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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/binomial_system_solvers.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
        !             2: with Standard_Integer_VecVecs;           use Standard_Integer_VecVecs;
        !             3: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             4: with Transformations;                    use Transformations;
        !             5:
        !             6: package Binomial_System_Solvers is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package contains a routine for the solution of a binomial system,
        !            10: --   where the i-th equation is defined as follows:
        !            11: --
        !            12: --         X^u_i - c_i = 0, for i = 1,2,..,n,
        !            13: --   with
        !            14: --        [ u ]_i a vector of degrees and [ c ]_i a vector of complex numbers,
        !            15: --
        !            16: --   using a multi_index notation:  X^u_i = x1^u_i1 x2^u_i2 . . . xn^u_in.
        !            17:
        !            18:   procedure Factorize ( v : in out VecVec; n : in natural; t : in out Transfo );
        !            19:
        !            20:   -- DESCRIPTION :
        !            21:   --   This routines factorizes the binomial system defined by the
        !            22:   --   degrees in the vector v.
        !            23:
        !            24:   -- ON ENTRY :
        !            25:   --   v          defines the degrees of binomial system;
        !            26:   --   n          the number of unknowns to be eliminated.
        !            27:
        !            28:   -- ON RETURN :
        !            29:   --   v          the factorized binomial system;
        !            30:   --   t          the transformations used to factorize.
        !            31:
        !            32:   procedure Solve ( v : in VecVec; cv : in Vector;
        !            33:                     n : in natural; sols : in out Solution_List );
        !            34:
        !            35:   -- DESCRIPTION :
        !            36:   --   This routine solves the binomial system defined by the degrees
        !            37:   --   in the vector v and by the constants in the vector cv.
        !            38:
        !            39:   -- REQUIRED :
        !            40:   --   The vector cv contains no zero components!
        !            41:
        !            42:   -- ON ENTRY :
        !            43:   --   v          defines the degrees of binomial system;
        !            44:   --   cv         is the vector of constants;
        !            45:   --   n          the dimension of the system.
        !            46:
        !            47:   -- ON RETURN :
        !            48:   --   sols       is the solution list of the binomial system.
        !            49:
        !            50:   procedure Residuals ( v : in VecVec; cv : in Vector;
        !            51:                        n : in natural; sols : in Solution_List;
        !            52:                        res : out Vector );
        !            53:
        !            54:   -- DESCRIPTION :
        !            55:   --   This routine computes the residuals of the solutions of
        !            56:   --   the binomial system defined by v and cv.
        !            57:
        !            58:   -- REQUIRED :
        !            59:   --   The dimension of res equals the number of solutions in sols.
        !            60:
        !            61:   -- ON ENTRY :
        !            62:   --   v          defines the degrees of the binomial system;
        !            63:   --   cv         the vector of constants;
        !            64:   --   n          the dimension of the system;
        !            65:   --   sols       is the solution list of the binomial system.
        !            66:
        !            67:   -- ON RETURN :
        !            68:   --   res        a vector of residuals.
        !            69:
        !            70: end Binomial_System_Solvers;