[BACK]Return to gfan.sm1 CVS log [TXT][DIR] Up to [local] / OpenXM / src / kan96xx / Doc

Diff for /OpenXM/src/kan96xx/Doc/gfan.sm1 between version 1.5 and 1.6

version 1.5, 2004/09/16 06:16:44 version 1.6, 2004/09/30 07:39:42
Line 1 
Line 1 
 %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.4 2004/09/15 07:41:59 takayama Exp $  %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.5 2004/09/16 06:16:44 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
   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %% Two examples are given below to get a global Grobner fan and
   %% a local Grobner fan ; cone.sample and cone.sample2
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%  Global Grobner Fan
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %% How to input data?  An example.   (cf. test13.sm1)
   %%  Modify the following or copy the /cone.sample { ... } def
   %%  to your own file,
   %%  edit it, and execute if by  " cone.sample ; "
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   /cone.sample {
     cone.load.cohom
   % write a comment about the problem.  "nl" means new line.
   /cone.comment [
     (Toric ideal for 1-simplex x 2-simplex, in k[x]) nl
   ] cat def
   
   % List of variables
   % If cone.type=1, then (H) should be added.
   /cone.vlist [(x11) (x12) (x13) (x21) (x22) (x23)
                (Dx11) (Dx12) (Dx13) (Dx21) (Dx22) (Dx23) (h)] def
   
   % List of variables in the form for define_ring.
   /cone.vv (x11,x12,x13,x21,x22,x23) def
   
   % If cone.type=0, then  x,Dx,
   % If cone.type=1, then  x,Dx,h,H    (Doubly homogenized)
   % If cone.type=2, then  x,Dx,h
   /cone.type 2 def
   
   % Set how to parametrize the weight space.
   % In the example below, 6 means the number of variables x11,x12,x13,x21,x22,x33
   %   p q parametrizeSmallFan  (p >= q) : Enumerate Grobner cones in the Small
   %                                       Grobner fan.
   %                                       The weights for the last p-q variables
   %                                       are 0.
   %     Example. 6 2 parametrizeSmallFan   weights for x12,x21,x22,x23 are 0.
   %
   %   p q parametrizeTotalFan  (p = q = number of variables in cone.vv)
   %                             p > q has not yet been implemented.
   %
   /cone.parametrizeWeightSpace {
     6 6 parametrizeSmallFan
   } def
   
   % If you want to enumerate Grobner cones in local order (i.e., x^e <= 0),
   % then  cone.local = 1  else cone.local = 0.
   /cone.local 0 def
   
   % Initial value of the weight in the weight space of which dimension is
   % cone.m
   % If it is null, then a random weight is used.
   /cone.w_start
     null
   def
   
   % If cone.h0=1, then the weight for h is 0.
   % It is usally set to 1.
   /cone.h0 1 def
   
   % Set input polynomials which generate the ideal.
   % Input must be homogenized.
   %    (see also data/test14.sm1 for double homogenization.)
   /cone.input
     [
       (x11 x22 - x12 x21)
       (x12 x23 - x13 x22)
       (x11 x23 - x13 x21)
     ]
   def
   
   % Set a function to compute Grobner basis.
   %  cone.gb_Dh   : For computing in Homogenized Weyl algebra h[1,1](D).
   %  cone.gb_DhH  : For computing in doubly homogenized Weyl algebra.
   %                  ( Computation in ^O and h[0,1](^D) need this
   %                    as the first step.  /cone.local  1 def )
   /cone.gb {
     cone.gb_Dh
   } def
   
   
   cone.comment message
   (cone.input = ) message
   cone.input message
   %%%% Step 1.  Enumerating the Grobner Cones in a global ring.
   %%%%   The result is stored in cone.fan
   getGrobnerFan
   
   %%%% If you want to print the output, then uncomment.
   printGrobnerFan
   
   %%%% If you want to save the data to the file sm1out.txt, then uncomment.
   % /cone.wightGblist 1 def saveGrobnerFan /ff set ff output
   
