[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 1.8 and 1.9

version 1.8, 2004/10/13 23:36:52 version 1.9, 2005/06/30 08:39:39
Line 1 
Line 1 
 %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.7 2004/09/30 07:45:04 takayama Exp $  %  $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.8 2004/10/13 23:36:52 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
   
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %% Two examples are given below to get a global Grobner fan and  %% Two examples are given below to get a global Grobner fan and
Line 12 
Line 13 
 %% How to input data?  An example.   (cf. test13.sm1)  %% How to input data?  An example.   (cf. test13.sm1)
 %%  Modify the following or copy the /cone.sample { ... } def  %%  Modify the following or copy the /cone.sample { ... } def
 %%  to your own file,  %%  to your own file,
 %%  edit it, and execute if by  " cone.sample ; "  %%  edit it, and execute it by  " cone.sample ; "
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 /cone.sample {  /cone.sample {
   cone.load.cohom    cone.load.cohom
Line 96  getGrobnerFan
Line 97  getGrobnerFan
 printGrobnerFan  printGrobnerFan
   
 %%%% 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.wightGblist 1 def saveGrobnerFan /ff set ff output  % /cone.withGblist 1 def saveGrobnerFan /ff set ff output
   
 %%%% 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 213  getGrobnerFan
Line 214  getGrobnerFan
 printGrobnerFan  printGrobnerFan
   
 %%%% 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.wightGblist 1 def saveGrobnerFan /ff set ff output  % /cone.withGblist 1 def saveGrobnerFan /ff set ff output
   
 %%%% 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 290  dhcone.printGrobnerFan 
Line 291  dhcone.printGrobnerFan 
      /dh.autoHomogenize 0 def       /dh.autoHomogenize 0 def
      [(AutoReduce) 1] system_variable       [(AutoReduce) 1] system_variable
      [ff { toString } map cone.vv       [ff { toString } map cone.vv
       [ww cone.vv generateD1_1]] dh.gb 0 get /arg1 set        [ww cone.vv generateD1_1]] ff getAttributeList setAttributeList
        dh.gb 0 get /arg1 set
   ] pop    ] pop
     popVariables
   arg1    arg1
 } def  } def
   
Line 2027  def
Line 2030  def
     [(AutoReduce) 1] system_variable      [(AutoReduce) 1] system_variable
     [cone.vv ring_of_differential_operators      [cone.vv ring_of_differential_operators
      [ww] weight_vector 0] define_ring       [ww] weight_vector 0] define_ring
     [ff {toString .} map] groebner 0 get /gg set      [ff {toString .} map] ff getAttributeList setAttributeList
       groebner 0 get /gg set
     /cone.gb_Dh.g gg def      /cone.gb_Dh.g gg def
     /arg1 gg def      /arg1 gg def
   ] pop    ] pop
Line 2323  def   
Line 2327  def   
 } def  } def
   
 %<  %<
 % usages: getNextFlip [cone, k]  % usages: getNextFlip [cone, k, cid]
 % cone.fan $B$r8!:w$7$F(B $B$^$@(B flip $B$7$F$J$$(B cone $B$H(B facet $B$NAH$rLa$9(B.  % cone.fan $B$r8!:w$7$F(B $B$^$@(B flip $B$7$F$J$$(B cone $B$H(B facet $B$NAH$rLa$9(B.
 % $B$b$&$J$$$H$-$K$O(B null $B$rLa$9(B.  % $B$b$&$J$$$H$-$K$O(B null $B$rLa$9(B.
   % cid $B$O(B cone $B$,(B cone.fan $B$N(B $B2?HVL\$G$"$k$+$N(B index.  cone.gblist $B$N8!:wEy$K(B
   % $BMQ$$$k(B.
 %>  %>
 /getNextFlip {  /getNextFlip {
   [/tcone /ans /ii ] pushVariables    [/tcone /ans /ii /cid] pushVariables
   [    [
     /ans null def      /ans null def /cid -1 def
     0 1 cone.fan length 1 sub {      0 1 cone.fan length 1 sub {
       /ii set        /ii set
       cone.fan  ii get /tcone set        cone.fan  ii get /tcone set
         /cid ii def
       tcone getNextFacet /ans set        tcone getNextFacet /ans set
       ans tag 0 eq { } { exit } ifelse        ans tag 0 eq { } { exit } ifelse
     } for      } for
     ans tag 0 eq { /arg1 null def }      ans tag 0 eq { /arg1 null def }
     { /arg1 [tcone ans] def } ifelse      { /arg1 [tcone ans cid] def } ifelse
   ] pop    ] pop
   popVariables    popVariables
   arg1    arg1
Line 2348  def   
Line 2355  def   
 %   flip $B$N;~$N(B epsilon  %   flip $B$N;~$N(B epsilon
 /cone.epsilon (1).. (10).. div def  /cone.epsilon (1).. (10).. div def
 /cone.epsilon.limit (1).. (100).. div def  /cone.epsilon.limit (1).. (100).. div def
   % cone.epsilon.limit $B$rIi$K$9$l$PDd;_$7$J$$(B.
   
