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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/random_product_system.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
                      2: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
                      3: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
                      4: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
                      5: with Lists_of_Integer_Vectors;           use Lists_of_Integer_Vectors;
                      6:
                      7: package Random_Product_System is
                      8:
                      9: -- DESCRIPTION :
                     10: --   This package enables the construction and the solution
                     11: --   of a polynomial system of which each polynomial is
                     12: --   represented as a product of hyperplanes.
                     13:
                     14: -- CONSTRUCTORS :
                     15:
                     16:   procedure Init ( n : in natural );
                     17:
                     18:   -- DESCRIPTION :
                     19:   --   The internal data for this package are initialised
                     20:   --   with n, this is the number of equations of the system
                     21:   -- NOTE :
                     22:   --   This operation must be the first one executed when
                     23:   --   using this package.
                     24:
                     25:   procedure Add_Hyperplane ( i : in natural; h : in Vector );
                     26:
                     27:   -- DESCRIPTION :
                     28:   --   The hyperplane h is added to the i-the equation of the
                     29:   --   random product system
                     30:   -- REQUIRED :                               __n_
                     31:   --   i <= n                                 \
                     32:   --   h : Vector(0..n) representing  h(0) +   >    h(j) x
                     33:   --                                          /___        j
                     34:   --                                           j=1
                     35:
                     36:   function Dimension return natural;
                     37:
                     38:   -- DESCRIPTION :
                     39:   --   returns the number of equations in the product system.
                     40:
                     41:   function Number_of_Hyperplanes (i : natural) return natural;
                     42:
                     43:   -- DESCRIPTION :
                     44:   --   returns the number of added hyperplanes for the i-th equation
                     45:
                     46:   function Get_Hyperplane ( i,j : in natural ) return Vector;
                     47:   function Get_Hyperplane ( i,j : in natural ) return Link_to_Vector;
                     48:
                     49:   -- DESCRIPTION :
                     50:   --   returns the j-th hyperplane for the i-th equation
                     51:
                     52:   procedure Change_Hyperplane ( i,j : in natural; h : in Vector );
                     53:
                     54:   -- DESCRIPTION :
                     55:   --   the (i,j)-th hyperplane will be changed into h
                     56:
                     57:   procedure Solve ( sols : in out Solution_List; nl : out natural );
                     58:
                     59:   -- DESCRIPTION :
                     60:   --   The random product system is solved and the solutions are
                     61:   --   put in the list sols.
                     62:   --   nl is the number of matrices that are factored.
                     63:   -- NOTE :
                     64:   --   All possible linear systems are factorized using Gaussian
                     65:   --   elimination, together with the estimation of the condition
                     66:   --   of the matrices.
                     67:   --   Systems with a bad condition are not solved.
                     68:
                     69:   procedure Solve ( sols : in out Solution_List;
                     70:                     nl : out natural; l : in List );
                     71:
                     72:   -- DESCRIPTION :
                     73:   --   Cf. Solve, but only those linear systems are factorized,
                     74:   --   for which the linear equations are as indicated in the list
                     75:   --   of positions l.
                     76:
                     77:   function Polynomial ( h : Vector ) return Poly;
                     78:
                     79:   -- DESCRIPTION :
                     80:   --   returns the linear polynomial defined by the coefficients in h.
                     81:
                     82:   function Polynomial_System return Poly_Sys;
                     83:
                     84:   -- DESCRIPTION :
                     85:   --   A polynomial system is constructed by multiplying all
                     86:   --   the hyperplanes from the equations of the random product system.
                     87:
                     88: -- DESTRUCTOR :
                     89:
                     90:   procedure Clear;
                     91:
                     92:   -- DESCRIPTION :
                     93:   --   This procedure frees all memory space used by the random
                     94:   --   product system.
                     95:
                     96: end Random_Product_System;