   %%%% Step 2. Dehomogenize the Grobner Cones
   %%%%  by the equivalence relation in a local ring (uncomment).
   % dhCones_h
   
   %%%% Generate the final data dhcone2.fan (a list of local Grobner cones.)
   % dhcone.rtable
   
   %%%%  Output dhcone2.fan with explanations
   % dhcone.printGrobnerFan
   
   } def
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %% End of " How to input data?  An example. "
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   
   
   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%  Local Grobner Fan
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %% How to input data?  The example 2 (cf. test14.sm1).
   %%  Modify the following or copy the /cone.sample2 { ... } def
   %%  to your own file,
   %%  edit it, and execute if by  " cone.sample2 ; "
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   /cone.sample2 {
     cone.load.cohom
   % write a comment about the problem.  "nl" means new line.
   /cone.comment [
     (BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl
     (The Grobner cones are dehomogenized to get local Grobner fan.) nl
   ] cat def
   
   % List of variables
   % If cone.type=1, then (H) should be added.
   /cone.vlist [(t1) (t2) (x) (y) (Dt1) (Dt2) (Dx) (Dy) (h) (H)] def
   
   % List of variables in the form for define_ring.
   /cone.vv (t1,t2,x,y) def
   
   % If cone.type=0, then  x,Dx,
   % If cone.type=1, then  x,Dx,h,H    (Doubly homogenized)
   % If cone.type=2, then  x,Dx,h
   /cone.type 1 def
   
   % Set how to parametrize the weight space.
   % In the example below, 6 means the number of variables x11,x12,x13,x21,x22,x33
   %   p q parametrizeSmallFan  (p >= q) : Enumerate Grobner cones in the Small
   %                                       Grobner fan.
   %                                       The weights for the last p-q variables
   %                                       are 0.
   %     Example. 6 2 parametrizeSmallFan   weights for x12,x21,x22,x23 are 0.
   %
   %   p q parametrizeTotalFan  (p = q = number of variables in cone.vv)
   %                             p > q has not yet been implemented.
   %
   /cone.parametrizeWeightSpace {
     4 2 parametrizeSmallFan
   } def
   
   % If you want to enumerate Grobner cones in local order (i.e., x^e <= 0),
   % then  cone.local = 1  else cone.local = 0.
   /cone.local 1 def
   
   % Initial value of the weight in the weight space of which dimension is
   % cone.m
   % If it is null, then a random weight is used.
   /cone.w_start
     null
   def
   
   % If cone.h0=1, then the weight for h is 0.
   % It is usally set to 1.
   /cone.h0 1 def
   
   % Set input polynomials which generate the ideal.
   % Input must be homogenized.
   %    (see also data/test14.sm1 for double homogenization.)
   /cone.input
     [
       (t1-y) (t2 - (y-(x-1)^2))
       ((-2 x + 2)*Dt2+Dx)
       (Dt1+Dt2+Dy)
     ]
   def
   % homogenize
     [cone.vv ring_of_differential_operators
      [[(t1) -1 (t2) -1 (Dt1) 1 (Dt2) 1]] ecart.weight_vector
     0] define_ring
     dh.begin
     cone.input { . homogenize toString } map /cone.input set
     dh.end
   
   % Set a function to compute Grobner basis.
   %  cone.gb_Dh   : For computing in Homogenized Weyl algebra h[1,1](D).
   %  cone.gb_DhH  : For computing in doubly homogenized Weyl algebra.
   %                  ( Computation in ^O and h[0,1](^D) need this
   %                    as the first step.  /cone.local  1 def )
   /cone.gb {
     cone.gb_DhH
   } def
   
   cone.comment message
   (cone.input = ) message
   cone.input message
   %%%% Step 1.  Enumerating the Grobner Cones in a global ring.
   %%%%   The result is stored in cone.fan
   getGrobnerFan
   
