===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/gfan.sm1,v
retrieving revision 1.4
retrieving revision 1.8
diff -u -p -r1.4 -r1.8
--- OpenXM/src/kan96xx/Doc/gfan.sm1	2004/09/15 07:41:59	1.4
+++ OpenXM/src/kan96xx/Doc/gfan.sm1	2004/10/13 23:36:52	1.8
@@ -1,8 +1,259 @@
-%  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.3 2004/09/14 08:30:47 takayama Exp $
+%  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.7 2004/09/30 07:45:04 takayama Exp $
 % cp cone.sm1 $OpenXM_HOME/src/kan96xx/Doc/gfan.sm1
-% $Id: gfan.sm1,v 1.4 2004/09/15 07:41:59 takayama Exp $
+% $Id: gfan.sm1,v 1.8 2004/10/13 23:36:52 takayama Exp $
 % 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    (Using doPolymake.OoHG ) message 
+%/polymake.start {polymake.start.OoHG} def (Using polymake.start.OoHG ) message 
+%% Choose it automatically.
+[(which) (polymake)] oxshell tag 0 eq {
+  (Polymake is not installed in this system.)  message
+  /doPolymake {doPolymake.OoHG} def    
+  (Using doPolymake.OoHG ) message 
+  /polymake.start {polymake.start.OoHG} def 
+  (Using polymake.start.OoHG ) message 
+} { (Local polymake will be used.) message } ifelse
+
 /cone.debug 1 def
 
 /ox.k0.loaded boundp {
@@ -10,12 +261,45 @@
  [(parse) (ox.sm1) pushfile] extension
 } ifelse
 
+/cone.load.cohom {
+ /cone.loaded boundp { }
+ {
+  [(parse) (cohom.sm1) pushfile] extension
+%  [(parse) (cone.sm1) pushfile] extension   % BUG? cone.sm1 overrides a global
+                                             % in cohom.sm1?
+  [(parse) (dhecart.sm1) pushfile] extension
+  /cone.loaded 1 def
+  oxNoX 
+  polymake.start  (  ) message
+ } ifelse
+} def
+
+%% Usages:  cone.gb_DhH.  h H (double homogenized) 用の GB.
+%%   dhecart.sm1 を load してあること. 入力は同次でないといけない.
+%% [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 などの方法で同次化できる.
+/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 に fan のデータがはいる.
 %
-
-%%%%<<<<  初期データの設定例  data/test13 より.  <<<<<<<<<<<<<<
-/cone.sample.test13 {
+%%%%<<<<  初期データの設定例. 日本語版  data/test13 より.  <<<<<<<<<<<<<<
+/cone.sample.test13.ja {
  /cone.loaded boundp { }
  {
   [(parse) (cohom.sm1) pushfile] extension
@@ -2935,9 +3219,9 @@ def   
        [(cones) [ ] cones] arrayToTree
        [(facets) [ ] facets] arrayToTree
        [(merged) [ ] merged] arrayToTree
-       [(nextcid) [ ] merged] arrayToTree
-       [(nextfid) [ ] merged] arrayToTree
-       [(coneid) [ ] merged] arrayToTree
+       [(nextcid) [ ] nextcid] arrayToTree
+       [(nextfid) [ ] nextfid] arrayToTree
+       [(coneid) [ ] coneid] arrayToTree
      ] 
    ] arrayToTree /arg1 set
   ] pop
@@ -2970,4 +3254,161 @@ def   
   dhcone.fan
 } def
 
