File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Stalift / bkk_bound_computations.adb (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:29 2000 UTC (23 years, 8 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 integer_io; use integer_io;
with Standard_Integer_Vectors; use Standard_Integer_Vectors;
with Lists_of_Integer_Vectors; use Lists_of_Integer_Vectors;
with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists;
with Standard_Complex_Laur_Systems; use Standard_Complex_Laur_Systems;
with Standard_Poly_Laur_Convertors; use Standard_Poly_Laur_Convertors;
with Power_Lists; use Power_Lists;
with Trees_of_Vectors; use Trees_of_Vectors;
with Trees_of_Vectors_io; use Trees_of_Vectors_io;
with Volumes;
with Mixed_Homotopy_Continuation;
with Integer_Lifting_Utilities; use Integer_Lifting_Utilities;
with Mixed_Volume_Computation;
with Integer_Mixed_Subdivisions; use Integer_Mixed_Subdivisions;
with Integer_Mixed_Subdivisions_io; use Integer_Mixed_Subdivisions_io;
with Integer_Polyhedral_Continuation; use Integer_Polyhedral_Continuation;
package body BKK_Bound_Computations is
function BKK_by_Implicit_Lifting ( p : Poly_Sys ) return natural is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
bkk : constant natural := Volumes.Mixed_Volume(n,supports);
begin
Deep_Clear(supports);
return bkk;
end BKK_by_Implicit_Lifting;
function BKK_by_Implicit_Lifting ( file : file_type; p : Poly_Sys )
return natural is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
tv : Tree_of_Vectors;
bkk : natural;
begin
Volumes.Mixed_Volume(n,supports,tv,bkk);
new_line(file);
put_line(file,"The tree of useful directions : "); put(file,tv);
new_line(file);
Deep_Clear(supports); Clear(tv);
return bkk;
end BKK_by_Implicit_Lifting;
function BKK_by_Static_Lifting ( p : Poly_Sys ) return natural is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
bkk : constant natural := Mixed_Volume_Computation.Mixed_Volume(n,supports);
begin
Deep_Clear(supports);
return bkk;
end BKK_by_Static_Lifting;
function BKK_by_Static_Lifting ( file : file_type; p : Poly_Sys )
return natural is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
bkk : constant natural
:= Mixed_Volume_Computation.Mixed_Volume(file,n,supports);
begin
Deep_Clear(supports);
return bkk;
end BKK_by_Static_Lifting;
function Solve_by_Implicit_Lifting ( p : Poly_Sys ) return Solution_List is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
tv : Tree_of_Vectors;
bkk : natural;
lp : Laur_Sys(p'range) := Polynomial_to_Laurent_System(p);
sols : Solution_List;
begin
Volumes.Mixed_Volume(n,supports,tv,bkk);
Deep_Clear(supports);
Mixed_Homotopy_Continuation.Solve(Standard_Output,lp,tv,bkk,sols);
Clear(tv); Clear(lp);
return sols;
end Solve_by_Implicit_Lifting;
function Solve_by_Implicit_Lifting ( file : file_type; p : Poly_Sys )
return Solution_List is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
tv : Tree_of_Vectors;
bkk : natural;
lp : Laur_Sys(p'range) := Polynomial_to_Laurent_System(p);
sols : Solution_List;
begin
Volumes.Mixed_Volume(n,supports,tv,bkk);
Deep_Clear(supports);
new_line(file);
put(file,"The BKK bound equals "); put(file,bkk,1); new_line(file);
put_line(file," with tree of useful directions : "); put(file,tv);
new_line(file);
Mixed_Homotopy_Continuation.Solve(file,lp,tv,bkk,sols);
Clear(tv); Clear(lp);
return sols;
end Solve_by_Implicit_Lifting;
function Solve_by_Static_Lifting ( p : Poly_Sys ) return Solution_List is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
mv : natural;
sols : Solution_List;
mix,per : Link_to_Vector;
mixsub : Mixed_Subdivision;
permp : Poly_Sys(p'range);
lp,pp : Laur_Sys(p'range);
use Mixed_Volume_Computation;
begin
Compute_Mixture(supports,mix,per);
permp := Permute(p,per); Clear(per);
declare
lifted : Array_of_Lists(mix'range);
begin
Mixed_Volume(n,mix.all,supports,lifted,mixsub,mv);
pp := Polynomial_to_Laurent_System(p);
lp := Perform_Lifting(n,mix.all,lifted,pp);
Mixed_Solve(lp,mix.all,mixsub,sols);
Deep_Clear(lifted);
end;
Clear(pp); Clear(lp);
Deep_Clear(supports);
Deep_Clear(mixsub);
Clear(mix);
return sols;
end Solve_by_Static_Lifting;
function Solve_by_Static_Lifting ( file : file_type; p : Poly_Sys )
return Solution_List is
n : constant natural := p'length;
supports : Array_of_Lists(p'range) := Create(p);
mv : natural;
sols : Solution_List;
mix,per : Link_to_Vector;
mixsub : Mixed_Subdivision;
permp : Poly_Sys(p'range);
lp,pp : Laur_Sys(p'range);
use Mixed_Volume_Computation;
begin
Compute_Mixture(supports,mix,per);
permp := Permute(p,per); Clear(per);
declare
lifted : Array_of_Lists(mix'range);
begin
Mixed_Volume(file,n,mix.all,supports,lifted,mixsub,mv);
put_line(file,"THE MIXED SUBDIVISION :");
put(file,n,mix.all,mixsub);
pp := Polynomial_to_Laurent_System(p);
lp := Perform_Lifting(n,mix.all,lifted,pp);
new_line(file); put_line(file,"POLYHEDRAL HOMOTOPY CONTINUATION");
Mixed_Solve(file,lp,mix.all,mixsub,sols);
Deep_Clear(lifted);
end;
Clear(pp); Clear(lp);
Deep_Clear(supports);
Deep_Clear(mixsub);
Clear(mix);
return sols;
end Solve_by_Static_Lifting;
end BKK_Bound_Computations;