMIAL :
        !            18:
        !            19:   function Expanded_Minors
        !            20:                ( cffmat : Standard_Floating_Matrices.Matrix;
        !            21:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            22:                  bm : Bracket_Monomial ) return Poly;
        !            23:
        !            24:   function Expanded_Minors
        !            25:                ( cffmat : Standard_Complex_Matrices.Matrix;
        !            26:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            27:                  bm : Bracket_Monomial ) return Poly;
        !            28:
        !            29:   function Expanded_Minors
        !            30:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            31:                  bm : Bracket_Monomial ) return Poly;
        !            32:
        !            33:   function Lifted_Expanded_Minors
        !            34:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            35:                  bm : Bracket_Monomial ) return Poly;
        !            36:
        !            37:   -- DESCRIPTION :
        !            38:   --   Expansion of coefficient and polynomial minors along the Laplace
        !            39:   --   expansion formula in bm creates a polynomial equation.
        !            40:   --   With the prefix Lifted_, the polynomials in polmat are extended
        !            41:   --   with a zero lifting.
        !            42:
        !            43:   -- ON ENTRY :
        !            44:   --   cffmat    coefficient matrix, represents m-plane;
        !            45:   --   cntmat    polynomial matrix, represents moving m-plane,
        !            46:   --             the continuation parameter is the last variable;
        !            47:   --   polmat    polynomial matrix, contains the pattern of the p-plane;
        !            48:   --   bm        quadratic bracket monomial, the first bracket is a coefficient
        !            49:   --             minor and has zero as its first entry, the second bracket is
        !            50:   --             a polynomial minor.
        !            51:
        !            52: -- EXPANDING ACCORDING A BRACKET POLYNOMIAL :
        !            53:
        !            54:   function Expanded_Minors
        !            55:                ( cffmat : Standard_Floating_Matrices.Matrix;
        !            56:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            57:                  bp : Bracket_Polynomial ) return Poly;
        !            58:
        !            59:   function Expanded_Minors
        !            60:                ( cffmat : Standard_Complex_Matrices.Matrix;
        !            61:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            62:                  bp : Bracket_Polynomial ) return Poly;
        !            63:
        !            64:   function Expanded_Minors
        !            65:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            66:                  bp : Bracket_Polynomial ) return Poly;
        !            67:
        !            68:   function Lifted_Expanded_Minors
        !            69:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            70:                  bp : Bracket_Polynomial ) return Poly;
        !            71:
        !            72:   -- DESCRIPTION :
        !            73:   --   Expansion of coefficient and polynomial minors along the Laplace
        !            74:   --   expansion formula in bp creates a polynomial equation.
        !            75:   --   With the prefix Lifted_, the polynomials in polmat are extended
        !            76:   --   with a zero lifting.
        !            77:
        !            78:   -- ON ENTRY :
        !            79:   --   cffmat    coefficient matrix, represents m-plane, m = n-p;
        !            80:   --   cntmat    polynomial matrix, represents moving m-plane, m = n-p,
        !            81:   --             the continuation parameter is the last variable;
        !            82:   --   polmat    polynomial matrix, contains the pattern of the p-plane;
        !            83:   --   bp        Laplace expansion of one minor, the coefficient minors come
        !            84:   --             first and have a zero as first element.
        !            85:
        !            86: -- EXPANDING TO CONSTRUCT POLYNOMIAL SYSTEMS :
        !            87:
        !            88:   function Expanded_Minors
        !            89:                ( cffmat : Standard_Floating_Matrices.Matrix;
        !            90:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            91:                  bs : Bracket_System ) return Poly_Sys;
        !            92:
        !            93:   function Expanded_Minors
        !            94:                ( cffmat : Standard_Complex_Matrices.Matrix;
        !            95:                  polmat : Standard_Complex_Poly_Matrices.Matrix;
        !            96:                  bs : Bracket_System ) return Poly_Sys;
        !            97:
        !            98:   function Expanded_Minors
        !            99:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !           100:                  bs : Bracket_System ) return Poly_Sys;
        !           101:
        !           102:   function Lifted_Expanded_Minors
        !           103:                ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
        !           104:                  bs : Bracket_System ) return Poly_Sys;
        !           105:
        !           106:   -- DESCRIPTION :
        !           107:   --   Expansion of coefficient and polynomial minors along the Laplace
        !           108:   --   expansion formulas in bs creates a polynomial system.
        !           109:   --   With the prefix Lifted_, the polynomials in polmat are extended
        !           110:   --   with zero lifting.
        !           111:
        !           112:   -- ON ENTRY :
        !           113:   --   cffmat    coefficient matrix, represents m-plane;
        !           114:   --   cntmat    polynomial matrix, represents moving m-plane,
        !           115:   --             the continuation parameter is the last variable;
        !           116:   --   polmat    polynomial matrix, contains the pattern of the p-plane;
        !           117:   --   bs        Laplace expansion of all minors, the first equation is
        !           118:   --             the generic one and should not count in the range of
        !           119:   --             the resulting polynomial system.
        !           120:
        !           121:   function Evaluate ( p : Poly; x : Standard_Complex_Matrices.Matrix )
        !           122:                     return Complex_Number;
        !           123:
        !           124:   -- DESCRIPTION :
        !           125:   --   Evaluates the polynomial p at the matrix x, where x is a value
        !           126:   --   for the polynomial matrix used above to define p.
        !           127:
        !           128:   function Evaluate ( p : Poly_Sys; x : Standard_Complex_Matrices.Matrix )
        !           129:                     return Standard_Complex_Vectors.Vector;
        !           130:
        !           131:   -- DESCRIPTION :
        !           132:   --   Evaluates the polynomial system p at the matrix x, where x is a value
        !           133:   --   for the polynomial matrix used above to define p.
        !           134:
        !           135:   procedure Embed ( t : in out Term );
        !           136:   procedure Embed ( p : in out Poly );
        !           137:   procedure Embed ( p : in out Poly_Sys );
        !           138:   procedure Embed ( m : in out Standard_Complex_Poly_Matrices.Matrix );
        !           139:
        !           140:   -- DESCRIPTION :
        !           141:   --   Augments the number of variables with one, as is required to embed
        !           142:   --   the polynomials in a homotopy.
        !           143:
        !           144:   function Linear_Homotopy ( target,start : Poly ) return Poly;
        !           145:
        !           146:   -- DESCRIPTION :
        !           147:   --   Returns (1-t)*start + t*target, with t an additional last variable.
        !           148:
        !           149:   function Linear_Interpolation
        !           150:               ( target,start : Poly; k : natural ) return Poly;
        !           151:
        !           152:   -- DESCRIPTION :
        !           153:   --   Returns (1-t)*start + t*target, with t the k-th variable.
        !           154:
        !           155:   procedure Divide_Common_Factor ( p : in out Poly; k : in natural );
        !           156:
        !           157:   -- DESCRIPTION :
        !           158:   --   If the k-th variable occurs everywhere in p with a positive power,
        !           159:   --   then it will be divided out.
        !           160:
        !           161: end Numeric_Minor_Equations;