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

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Diff for /OpenXM/src/kan96xx/Doc/ecart.sm1 between version 1.18 and 1.20

-version 1.18, 2003/09/30 00:06:56
+version 1.20, 2004/05/04 08:03:30
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- % $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.17 2003/09/20 22:10:04 takayama Exp $
+ % $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.19 2004/04/29 12:04:45 takayama Exp $
  %[(parse) (hol.sm1) pushfile] extension
  %[(parse) (appell.sm1) pushfile] extension
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    (       No automatic homogenization.)
    $  [(degreeShift) ds (noAutoHomogenize) 1 (sugar) 1] -->use the sugar strate $
    (  )
-   $cf. ecarth.gb (homogenized),  ecartd.gb (dehomogenize) $
+   $cf. ecarth.gb (homogenized),  ecartd.gb (dehomogenize), ecartd.reduction $
    ( )
    $Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $
    $             [ [ (Dx) 1 ] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $
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  } def
  %% end of for ecart.define_ring
+ /ecartd.reduction {
+   /arg2 set
+   /arg1 set
+   [/in-ecartd.reduction /gbasis /flist /ans /gbasis2] pushVariables
+   [(CurrentRingp) (KanGBmessage)] pushEnv
+   [
+      /gbasis arg2  def
+      /flist  arg1  def
+      gbasis 0 get tag 6 eq { }
+      { (ecartd.reduction: the second argument must be a list of lists) error }
+      ifelse
+      gbasis length 1 eq {
+        gbasis getRing ring_def
+        /gbasis2 gbasis 0 get def
+      } {
+        [ [(1)] ] gbasis rest join ecartd.gb 0 get getRing ring_def
+        /gbasis2 gbasis 0 get ,,, def
+      } ifelse
+      ecartd.begin
+      flist ,,, /flist set
+      flist tag 6 eq {
+        flist { gbasis2 reduction } map /ans set
+      }{
+        flist gbasis2 reduction /ans set
+      } ifelse
+      /arg1 ans def
+      ecartd.end
+   ] pop
+   popEnv
+   popVariables
+   arg1
+ } def
+ /ecartd.reduction.test {
+   [
+     [( 2*(1-x-y) Dx + 1 ) ( 2*(1-x-y) Dy + 1 )]
+     (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]]
+   ecartd.gb /gg set
+   (Dx) [gg 0 get] ecartd.reduction /gg2 set
+   gg2 message
+   (-----------------------------) message
+   [(Dx) (Dy) (Dx+x*Dy)] [gg 0 get] ecartd.reduction /gg3 set
+   gg3 message
+   (-----------------------------) message
+     [[( 2*(1-x-y) Dx + h ) ( 2*(1-x-y) Dy + h )]
+       (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set
+    (Dx) ggg ecartd.reduction /gg4 set
+    gg4 message
+   [gg2  gg3 gg4]
+ } def
+ /ecarth.reduction {
+   /arg2 set
+   /arg1 set
+   [/in-ecarth.reduction /gbasis /flist /ans /gbasis2] pushVariables
+   [(CurrentRingp) (KanGBmessage)] pushEnv
+   [
+      /gbasis arg2  def
+      /flist  arg1  def
+      gbasis 0 get tag 6 eq { }
+      { (ecarth.reduction: the second argument must be a list of lists) error }
+      ifelse
+      gbasis length 1 eq {
+        gbasis getRing ring_def
+        /gbasis2 gbasis 0 get def
+      } {
+        [ [(1)] ] gbasis rest join ecarth.gb 0 get getRing ring_def
+        /gbasis2 gbasis 0 get ,,, def
+      } ifelse
+      ecarth.begin
+      flist ,,, /flist set
+      flist tag 6 eq {
+        flist { gbasis2 reduction } map /ans set
+      }{
+        flist gbasis2 reduction /ans set
+      } ifelse
+      /arg1 ans def
+      ecarth.end
+   ] pop
+   popEnv
+   popVariables
+   arg1
+ } def
+ [(ecartd.reduction)
+ [ (f basis ecartd.reduction r)
+   (f is reduced by basis by the tangent cone algorithm.)
+   (The first element of basis <g_1,...,g_m> must be a standard basis.)
+   (r is the return value format of reduction.)
+   (r=[h,c0,syz,input], h = c0 f + \sum syz_i g_i)
+   (basis is given in the argument format of ecartd.gb.)
+   (cf. reduction, ecartd.gb, ecartd.reduction.test )
+   $Example:$
+   $ [[( 2*(1-x-y) Dx + h ) ( 2*(1-x-y) Dy + h )] $
+   $   (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set $
+   $ (Dx+Dy) ggg ecartd.reduction :: $
+ ]] putUsages
  ( ) message-quiet

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