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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/binomial_system_solvers.ads, Revision 1.1.1.1

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;