File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Implift / set_structures_and_volumes.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:29 2000 UTC (23 years, 11 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
lines
Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with text_io; use text_io;
with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
with Standard_Complex_Solutions; use Standard_Complex_Solutions;
with Trees_of_Vectors; use Trees_of_Vectors;
package Set_Structures_and_Volumes is
-- DESCRIPTION :
-- This package contains routines for implementing the
-- hybrid approach of working with set structures and
-- computing mixed volumes.
procedure Build_RPS ( k,n : in natural; p : in Poly_Sys );
-- DESCRIPTION :
-- If the set structure is empty, then a set structure will
-- be constructed for the first k polynomials of p.
-- This allows the construction of random product polynomials.
-- ON ENTRY :
-- k number of polynomials for which a random product structure
-- needs to be constructed, 0 < k <= n;
-- n total number of polynomials in the system;
-- p polynomial system.
-- ON RETURN :
-- The result of this operation can be found in
-- the data of the package Random_Product_System.
function Bezout_BKK ( k,n : natural; p : Poly_Sys ) return natural;
function Bezout_BKK ( k,n : natural; p : Poly_Sys; tv : Tree_of_Vectors )
return natural;
procedure Bezout_BKK ( k,n : in natural; p : in Poly_Sys;
tv : in out Tree_of_Vectors; bb : out natural );
-- DESCRIPTION :
-- If the set structure is empty, then a set structure will be
-- constructed for the first k equations.
-- This set structure will be used to eliminate k unknowns,
-- for the last equations of p, the BKK bound will be computed.
-- ON ENTRY :
-- k number of polynomials for which a random product
-- structure needs to be constructed, 0 <= k <= n;
-- ON RETURN :
-- tv tree of useful directions used to compute mixed volume,
-- once tv has been constructed, the mixed volume
-- can be computed more efficiently;
-- bb if k = 0, then the BKK bound is returned,
-- if 0 < k < n, then for the first k polynomials a product
-- structure has been used to eliminate k unknowns,
-- if k = n, then the Bezout number based on the set structure
-- will be returned;
procedure Mixed_Solve
( file : in file_type; k,n : in natural; p : in Poly_Sys;
bb : out natural;
g : in out Poly_Sys; sols : in out Solution_List );
procedure Mixed_Solve
( file : in file_type; k,n : in natural; p : in Poly_Sys;
tv : in Tree_of_Vectors;
bb : out natural; g : in out Poly_Sys;
sols : in out Solution_List );
-- DESCRIPTION :
-- Constructs a random product coefficient start system for p.
-- ON ENTRY :
-- file needed to write intermediate results on;
-- k a number between 0 and n;
-- n the number of variables and equations;
-- p a polynomial system;
-- tv the tree of useful directions.
-- ON RETURN :
-- g a random product coefficient start system;
-- if k = 0, then a random coefficient start system,
-- if k = n, then a random product start system;
-- bb the Bezout BKK bound for the system p;
-- if k = 0, then bb = BKK bound,
-- if k = n, then bb = Bezout number based on set structure;
-- sols the solutions of g.
end Set_Structures_and_Volumes;