File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Dynlift / cayley_embedding.adb (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:28 2000 UTC (23 years, 9 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
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Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with Standard_Integer_VecVecs; use Standard_Integer_VecVecs;
package body Cayley_Embedding is
-- AUXILIARIES :
function Is_Good_Point
( cnt,n : natural; pt : Link_to_Vector ) return boolean is
-- DESCRIPTION :
-- Returns true if the point pt is a point of the type indicated
-- by the parameter cnt, i.e. whether it belongs to the polytope
-- placed on the vertex with number cnt.
goodpoint : boolean;
begin
if cnt = 0
then goodpoint := true;
for l in pt'first..pt'last-n-1 loop
if pt(l) /= 0
then goodpoint := false;
end if;
exit when not goodpoint;
end loop;
else goodpoint := (pt(cnt) = 1);
end if;
return goodpoint;
end Is_Good_Point;
procedure Project ( n : natural; v : in out Link_to_Vector ) is
-- DESCRIPTION :
-- After application, v points to a vector of length n+1.
newv : Link_to_Vector;
begin
newv := new Vector(1..n+1);
newv(1..n+1) := v(v'last-n..v'last);
Clear(v);
v := newv;
end Project;
-- TARGET ROUTINES :
function Embedding_Before_Lifting
( supports : Array_of_Lists ) return List is
tmp,res,res_last : List;
r1 : constant natural := supports'length-1;
pt : Link_to_Vector;
cnt : natural := 0;
begin
for k in supports'range loop
tmp := supports(k);
while not Is_Null(tmp) loop
pt := Head_Of(tmp);
declare
npt : Vector(pt'first..pt'last+r1);
begin
npt(npt'last-pt'length+1..npt'last) := pt.all;
npt(npt'first..npt'first+r1-1) := (npt'first..npt'first+r1-1 => 0);
if cnt > 0
then npt(cnt) := 1;
end if;
Append(res,res_last,npt);
end;
tmp := Tail_Of(tmp);
end loop;
cnt := cnt + 1;
end loop;
return res;
end Embedding_Before_Lifting;
function Extract ( vtp,n : natural; pts : VecVec ) return List is
res,res_last : List;
begin
for k in pts'range loop
if Is_Good_Point(vtp,n,pts(k))
then Append(res,res_last,pts(k).all);
end if;
end loop;
return res;
end Extract;
function Extract ( vtp,n : natural; pts : List ) return List is
-- DESCRIPTION :
-- Extracts the points out of the list that are of the type
-- indicated by vtp.
tmp,res,res_last : List;
pt : Link_to_Vector;
begin
tmp := pts;
while not Is_Null(tmp) loop
pt := Head_Of(tmp);
if Is_Good_Point(vtp,n,pt)
then Append(res,res_last,pt.all);
end if;
tmp := Tail_Of(tmp);
end loop;
return res;
end Extract;
function Extract_Mixed_Cell
( n : natural; mix : Vector; s : Simplex ) return Mixed_Cell is
res : Mixed_Cell;
work : Array_of_Lists(mix'range);
cnt : natural := 0;
iscell : boolean;
pts : constant VecVec := Vertices(s);
begin
for k in mix'range loop
work(k) := Extract(cnt,n,pts);
iscell := (Length_Of(work(k)) = mix(k)+1);
exit when not iscell;
cnt := cnt + 1;
end loop;
if iscell
then res.pts := new Array_of_Lists'(work);
res.nor := new vector'(Normal(s));
else Deep_Clear(work);
end if;
return res;
end Extract_Mixed_Cell;
function Extract_Mixed_Cells
( n : natural; mix : Vector; t : Triangulation )
return Mixed_Subdivision is
res,res_last : Mixed_Subdivision;
s : Simplex;
tmp : Triangulation;
begin
tmp := t;
while not Is_Null(tmp) loop
s := Head_Of(tmp);
declare
mic : Mixed_Cell := Extract_Mixed_Cell(n,mix,s);
begin
if mic.nor /= null
then Append(res,res_last,mic);
end if;
end;
tmp := Tail_Of(tmp);
end loop;
return res;
end Extract_Mixed_Cells;
function Extract_non_Flat_Mixed_Cells
( n : natural; mix : Vector; t : Triangulation )
return Mixed_Subdivision is
res,res_last : Mixed_Subdivision;
s : Simplex;
tmp : Triangulation;
begin
tmp := t;
while not Is_Null(tmp) loop
s := Head_Of(tmp);
exit when Is_Flat(s);
declare
mic : Mixed_Cell := Extract_Mixed_Cell(n,mix,s);
begin
if mic.nor /= null
then Append(res,res_last,mic);
end if;
end;
tmp := Tail_Of(tmp);
end loop;
return res;
end Extract_non_Flat_Mixed_Cells;
procedure Deflate ( n : natural; l : in out List ) is
tmp : List := l;
begin
while not Is_Null(tmp) loop
declare
pt : Link_to_Vector := Head_Of(tmp);
begin
Project(n,pt);
Set_Head(tmp,pt);
end;
tmp := Tail_Of(tmp);
end loop;
end Deflate;
procedure Deflate ( n : natural; mic : in out Mixed_Cell ) is
begin
Project(n,mic.nor);
for k in mic.pts'range loop
Deflate(n,mic.pts(k));
end loop;
end Deflate;
procedure Deflate ( n : natural; mixsub : in out Mixed_Subdivision ) is
tmp : Mixed_Subdivision := mixsub;
begin
while not Is_Null(tmp) loop
declare
mic : Mixed_Cell := Head_Of(tmp);
begin
Deflate(n,mic);
Set_Head(tmp,mic);
end;
tmp := Tail_Of(tmp);
end loop;
end Deflate;
end Cayley_Embedding;