| version 1.15, 2009/09/04 00:53:48 |
version 1.20, 2018/05/02 02:28:13 |
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| % $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.14 2009/08/26 05:03:49 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 |
| %%Ref: @s/2004/08/21-note.pdf |
%%Ref: @s/2004/08/21-note.pdf |
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%% gfan.sm1 works only for polymake 2.0 Use webservice of 2.0. |
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[(gfan) |
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[ |
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(gfan.sm1 is a package to compute global and local Grobner fans.) |
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(See R.Bahloul and N.Takayama, arxiv, math.AG/0412044 and references as to algorithms.) |
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(At the beginning of the source code gfan.sm1, there are sample inputs cone.sample and cone.sample2.) |
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( ) |
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(gfan.sm1 works only with polymake 2.0. We provide a web service of computing ) |
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(with polymake 2.0. /@@@polymake.web 1 def is set by default in gfan.sm1.) |
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(See changelog-ja.tex as to details on the difference between 2.0 and later versions.) |
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( ) |
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(*cone.sample ; is an example. See the source code. The state polytope is the hexagon.) |
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( ) |
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(*cone.Wt cone.Lpt {vertices in the output} are weights on the rays of the Grobner cone.) |
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(*cone.L gives a basis of the linearity space.) |
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(*cone.Lp gives a basis of the pointed cone. cone.Lpt is the transpose of cone.Lp.) |
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$*When v is a row vector in an ouput cone, (v cone.Lp cone.W) gives $ |
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( the corresponding weight vector in the full variable space in D) |
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(*cone.incidence is a list of [[cone num1,facet num1], [cone num2,facet num2]]) |
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( which means that cone num1 and cone num2 are adjacent and shares ) |
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( the facet num1 and the facet num2) |
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(*/cone.withGblist 1 def saves the Grobner basis standing for each cone.) |
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( ) |
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(*Cone descriptions: cone.fan) |
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(**A facet is given by its normal vector n of a cone. It gives facet num of the cone.) |
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(**A cone is defined by facet normal vectors n1, n2, ... as n1.x>=0 and n2.x >=0 and ...) |
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(**facetsv is a list of facets expressed by generators.) |
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(**nextcid is a list of the adjacent cone numbers.) |
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(**nextfid is a list of the shared facet numbers.) |
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(**vertices is the generators of a cone.) |
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(**inequalities are not necessarily unique.) |
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] |
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] putUsages |
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| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| %% Two examples are given below to get a global Grobner fan and |
%% Two examples are given below to get a global Grobner fan and |
| %% a local Grobner fan ; cone.sample and cone.sample2 |
%% a local Grobner fan ; cone.sample and cone.sample2 |
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| cone.comment message |
cone.comment message |
| (cone.input = ) message |
(cone.input = ) message |
| cone.input message |
cone.input message |
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%%% Step 0. If you want to output Grobner basis standing for each cone, then uncomment |
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% /cone.withGblist 1 def |
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| %%%% 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 |
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| printGrobnerFan |
printGrobnerFan |
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| %%%% 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 |
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| %%%% 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 250 dhcone.printGrobnerFan |
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| Line 287 dhcone.printGrobnerFan |
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| % If you use the cgi/polymake on the net, then uncomment out. |
% If you use the cgi/polymake on the net, then uncomment out. |
| %/doPolymake {doPolymake.OoHG} def (Using doPolymake.OoHG ) message |
%/doPolymake {doPolymake.OoHG} def (Using doPolymake.OoHG ) message |
| %/polymake.start {polymake.start.OoHG} def (Using polymake.start.OoHG ) message |
%/polymake.start {polymake.start.OoHG} def (Using polymake.start.OoHG ) message |
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/@@@polymake.web 1 def |
| %% Choose it automatically. |
%% Choose it automatically. |
| [(which) (polymake)] oxshell tag 0 eq { |
[(which) (polymake)] oxshell tag 0 eq |
| (Polymake is not installed in this system.) message |
@@@polymake.web 1 eq |
| /doPolymake {doPolymake.OoHG} def |
or |
| (Using doPolymake.OoHG ) message |
{ |
| /polymake.start {polymake.start.OoHG} def |
(Polymake is not installed in this system or @@@polymake.web is set.) message |
| (Using polymake.start.OoHG ) message |
usePolymake.OoHG.curl |
| } { (Local polymake will be used.) message } ifelse |
(Using doPolymake.OoHG.curl ) message |
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} { usePolymake.local (Local polymake will be used.) message } ifelse |
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| /cone.debug 1 def |
/cone.debug 1 def |
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| rr (VERTICES) getNode tag 0 eq { |
rr (VERTICES) getNode tag 0 eq { |
| (internal error: VERTICES is not found.) error |
(internal error: VERTICES is not found.) error |
| } { } ifelse |
} { |
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rr (VERTICES) getNode |
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(UNDEF) getNode tag 0 eq { } |
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{ (internal error: VERTICES is UNDEF. See rr. Set /@@@polymake.web 1 def) error } ifelse |
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} ifelse |
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| /cone.getConeInfo.rr1 rr def |
/cone.getConeInfo.rr1 rr def |
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| /printGrobnerFan { |
/printGrobnerFan { |
| [/i] pushVariables |
[/i] pushVariables |
| [ |
[ |
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$(gfan) usage to find explanations on variables.$ message |
| (========== Grobner Fan ====================) message |
(========== Grobner Fan ====================) message |
| [ |
[ |
| (cone.comment) |
(cone.comment) |
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