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Diff for /OpenXM/src/kan96xx/Doc/gfan.sm1 between version 1.10 and 1.11

version 1.10, 2005/07/07 01:31:21 version 1.11, 2005/07/07 06:07:46
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 %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.9 2005/06/30 08:39:39 takayama Exp $  %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.10 2005/07/07 01:31:21 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
Line 17 
Line 17 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 /cone.sample {  /cone.sample {
   cone.load.cohom    cone.load.cohom
     /cone.ckmFlip  1 def
 % write a comment about the problem.  "nl" means new line.  % write a comment about the problem.  "nl" means new line.
 /cone.comment [  /cone.comment [
   (Toric ideal for 1-simplex x 2-simplex, in k[x]) nl    (Toric ideal for 1-simplex x 2-simplex, in k[x]) nl
Line 129  printGrobnerFan 
Line 130  printGrobnerFan 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 /cone.sample2 {  /cone.sample2 {
   cone.load.cohom    cone.load.cohom
     /cone.ckmFlip  1 def
 % write a comment about the problem.  "nl" means new line.  % write a comment about the problem.  "nl" means new line.
 /cone.comment [  /cone.comment [
   (BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl    (BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl
Line 2384  def   
Line 2386  def   
 %  Usages: result_getNextFlip getNextCone ncone  %  Usages: result_getNextFlip getNextCone ncone
 %  flip $B$7$F?7$7$$(B ncone $B$rF@$k(B.  %  flip $B$7$F?7$7$$(B ncone $B$rF@$k(B.
 %>  %>
 /getNextCone {  /getNextCone.orig {
  /arg1 set   /arg1 set
  [/ncone /ccone /kk /w /next_weight_w_wv] pushVariables   [/ncone /ccone /kk /w /next_weight_w_wv] pushVariables
  [   [
Line 3453  def   
Line 3455  def   
 %  gb $B$N(B check $B$r$d$k$N$G(B, $B$=$l$K<:GT$7$?$i(B null $B$rLa$9(B.  %  gb $B$N(B check $B$r$d$k$N$G(B, $B$=$l$K<:GT$7$?$i(B null $B$rLa$9(B.
 %  weight $B$O$9$Y$F(B vw $B7A<0$G(B. vw $B7A<0(B = variable weight $B$N7+$jJV$7$N7A<0(B  %  weight $B$O$9$Y$F(B vw $B7A<0$G(B. vw $B7A<0(B = variable weight $B$N7+$jJV$7$N7A<0(B
 %  reducedGb $B$OJ8;zNs$N%j%9%H$G$O$J$/B?9`<0$N7A<0$N$3$H(B.  %  reducedGb $B$OJ8;zNs$N%j%9%H$G$O$J$/B?9`<0$N7A<0$N$3$H(B.
   %   $BM}M3$O(B reducedGb $B$h$j(B ring $B$N9=B$$rFI$`$?$a(B.
 %>  %>
 /ckmFlip {  /ckmFlip {
   /arg1 set    /arg1 set
Line 3499  def   
Line 3502  def   
 % $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2]  % $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2]
     facetWeight { dup isString { . rTable replace toString }      facetWeight { dup isString { . rTable replace toString }
                                { } ifelse } map /facetWeight_gr set                                 { } ifelse } map /facetWeight_gr set
   
   % newWeight $B$b(B $B?7$7$$4D(B gr_ww  $B$N(B weight $B$KJQ49(B.
   % $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2]
       newWeight { dup isString { . rTable replace toString }
                                  { } ifelse } map /newWeight_gr set
   
 % Dx x = x Dx + h H  or Dx x = x Dx + h^2 $B$G7W;;(B.  % Dx x = x Dx + h H  or Dx x = x Dx + h^2 $B$G7W;;(B.
 % $B$I$A$i$r$H$k$+$O(B cone.gb_gr $B$G6hJL$9$k$7$+$J$7(B  % $B$I$A$i$r$H$k$+$O(B cone.gb_gr $B$G6hJL$9$k$7$+$J$7(B
     %% [ch1 vlist_gr oldWeight_gr] /ttt set      %% [ch1 vlist_gr oldWeight_gr] /ttt set
Line 3507  def   
Line 3516  def   
     ch1 {toString .} map  /ch1 set      ch1 {toString .} map  /ch1 set
 %% $B$3$3$^$G$G$H$j$"$($:%F%9%H$r$7$h$&(B.  %% $B$3$3$^$G$G$H$j$"$($:%F%9%H$r$7$h$&(B.
 %%    ch1 /arg1 set  %%    ch1 /arg1 set
 % newWeight $B$b(B $B?7$7$$4D(B gr_ww  $B$N(B weight $B$KJQ49(B.  
 % $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2]  
     newWeight { dup isString { . rTable replace toString }  
                                { } ifelse } map /newWeight_gr set  
     [ch1 { toString } map vlist_gr newWeight_gr] cone.gb_gr /ch2 set      [ch1 { toString } map vlist_gr newWeight_gr] cone.gb_gr /ch2 set
   