 %<  %<
 %  Usages: result_getNextFlip getNextCone ncone  %  Usages: result_getNextFlip getNextCone ncone
Line 3412  def   
Line 3420  def   
 %  %
   
 % Todo: save functions.  % Todo: save functions.
   
   %<
   % Collart, Kalkbrener, Mall $B$N%"%k%4%j%:%`$K$h$k(B gb $B$N(B flip.
   % See also Sturmfels' book, p.22, 23.
   % Usages: [reducedGb, vlist, oldWeight, facetWeight, newWeight] ckmFlip rGb
   %  If it fails, then it returns null, else it returns the reducedGb for the
   %  newWeight.
   %  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
   %  reducedGb $B$OJ8;zNs$N%j%9%H$G$O$J$/B?9`<0$N7A<0$N$3$H(B.
   %>
   /ckmFlip {
     /arg1 set
     [/arg_ckmFlip /gOld /vlist /oldWeight /facetWeight /newWeight
      /gNew
      /ww /ww1 /ww2  % $BK\$NCf$N(B w1, w, w2  ($B8E$$(B, facet, $B?7$7$$(B)
      /ch1 /ch2      % $BK\$NCf$N(B {\cal H}_1, {\cal H}_2
      /grData  /rTable
      /rTable2 % rTable $B$NH?BP$NJQ49(B.
      /facetWeight_gr /vlist_gr  % graded ring $BMQ(B.
      /oldWeight_gr
      /ccf  % reduction $B$7$?78?t(B.
      /rwork /ccf2 /gNew
     ] pushVariables
     [
       arg1 /arg_ckmFlip set
       arg_ckmFlip 0 get /gOld set
       arg_ckmFlip 1 get /vlist set
       arg_ckmFlip 2 get /oldWeight set
       arg_ckmFlip 3 get /facetWeight set
       arg_ckmFlip 4 get /newWeight set
   
   % facet weight vector ww $B$K$D$$$F$N(B initial $B$r<h$j=P$9(B. ch1 $B$X$$$l$k(B.
       gOld getRing ring_def
       facetWeight weightv /ww set
       gOld { ww init } map /ch1 set  % facetWeight $B$K$h$k(B initial $B$N<h$j=P$7(B.
   
   
   %  $BNc(B: [(x,y) [(x) -1 (Dx) 1 (y) -1 (Dy) 2]] getGrRing
   %      [$x,y,y',$ , [    $x$ , $y$ ]  , [    [    $Dy$ , $y'$ ]  ]  ]
   %       $BJQ?t%j%9%H(B                            $BCV49I=(B
   %  ch1 $B$r(B gr_ww $B$N85$KJQ49(B.
       [vlist facetWeight] getGrRing /grData set
       [grData 0 get ring_of_differential_operators 0]  define_ring /rwork set
       grData 2 get { { . } map } map /rTable set
       rTable { reverse } map /rTable2 set
       grData 0 get /vlist_gr set
       ch1 { toString . rTable replace toString } map /ch1 set
   
       oldWeight { dup isString { . rTable replace toString }
                                  { } ifelse } map /oldWeight_gr set
   
   % facetWeight $B$b(B $B?7$7$$4D(B gr_ww  $B$N(B weight $B$KJQ49(B.
   % $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2]
       facetWeight { dup isString { . rTable replace toString }
                                  { } ifelse } map /facetWeight_gr set
   % Dx x = x Dx + h H  or Dx x = x Dx + h^2 $B$G7W;;(B.
   % $B$I$A$i$r$H$k$+$O(B cone.gb_gr $B$G6hJL$9$k$7$+$J$7(B
       %% [ch1 vlist_gr oldWeight_gr] /ttt set
       %% ttt cone.gb_gr /ch1 set %$B:FEY$N7W;;$OITMW(B.
       [[(1)] vlist_gr oldWeight_gr] cone.gb_gr getRing ring_def % Set Ring.
       ch1 {toString .} map  /ch1 set
   %% $B$3$3$^$G$G$H$j$"$($:%F%9%H$r$7$h$&(B.
   %%    ch1 /arg1 set
   % newWeight $B$b(B $B?7$7$$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
   
   % 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.reduction_gr $B$G6hJL$9$k$7$+$J$7(B
       ch1 getRing ring_def ;
       ch2 {toString .} map {ch1 cone.reduction} map /ccf set
       %ccf pmat
       % $B$H$j$"$($:%F%9%H(B.
       % [ch1 ch2] /arg1 set
       %% ccf[i][0] $B$O(B 0 $B$G$J$$$HL7=b(B.  check $B$^$@$7$F$J$$(B.
   
