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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/standard_complex_substitutors.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Complex_Numbers;           use Standard_Complex_Numbers;
        !             2: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
        !             3: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             4: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             5:
        !             6: package Standard_Complex_Substitutors is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package contains routines for substituting
        !            10: --   equations into polynomials and polynomial systems.
        !            11:
        !            12:   function  Substitute ( k : integer; c : Complex_Number; t : Term )
        !            13:                        return Term;
        !            14:   procedure Substitute ( k : in integer; c : in Complex_Number;
        !            15:                          t : in out Term );
        !            16:
        !            17:   function  Substitute ( k : integer; c : Complex_Number; p : Poly )
        !            18:                        return Poly;
        !            19:   procedure Substitute ( k : in integer; c : in Complex_Number;
        !            20:                          p : in out Poly );
        !            21:
        !            22:   function  Substitute ( k : integer; c : Complex_Number; p : Poly_Sys )
        !            23:                        return Poly_Sys;
        !            24:   procedure Substitute ( k : in integer; c : in Complex_Number;
        !            25:                          p : in out Poly_Sys );
        !            26:
        !            27:    -- DESCRIPTION :
        !            28:    --   These routines substitute the kth unknown of the term t or
        !            29:    --   polynomial (system) p by a complex constant c.
        !            30:
        !            31:    -- ON ENTRY :
        !            32:    --   k         an unknown in the polynomial p;
        !            33:    --   c         a complex constant;
        !            34:    --   t         a term;
        !            35:    --   p         a polynomial (system).
        !            36:
        !            37:    -- ON RETURN :
        !            38:    --   t         a term where the kth unknonw has been replaced by the
        !            39:    --             complex constant c;
        !            40:    --   p         a polynomial (system) where the kth unknown has been
        !            41:    --             replaced by the complex constant c.
        !            42:
        !            43:   function  Substitute ( k : integer; h : Vector; p : Poly ) return Poly;
        !            44:   procedure Substitute ( k : in integer; h : in Vector; p : in out Poly );
        !            45:
        !            46:   -- DESCRIPTION :
        !            47:   --   These routines substitute the kth unknown of the polynomial p
        !            48:   --   by a linear equation defined by h.
        !            49:
        !            50:   -- ON ENTRY :
        !            51:   --   k          an unknown in the polynomial p;
        !            52:   --   h          a vector h(0..n), n = Number_of_Unknowns(p),
        !            53:   --              defines h(0) + h(1)*x1 + ... + h(n)*xn;
        !            54:   --   p          a polynomial.
        !            55:
        !            56:   -- REQUIRED : h(k) /= 0.
        !            57:
        !            58:   -- ON RETURN :
        !            59:   --   p          a polynomial where the kth unknown has been replaced
        !            60:   --              by a linear equation defined by h.
        !            61:
        !            62:   function  Substitute ( k : integer; s,p : Poly ) return Poly;
        !            63:   procedure Substitute ( k : in integer; s : in Poly; p : in out Poly );
        !            64:
        !            65:   -- DESCRIPTION :
        !            66:   --   These routines substitute the kth unknown of the polynomial p
        !            67:   --   by a polynomial s.
        !            68:
        !            69:   -- ON ENTRY :
        !            70:   --   k          an unknown in the polynomial p;
        !            71:   --   s          a polynomial so that xk = s;
        !            72:   --   p          a polynomial.
        !            73:
        !            74:   -- ON RETURN :
        !            75:   --   p          a polynomial where the kth unknown has been replaced
        !            76:   --              by the polynomial s.
        !            77:
        !            78:   function  Substitute ( k : integer; h : Vector; p : Poly_Sys )
        !            79:                        return Poly_Sys;
        !            80:   procedure Substitute ( k : in integer; h : in Vector; p : in out Poly_Sys );
        !            81:
        !            82:   -- DESCRIPTION :
        !            83:   --   These routines substitute the kth unknown of the polynomials in the
        !            84:   --   system p by a linear equation defined by h.
        !            85:
        !            86:   -- ON ENTRY :
        !            87:   --   k          an unknown in the polynomials in the system p;
        !            88:   --   h          a vector h(0..n), n = Number_of_Unknowns(p(i)),
        !            89:   --              defines h(0) + h(1)*x1 + ... + h(n)*xn;
        !            90:   --   p          a polynomial system.
        !            91:
        !            92:   -- REQUIRED : h(k) /= 0
        !            93:
        !            94:   -- ON RETURN :
        !            95:   --   p          a polynomial system where the kth unknown has been replaced
        !            96:   --              by a linear equation defined by h.
        !            97:
        !            98:   function  Substitute ( k : integer; s : Poly; p : Poly_Sys ) return Poly_Sys;
        !            99:   procedure Substitute ( k : in integer; s : in Poly; p : in out Poly_Sys );
        !           100:
        !           101:   -- DESCRIPTION :
        !           102:   --   These routines substitute the kth unknown of the polynomials in p
        !           103:   --   by a polynomial s.
        !           104:
        !           105:   -- ON ENTRY :
        !           106:   --   k          an unknown in the polynomial p;
        !           107:   --   s          a polynomial so that xk = s;
        !           108:   --   p          a polynomial.
        !           109:
        !           110:   -- ON RETURN :
        !           111:   --   p          a polynomial system where the kth unknown has been replaced
        !           112:   --              by the polynomial s.
        !           113:
        !           114: end Standard_Complex_Substitutors;