| version 1.17, 2009/09/04 11:13:11 |
version 1.20, 2018/05/02 02:28:13 |
|
|
| % $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.16 2009/09/04 02:59:55 takayama Exp $ |
% $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.19 2013/10/11 01:08:35 takayama Exp $ |
| % cp cone.sm1 $OpenXM_HOME/src/kan96xx/Doc/gfan.sm1 |
% cp cone.sm1 $OpenXM_HOME/src/kan96xx/Doc/gfan.sm1 |
| % $Id$ |
% $Id$ |
| % iso-2022-jp |
% iso-2022-jp |
|
|
| [ |
[ |
| (gfan.sm1 is a package to compute global and local Grobner fans.) |
(gfan.sm1 is a package to compute global and local Grobner fans.) |
| (See R.Bahloul and N.Takayama, arxiv, math.AG/0412044 and references as to algorithms.) |
(See R.Bahloul and N.Takayama, arxiv, math.AG/0412044 and references as to algorithms.) |
| (At the beginning of gfan.sm1, there are sample inputs cone.sample and cone.sample2.) |
(At the beginning of the source code gfan.sm1, there are sample inputs cone.sample and cone.sample2.) |
| ( ) |
( ) |
| (gfan.sm1 works only with polymake 2.0. We provides a web service of computing ) |
(gfan.sm1 works only with polymake 2.0. We provide a web service of computing ) |
| (with polymake 2.0. /@@@polymake.web 1 def is set by default in gfan.sm1.) |
(with polymake 2.0. /@@@polymake.web 1 def is set by default in gfan.sm1.) |
| (See changelog-ja.tex as to details on the difference between 2.0 and later versions.) |
(See changelog-ja.tex as to details on the difference between 2.0 and later versions.) |
| ( ) |
( ) |
| ( cone.Wt cone.Lpt {vertices in the output} are weights on the rays of the Grobner cone.) |
(*cone.sample ; is an example. See the source code. The state polytope is the hexagon.) |
| ( cone.L gives a basis of the linearity space.) |
( ) |
| |
(*cone.Wt cone.Lpt {vertices in the output} are weights on the rays of the Grobner cone.) |
| |
(*cone.L gives a basis of the linearity space.) |
| |
(*cone.Lp gives a basis of the pointed cone. cone.Lpt is the transpose of cone.Lp.) |
| |
$*When v is a row vector in an ouput cone, (v cone.Lp cone.W) gives $ |
| |
( the corresponding weight vector in the full variable space in D) |
| |
(*cone.incidence is a list of [[cone num1,facet num1], [cone num2,facet num2]]) |
| |
( which means that cone num1 and cone num2 are adjacent and shares ) |
| |
( the facet num1 and the facet num2) |
| |
(*/cone.withGblist 1 def saves the Grobner basis standing for each cone.) |
| |
( ) |
| |
(*Cone descriptions: cone.fan) |
| |
(**A facet is given by its normal vector n of a cone. It gives facet num of the cone.) |
| |
(**A cone is defined by facet normal vectors n1, n2, ... as n1.x>=0 and n2.x >=0 and ...) |
| |
(**facetsv is a list of facets expressed by generators.) |
| |
(**nextcid is a list of the adjacent cone numbers.) |
| |
(**nextfid is a list of the shared facet numbers.) |
| |
(**vertices is the generators of a cone.) |
| |
(**inequalities are not necessarily unique.) |
| ] |
] |
| ] putUsages |
] putUsages |
| |
|
|
|
| cone.comment message |
cone.comment message |
| (cone.input = ) message |
(cone.input = ) message |
| cone.input message |
cone.input message |
| |
%%% Step 0. If you want to output Grobner basis standing for each cone, then uncomment |
| |
% /cone.withGblist 1 def |
| |
|
| %%%% Step 1. Enumerating the Grobner Cones in a global ring. |
%%%% Step 1. Enumerating the Grobner Cones in a global ring. |
| %%%% The result is stored in cone.fan |
%%%% The result is stored in cone.fan |
| getGrobnerFan |
getGrobnerFan |
|
|
| printGrobnerFan |
printGrobnerFan |
| |
|
| %%%% If you want to save the data to the file sm1out.txt, then uncomment. |
%%%% If you want to save the data to the file sm1out.txt, then uncomment. |
| % /cone.withGblist 1 def saveGrobnerFan /ff set ff output |
%saveGrobnerFan /ff set ff output |
| |
|
| %%%% Step 2. Dehomogenize the Grobner Cones |
%%%% Step 2. Dehomogenize the Grobner Cones |
| %%%% by the equivalence relation in a local ring (uncomment). |
%%%% by the equivalence relation in a local ring (uncomment). |
| Line 273 dhcone.printGrobnerFan |
|
| Line 294 dhcone.printGrobnerFan |
|
| or |
or |
| { |
{ |
| (Polymake is not installed in this system or @@@polymake.web is set.) message |
(Polymake is not installed in this system or @@@polymake.web is set.) message |
| /doPolymake {doPolymake.OoHG} def |
usePolymake.OoHG.curl |
| (Using doPolymake.OoHG ) message |
(Using doPolymake.OoHG.curl ) message |
| /polymake.start {polymake.start.OoHG} def |
} { usePolymake.local (Local polymake will be used.) message } ifelse |
| (Using polymake.start.OoHG ) message |
|
| } { (Local polymake will be used.) message } ifelse |
|
| |
|
| /cone.debug 1 def |
/cone.debug 1 def |
| |
|
|
|
| /printGrobnerFan { |
/printGrobnerFan { |
| [/i] pushVariables |
[/i] pushVariables |
| [ |
[ |
| |
$(gfan) usage to find explanations on variables.$ message |
| (========== Grobner Fan ====================) message |
(========== Grobner Fan ====================) message |
| [ |
[ |
| (cone.comment) |
(cone.comment) |
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to gfan.sm1 CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / kan96xx / Doc