       %% ccf[i][2] (syzygy) $B$r(B gr $B$+$i(B $B$b$H$N(B ring $B$XLa$7(B,
       %% $B?7$7$$(B reduced gbasis $B$r(B ccf[i][2] * gOld $B$G:n$k(B.
       rwork ring_def
       ccf { 2 get {toString  . rTable2 replace toString} map } map /ccf2 set
       %% ccf2 $B$O(B gr $B$G$J$$(B ring $B$N85(B.
       gOld getRing ring_def
       cone.beginH  % Hh $B$+(B h^2 $B$+(B.
       ccf2 { {.} map gOld mul } map /gNew set
       gNew { toString } map /gNew set
       cone.endH
       % gNew /arg1 set
       %gNew $B$,(B newWeight $B$G$N(B GB $B$+(B check. Yes $B$J$i(B reduced basis $B$X(B.
       %No $B$J$i(B null $B$rLa$9(B.
       gNew [(gbCheck) 1] setAttributeList newWeight
          cone.gb (gb) getAttribute
       1 eq {
        gNew [(reduceOnly) 1] setAttributeList newWeight cone.gb /arg1 set
       }{ /arg1 null def } ifelse
     ] pop
     popVariables
     arg1
   } def
   
   %<
   % Usages: f gbasis cone.reduction_DhH
   %>
   /cone.reduction_DhH {
     /arg2 set /arg1 set
     [/ff /ggbasis /eenv /ans] pushVariables
     [
       /ff arg1 def /ggbasis arg2 def
       cone.beginH
       ff ggbasis reduction /ans set
       cone.endH
       /arg1 ans def
     ] pop
     popVariables
     arg1
   } def
   
   /cone.begin_DhH {
     [(Homogenize) (AutoReduce) (KanGBmessage)] pushEnv /cone.eenv set
     [(Homogenize) 3] system_variable
   } def
   
   /cone.end_DhH {
     cone.eenv popEnv
   } def
   
   /test1.ckmFlip {
    % cf. cone.sample2
      cone.load.cohom
    /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
    /cone.vlist [(t1) (t2) (x) (y) (Dt1) (Dt2) (Dx) (Dy) (h) (H)] def
    /cone.vv (t1,t2,x,y) def
    /cone.type 1 def
    /cone.parametrizeWeightSpace {
      4 2 parametrizeSmallFan
    } def
    /cone.local 1 def
    /cone.w_start  null def
    /cone.h0 1 def
    /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
   
    /cone.gb {
      cone.gb_DhH
    } def
   
    /cone.reduction {
      cone.reduction_DhH
    } def
   
    /cone.beginH {
      cone.begin_DhH
    } def
    /cone.endH {
      cone.end_DhH
    } def
   % $B%F%9%H$r3+;O$9$k(B.
    /cone.gb_gr {
     /arg1 set
     [/ff /ww /vv] pushVariables
     [
        /ff arg1 0 get def
        /vv arg1 1 get def
        /ww arg1 2 get def
        /dh.gb.verbose 1 def
        /dh.autoHomogenize 0 def
        [(AutoReduce) 1] system_variable
        [ff { toString } map vv
         [ww vv generateD1_1]] dh.gb 0 get /arg1 set
     ] pop
     popVariables
     arg1
    } def
   
   % getStartingCone /cone.ncone set
   % cone.ncone updateFan
   % cone.gblist 0 get message
   % cone.ncone /cone.ccone set
   % getNextFlip /cone.nextflip set
   % cone.nextflip message
   
    /wOld  [(t1) , -29 , (t2) , -38 , (Dt1) , 29 , (Dt2) , 38 ]  def
    /wFacet [(t1) , -1 , (t2) , -1 , (Dt1) , 1 , (Dt2) , 1 ]  def
    /wNew  [(t1) , -39 , (t2) , -38 , (Dt1) , 39 , (Dt2) , 38 ]  def
    cone.input wOld cone.gb /ff set
    [ff (t1,t2,x,y) wOld wFacet wNew] ckmFlip /ff2 set
    (See ff and ff2) message
   
   } def
Legend:
Removed from v.1.8  
changed lines
  Added in v.1.9
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>