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

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Diff for /OpenXM/src/kan96xx/Doc/hol.sm1 between version 1.14 and 1.16

-version 1.14, 2004/05/04 07:48:47
+version 1.16, 2004/05/04 08:29:35
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- % $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.13 2003/07/29 08:36:39 takayama Exp $
+ % $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.15 2004/05/04 08:03:30 takayama Exp $
  %% hol.sm1, 1998, 11/8, 11/10, 11/14, 11/25, 1999, 5/18, 6/5. 2000, 6/8
  %% rank, rrank, characteristic
  %% This file is error clean.
 Line 1822  message-quiet
 Line 1822  message-quiet
 Line 1822  message-quiet
   $       [[(x Dx -h^2) (0)] [(Dx^2) (1)] [(Dx^3) (Dx)]] (x,y)] isSameIdeal_h $
  ]] putUsages
+ /gb.reduction {
+   /arg2 set
+   /arg1 set
+   [/in-gb.reduction /gbasis /flist /ans /gbasis2
+   ] pushVariables
+   [(CurrentRingp) (KanGBmessage)] pushEnv
+   [
+      /gbasis arg2  def
+      /flist  arg1  def
+      gbasis 0 get tag 6 eq { }
+      { (gb.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 gb 0 get getRing ring_def
+        /gbasis2 gbasis 0 get ,,, def
+      } ifelse
+      flist ,,, /flist set
+      flist tag 6 eq {
+        flist { gbasis2 reduction } map /ans set
+      }{
+        flist gbasis2 reduction /ans set
+      } ifelse
+      /arg1 ans def
+   ] pop
+   popEnv
+   popVariables
+   arg1
+ } def
+ /gb.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]]]
+   gb /gg set
+   ((h-x-y)*Dx) [gg 0 get] gb.reduction /gg2 set
+   gg2 message
+   (-----------------------------) message
+     [[( 2*(h-x-y) Dx + h^2 ) ( 2*(h-x-y) Dy + h^2 )]
+       (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set
+    ((h-x-y)*Dx) ggg gb.reduction /gg4 set
+    gg4 message
+   (-----------------------------) message
+   [gg2 gg4]
+ } def
+ [(gb.reduction)
+ [ (f basis gb.reduction r)
+   (f is reduced by basis by the normal form algorithm.)
+   (The first element of basis <g_1,...,g_m> must be a Grobner 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 gb.)
+   $h[1,1](D)-homogenization is used.$
+   (cf. reduction, gb, ecartd.gb, gb.reduction.test )
+   $Example:$
+   $ [[( 2*(h-x-y) Dx + h^2 ) ( 2*(h-x-y) Dy + h^2 )] $
+   $   (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set $
+   $ ((h-x-y)^2*Dx*Dy) ggg gb.reduction :: $
+ ]] putUsages
  ( ) message-quiet ;

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