-% Todo: print, save functions.  Representative of weight & init.
+%<
+% Usages: dhcone.rtable
+% dhcone の番号と cone の番号の 置換表を生成し dhcone2.fan (merge した cone の情報)
+% を dhcone.fan から作る. dhcone2.gblist も作る補助関数.
+% dhCones_h してから dhcone.rable する.
+%>
+/dhcone.rtable {
+  [/i /j /vv /cones /facets /facets2 /merged /nextcid /nextcid2 /ii /ww] pushVariables
+  [
+% 置換表 dhcone.h2dh を作る.
+    /dhcone.h2dh cone.fan length newVector.with-1 def
+    0 1 , dhcone.fan length 1 sub {
+      /i set
+      dhcone.fan i get , (cones) getNode 2 get /vv set
+      0 1 vv length 1 sub {
+        /j set
+        dhcone.h2dh , vv j get , i to_univNum , put
+      } for
+    } for
+% merge した dhcone を整理したもの, dhcone2.fan を作る.
+    /dhcone2.fan dhcone.fan length newVector def
+    0 1 , dhcone.fan length 1 sub {
+      /i set
+      dhcone.fan i get (facets) getNode 2 get /facets set
+      dhcone.fan i get (merged) getNode 2 get /merged set
+      dhcone.fan i get (nextcid) getNode 2 get /nextcid set
+      dhcone.fan i get (cones) getNode 2 get /cones set
+      /facets2 [ ] def
+      /nextcid2 [ ] def
+      0 1 , facets length 1 sub {
+         /j set
+         merged j get , (3).. eq {
+            facets2 [ facets j get ] join /facets2 set
+% となりの cone があるとき 変換表にしたがい, cone 番号を変換
+            nextcid2 [ dhcone.h2dh , nextcid j get , get ] join /nextcid2 set
+         } {  } ifelse
+         merged j get , (2).. eq {
+            facets2 [ facets j get ] join /facets2 set
+% 境界のとき -2 を入れる.
+            nextcid2 [ (-2).. ] join /nextcid2 set
+         } { } ifelse
+      } for
+
+      dhcone2.fan i ,
+      [(dhcone) [ ]
+       [
+         [(facets) [ ] facets2] arrayToTree
+         [(nextcid) [ ] nextcid2] arrayToTree
+         [(cones) [ ] cones] arrayToTree
+       ] 
+      ] arrayToTree , put
+
+    } for
+
+% 最後に dhcone2.gblist を作る.
+    /dhcone2.gblist , dhcone2.fan length newVector , def
+    0 1 , dhcone2.fan length 1 sub {
+      /i set
+      dhcone2.fan i get (cones) getNode 2 get /cones set
+      cone.grGblist , cones 0 get , get , /ii set % GB of initial (H->1).
+      cone.gblist i get , (weight) getNode , [ 2 0 2 ] get  /ww set
+
+      dhcone2.gblist i,
+      [(gbasis) [ ]
+       [
+         [(initial) [ ] ii] arrayToTree
+         [(weight) [ ] ww] arrayToTree
+       ] 
+      ] arrayToTree , put
+      
+    } for
+    (dhcone2.fan, dhcone2.gblist, dhcone.h2dh are set.) message
+
+  ] pop
+  popVariables
+} def
+
+%<
+% 表の見方の解説を印刷する関数.
+% Usages: dhcone.explain
+%>
+/dhcone.explain {
+  [
+    ( ) nl 
+    (Data format in << dhcone2.fan >>, which is a dehomogenized Grobner fan.) nl nl
+    (<< cone.vlist >> is the list of the variables.) nl
+    @@@.Hsymbol  ( is the homogenization variable to be dehomogenized.) nl nl
+    (<< cone.input >> is generators of a given ideal.) nl nl
+    (<< cone.d >> is the dimension of parametrization space of the weights P_w) nl
+    (    P_w is a cone in R^m  where the number m is stored in << cone.m >>) nl
+    (    P_w --- W --->  R^n [weight space].  ) nl
+    (    W is stored in << cone.W >> ) nl 
+    (    << u   cone.W  mul >> gives the weight vector standing for u) nl nl
+    (All cones in the data lie in the weight parametrization space P_w.) nl
+    ( "facets" are the inner normal vector of the cone. )  nl
+    ( "nextcid" is a list of the cone id's of the adjacent cones.) nl
+    (   -2 in "nextcid" means that this facet lies on the border of the weight space.) nl
+    ( "cones" is a list of the cone id's of the NON-dehomonized Grobner fan) nl
+    (                                               stored in << cone.fan >>) nl
+  ] cat 
+} def
+
+%<
+%  dhcone.printGrobnerFan
+%  dhcone の印刷関数
+%>
+/dhcone.printGrobnerFan {
+  [/i] pushVariables
+  [
+  (==========  Grobner Fan (for dehomogenized cones) ============) message
+   [
+      (cone.comment)
+      (cone.vlist) (cone.vv)
+      (cone.input)
+      (cone.type)  (cone.local) (cone.h0)
+      (cone.n) (cone.m) (cone.d) 
+      (cone.W) (cone.Wpos) (cone.Wt)
+      (cone.L) (cone.Lp) (cone.Lpt)
+      (cone.weightBorder)
+      (cone.incidence)
+   ] { printGrobnerFan.1 } map
+   (   ) message
+   (The number of cones = ) messagen dhcone.fan length message
+   (   ) message
+   0 1 dhcone2.fan length 1 sub {
+     /ii set
+     ii messagen ( : ) messagen
+     dhcone2.fan ii get printTree
+   } for
+   1 {
+    0 1 dhcone2.gblist length 1 sub {
+      /ii set
+      ii messagen ( : ) messagen
+      dhcone2.gblist ii get printTree
+    } for
+  } {  } ifelse
+
+
+  (=========================================) message
+  %(cone.withGblist = ) messagen cone.withGblist message
+  dhcone.explain message
+  (  ) message
+  ] pop
+  popVariables
+} def
+
+%
+% 試し方  test14, 22, 25
+%
+%  (data/test14.sm1) run (data/test14-data.sm1) run
+%   printGrobnerFan ;  % H 付きで印刷.
+%   dhCones_h ;   %  dehomogenize Cones.
+%   dhcone.rtable ; % dhcone2.fan 等を生成.
+%   dhcone.printGrobnerFan ; % 印刷.
+%   印刷したものは  test*-print.txt へ格納してある.
+%  
+
+% Todo: save functions.