   %%%% If you want to print the output, then uncomment.
   printGrobnerFan
   
   %%%% If you want to save the data to the file sm1out.txt, then uncomment.
   % /cone.wightGblist 1 def saveGrobnerFan /ff set ff output
   
   %%%% Step 2. Dehomogenize the Grobner Cones
   %%%%  by the equivalence relation in a local ring (uncomment).
   dhCones_h
   
   %%%% Generate the final data dhcone2.fan (a list of local Grobner cones.)
   dhcone.rtable
   
   %%%%  Output dhcone2.fan with explanations
   dhcone.printGrobnerFan
   
   } def
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %% End of " How to input data?  The example 2. "
   %% Do not touch below.
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   
   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   
   [(parse) (cgi.sm1) pushfile] extension
   
   % If you use local polymake, then comment out.
   % If you use the cgi/polymake on the net, then uncomment out.
   %/doPolymake {doPolymake.OoHG} def
   
   % My setting.
   [(getenv) (HOST)] extension /cone.hostname set
   cone.hostname tag 0 eq { /cone.hostname (?) def }  { } ifelse
   cone.hostname (orange2.math.sci.kobe-u.ac.jp) eq
   cone.hostname (orange2-clone.math.sci.kobe-u.ac.jp) eq
   or
   {
      (Using doPolymake.OoHG ) message
      /doPolymake {doPolymake.OoHG} def
   } {  } ifelse
   
 /cone.debug 1 def  /cone.debug 1 def
   
 /ox.k0.loaded boundp {  /ox.k0.loaded boundp {
Line 10 
Line 263 
  [(parse) (ox.sm1) pushfile] extension   [(parse) (ox.sm1) pushfile] extension
 } ifelse  } ifelse
   
   /cone.load.cohom {
    /cone.loaded boundp { }
    {
     [(parse) (cohom.sm1) pushfile] extension
     [(parse) (cone.sm1) pushfile] extension
     [(parse) (dhecart.sm1) pushfile] extension
     /cone.loaded 1 def
     oxNoX polymake.start  (  ) message
    } ifelse
   } def
   
   %% Usages:  cone.gb_DhH.  h H (double homogenized) $BMQ$N(B GB.
   %%   dhecart.sm1 $B$r(B load $B$7$F$"$k$3$H(B. $BF~NO$OF1<!$G$J$$$H$$$1$J$$(B.
   %% [cone.vv ring_of_differential_operators
   %%  [[(t1) -1 (t2) -1 (Dt1) 1 (Dt2) 1]] ecart.weight_vector
   %%  0] define_ring
   %%   dh.begin  homogenize dh.end $B$J$I$NJ}K!$GF1<!2=$G$-$k(B.
   /cone.gb_DhH {
     /arg2 set /arg1 set
     [/ff /ww] pushVariables
     [
        /ff arg1 def
        /ww arg2 def
        /dh.gb.verbose 1 def
        /dh.autoHomogenize 0 def
        [(AutoReduce) 1] system_variable
        [ff { toString } map cone.vv
         [ww cone.vv generateD1_1]] dh.gb 0 get /arg1 set
     ] pop
     arg1
   } def
   
 %  %
 % cone.fan, cone.gblist $B$K(B fan $B$N%G!<%?$,$O$$$k(B.  % cone.fan, cone.gblist $B$K(B fan $B$N%G!<%?$,$O$$$k(B.
 %  %
   %%%%<<<<  $B=i4|%G!<%?$N@_DjNc(B. $BF|K\8lHG(B  data/test13 $B$h$j(B.  <<<<<<<<<<<<<<
 %%%%<<<<  $B=i4|%G!<%?$N@_DjNc(B  data/test13 $B$h$j(B.  <<<<<<<<<<<<<<  /cone.sample.test13.ja {
 /cone.sample.test13 {  
  /cone.loaded boundp { }   /cone.loaded boundp { }
  {   {
   [(parse) (cohom.sm1) pushfile] extension    [(parse) (cohom.sm1) pushfile] extension
Legend:
Removed from v.1.5  
changed lines
  Added in v.1.6
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>