![]() ![]() | ![]() |
File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Product / degree_structure.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:29 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Standard_Natural_Vectors; with Sets_of_Unknowns; use Sets_of_Unknowns; with Partitions_of_Sets_of_Unknowns; use Partitions_of_Sets_of_Unknowns; with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems; package Degree_Structure is -- DESCRIPTION : -- This package analyzes the structure of a given -- polynomial system, with respect to its degrees. -- CREATORS : procedure Create ( p : in Poly_Sys ); -- DESCRIPTION : -- For each equation of the polynomial system p, a heuristic is applied -- for constructing a good tuple of partitions. -- This degree structure will be contained by the package itself. procedure Put ( p : in Poly_Sys; i,m : in natural; z : in Partition ); -- DESCRIPTION : -- A partition for the set of unknowns of the ith polynomial -- of the system p is added. -- SELECTORS : function Empty return boolean; -- DESCRIPTION : -- is true initially and after the Clear procedure. function Get ( i : natural ) return natural; -- DESCRIPTION : -- returns the number of sets for the partition of -- the i-th equation of a polynomial system p for -- which the Create operation must be performed. procedure Get ( i : in natural; z : in out Partition; d : out Standard_Natural_Vectors.Vector ); -- DESCRIPTION : -- The partition for the i-the equation of the polynomial -- system p is returned together with its degrees; -- for j in d'range : d(j) = Degree(p(i),z(j)). -- REQUIRED : -- The Create operation or Put operations have been performed on a -- polynomial system p having at least i equations. -- COMPUTING THE GENERALIZED BEZOUT NUMBER : function Admissible ( z : Partition; n : natural ) return boolean; -- DESCRIPTION : -- return true if the following holds: -- `Any union of k sets of z contains at least k unknowns', -- for k in 2..n. -- NOTE : -- z is not necessary a partition, it is rather a set of n sets -- of unknowns. function Admissible ( z : Partition; n : natural; s : Set ) return boolean; -- DESCRIPTION : -- given admissible(z,n) = true, this function returns -- admissible(union(z,s),n+1). function Admissible ( z : Partition; k,n : natural; s : Set ) return boolean; -- DESCRIPTION : -- returns true if admissible(union(z,s),n+1), with respect to k. function Generalized_Bezout_Number return natural; -- DESCRIPTION : -- This function returns a Bezout number based on the -- degree structure of the system. function Generalized_Bezout_Number ( p : in Poly_Sys ) return natural; -- DESCRIPTION : -- Calling this function is equivalent to : -- Degree_Structure.Create(p); -- return Degree_Structure.Generalized_Bezout_Number; -- DESTRUCTOR : procedure Clear; -- DESCRIPTION : -- All allocated memory space is freed. end Degree_Structure;