OpenXM/src/kan96xx/Doc/gfan.sm1 - diff

Return to gfan.sm1 CVS log

Up to [local] / OpenXM / src / kan96xx / Doc

Diff for /OpenXM/src/kan96xx/Doc/gfan.sm1 between version 1.12 and 1.20

version 1.12, 2005/07/07 07:53:37

version 1.20, 2018/05/02 02:28:13

Line 1

% $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.11 2005/07/07 06:07:46 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

% $Id$

% iso-2022-jp

%%Ref: @s/2004/08/21-note.pdf

%% gfan.sm1 works only for polymake 2.0 Use webservice of 2.0.

[(gfan)

[

(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.)

(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 provide a web service of computing )

(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.)

( )

(*cone.sample ; is an example. See the source code. The state polytope is the hexagon.)

( )

(*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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Two examples are given below to get a global Grobner fan and

%% a local Grobner fan ; cone.sample and cone.sample2

Line 91 def

Line 125 def

cone.comment 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.

%%%% The result is stored in cone.fan

getGrobnerFan

Line 99 getGrobnerFan

Line 136 getGrobnerFan

printGrobnerFan

%%%% 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

%%%% by the equivalence relation in a local ring (uncomment).

Line 250 dhcone.printGrobnerFan

Line 287 dhcone.printGrobnerFan

% If you use the cgi/polymake on the net, then uncomment out.

%/doPolymake {doPolymake.OoHG} def (Using doPolymake.OoHG ) message

%/polymake.start {polymake.start.OoHG} def (Using polymake.start.OoHG ) message

/@@@polymake.web 1 def

%% 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

(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

} { usePolymake.local (Local polymake will be used.) message } ifelse

/cone.debug 1 def

Line 1020 def

Line 1059 def

/getConeInfo {

/arg1 set

[/ww /g /ceq /ceq2 /cdim /mmc /mmL /rr /ineq /ppt] pushVariables

[/ww /g /ceq /ceq2 /cdim /mmc /mmL /rr /ineq /ppt /rr0 /mm0 /mm1] pushVariables

[

/ceq arg1 def

ceq pruneZeroVector /ceq set

ceq length 0 eq {

(Monomial ideal is not accepted as an input.) cone_ir_input

} { } ifelse

/mm1

( Use [(keep_tmp_files) 1] oxshell to check the input to polymake2tfb. See /tmp or $TMP )

def

ceq genPo2 /ceq2 set

% ceq2 $B$O(B polymake.data(polymake.INEQUALITIES(...)) $B7A<0(B

% polymake $B$G(B ceq2 $B$N<!85$N7W;;(B.

/getConeInfo.ceq ceq def /getConeInfo.ceq2 ceq2 def

cone.debug { (Calling polymake DIM.) message } { } ifelse

[(DIM) ceq2] doPolymake 1 get /rr set

[(DIM) ceq2] doPolymake /rr0 set

% rr0 2 get message

rr0 2 get 1 get 0 get /mm0 set

mm0 length 0 eq { }

{ [mm0 mm1] cat error } ifelse

rr0 1 get /rr set

cone.debug {(Done.) message } { } ifelse

% test5 $B$K$O<!$N%3%a%s%H$H$j$5$k(B. $B>e$N9T$r%3%a%s%H%"%&%H(B.

% test5.data tfbToTree /rr set

Line 1045 def

Line 1098 def

% FACETS $B$r;}$C$F$$$J$$$J$i:FEY7W;;$9$k(B.

% POINTED, NOT__POINTED $B$bF@$i$l$k(B

cone.debug { (Calling polymake FACETS.) message } { } ifelse

[(FACETS) ceq2] doPolymake 1 get /rr set

[(FACETS) ceq2] doPolymake /rr0 set

% rr0 2 get message

rr0 2 get 1 get 0 get /mm0 set

mm0 length 0 eq { }

{ [mm0 mm1] cat error } ifelse

rr0 1 get /rr set

cone.debug { (Done.) message } { } ifelse

} { } ifelse

rr (VERTICES) getNode tag 0 eq {

(internal error: VERTICES is not found.) error

} { } ifelse

} {

rr (VERTICES) getNode

(UNDEF) getNode tag 0 eq { }

{ (internal error: VERTICES is UNDEF. See rr. Set /@@@polymake.web 1 def) error } ifelse

} ifelse

/cone.getConeInfo.rr1 rr def

Line 1621 def

Line 1685 def

/vlist arg1 def

/wlist arg2 def

wlist length vlist length eq {

} { (cone_wtowv: length of the argument must be the same.) error} ifelse

} { (cone_wtowv: length of the argument must be the same. Please check the values of cone.vlist cone.vv cone.type parametrizeWeightSpace) error} ifelse

wlist to_int32 /wlist set

[

Line 1878 def

Line 1942 def

% note: 2004.9.2

cone (facetsv) getNode 2 get facet_i get /v set

cone (facets) getNode 2 get facet_i get /f set

v length 0 eq {

(The codimension of the linarity space of the Grobner cone seems to be 1 or 0.) cone_ir_input

} { } ifelse

/vp v 0 get def

1 1 v length 1 sub {

/ii set

Line 2732 def

Line 2801 def

/printGrobnerFan {

[/i] pushVariables

[

$(gfan) usage to find explanations on variables.$ message

(========== Grobner Fan ====================) message

[

(cone.comment)

Line 3843 def

Line 3913 def

] pop

popVariables

arg1

} def

%%change

/cone_ir_input {

/arg1 set

[/msg ] pushVariables

[

/msg arg1 def

(---------------) message

msg message

( ) message

(Please also refer to the value of the variables cone.getConeInfo.rr0) message

( cone.getConeInfo.rr1 cone.Lp cone.cinit) message

$ cone.cinit (FACETS) getNode :: $ message

(We are sorry that we cannot accept this input.) error

] pop

popVariables

} def

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>