 % Dx x = x Dx + h H  or Dx x = x Dx + h^2 $B$G7W;;(B.  % Dx x = x Dx + h H  or Dx x = x Dx + h^2 $B$G7W;;(B.
Line 3625  def   
Line 3630  def   
 %>  %>
 /cone.gb_gr_Dh {  /cone.gb_gr_Dh {
   /arg1 set    /arg1 set
   [/ff /ww /vv] pushVariables    [/ff /ww /vv /gg /envtmp] pushVariables
   [    [
      /ff arg1 0 get def       /ff arg1 0 get def
      /vv arg1 1 get def       /vv arg1 1 get def
      /ww arg1 2 get def       /ww arg1 2 get def
      /gb.verbose 1 def  
      /gb.autoHomogenize 0 def       [(AutoReduce) (KanGBmessage)] pushEnv /envtmp set
      [(AutoReduce) 1] system_variable       [(AutoReduce) 1] system_variable
      [ff { toString } map vv       [(KanGBmessage) 1] system_variable
       [ww vv generateD1_1]] gb 0 get /arg1 set       [vv ring_of_differential_operators
      /gb.autoHomogenize 1 def       [ww] weight_vector 0] define_ring
        [ff {toString .} map] ff getAttributeList setAttributeList
        groebner 0 get /gg set
        envtmp popEnv
   
        /arg1 gg def
   ] pop    ] pop
   popVariables    popVariables
   arg1    arg1
Line 3710  def   
Line 3720  def   
  [ff (t1,t2,x,y) wOld wFacet wNew] ckmFlip /ff2 set   [ff (t1,t2,x,y) wOld wFacet wNew] ckmFlip /ff2 set
  (See ff and ff2) message   (See ff and ff2) message
   
   } def
   
   %<
   % Usages: cone i getaVectorOnFacet
   % cone $B$N(B i $BHVL\$N(B facet $B$N>e$N(B vector $B$r5a$a$k(B.
   % cf. liftWeight
   %>
   /getaVectorOnFacet {
     /arg2 set /arg1 set
     [/cone /facet_i /ep /vp /v /v /ii] pushVariables
     [
       /cone arg1 def /facet_i arg2 def
       facet_i to_int32 /facet_i set
   
       cone (facetsv) getNode 2 get facet_i get /v set
       /vp v 0 get def
       1 1 v length 1 sub {
         /ii set
         vp v ii get  add /vp set
       } for
       vp nnormalize_vec /vp set
       /arg1 vp def
     ] pop
     popVariables
     arg1
   } def
   
   /getNextCone {
     getNextCone_ckm
   } def
   
   %<
   %  Usages: result_getNextFlip getNextCone_ckm ncone
   %  flip $B$7$F?7$7$$(B ncone $B$rF@$k(B.  Collar-Kalkbrener-Moll $B$N%"%k%4%j%:%`$r;H$&(B
   %  if (cone.ckmFlip == 0) $BIaDL$N7W;;(B else CKM.
   %>
   /getNextCone_ckm {
    /arg1 set
    [/ncone /ccone /kk /w /next_weight_w_wv /cid /ttt] pushVariables
    [
     /ccone arg1 def
     /ncone null def
     /kk ccone 1 get def  % kk $B$O(B cid $BHVL\$N(B cone $B$N(B kk $BHVL\$N(B facet $B$rI=$9(B.
     /cid ccone 2 get def % cid $B$O(B cone $B$N(B $BHV9f(B.
     ccone 0 get /ccone set
     {
      ccone tag 0 eq { exit } {  } ifelse
   
   % ccone $B$N(B kk $BHVL\$N(B facet $B$K$D$$$F(B flip $B$9$k(B.
      ccone kk cone.epsilon flipWeight  /w set
      (Trying new weight is ) messagen w message
      w liftWeight /next_weight_w_wv set
      (Trying new weight [w,wv] is ) messagen next_weight_w_wv message
   
      cone.ckmFlip {
       [
        cone.gblist cid get (grobnerBasis) getNode 2 get % reduce gb
        cone.vv
        cone.gblist cid get (weight) getNode [2 0 2] get % weight
        ccone kk getaVectorOnFacet liftWeight 1 get  % weight on facet
        next_weight_w_wv 1 get  % new weight
       ] /ttt set
        ttt message
        ttt ckmFlip /cone.cgb set
      }{
        cone.input next_weight_w_wv 1 get cone.gb /cone.cgb set
      } ifelse
   
     cone.cgb tag 0 eq not {
      [w] next_weight_w_wv join /cone.cgb_weight set
      next_weight_w_wv 1 get cone.cgb coneEq /cone.g_ineq set
      cone.g_ineq cone.w_ineq join cone.Wt mul cone.Lpt mul
      pruneZeroVector /cone.gw_ineq_projectedWtLpt set
   
      (cone.gw_ineq_projectedWtLpt is obtained.) message
   
      cone.gw_ineq_projectedWtLpt getConeInfo /cone.nextConeInfo set
   % $B<!85$rD4$Y$k(B.  $B$@$a$J$i(B retry
      cone.nextConeInfo 0 get 0 get to_int32 cone.d eq {
        cone.nextConeInfo 1 get newCone /ncone set
        ccone ncone getCommonFacet 0 get {
          (Flip succeeded.) message
          exit
        } { } ifelse
      } { } ifelse
   % common face $B$,$J$1$l$P(B $B$d$O$j(B epsilon $B$r>.$5$/(B.
      cone.nextConeInfo 0 get 0 get to_int32 cone.d eq {
       (ccone and ncone do not have a common facet.) message
      } {
       (ncone is not maximal dimensional. ) message
      } ifelse
     }{ } ifelse
   
      (Decreasing epsilon to ) messagen
      cone.epsilon (1).. (2).. div mul /cone.epsilon set
        cone.epsilon cone.epsilon.limit sub numerator (0).. lt {
          (Too small cone.epsilon ) error
        }  {  } ifelse
      cone.epsilon message
     } loop
     /arg1 ncone def
    ] pop
    popVariables
    arg1
 } def  } def
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