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

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Diff for /OpenXM/src/kan96xx/Doc/ecart.sm1 between version 1.28 and 1.29

-version 1.28, 2004/05/27 11:13:49
+version 1.29, 2004/05/28 08:11:31
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- % $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.27 2004/05/15 12:00:48 takayama Exp $
+ % $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.28 2004/05/27 11:13:49 takayama Exp $
  %[(parse) (hol.sm1) pushfile] extension
  %[(parse) (appell.sm1) pushfile] extension
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    $ [[( 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
+ /ecartd.reduction_noh {
+   /arg2 set
+   /arg1 set
+   [/in-ecarth.reduction_noh /gbasis /flist] pushVariables
+   [(Homogenize)] pushEnv
+   [
+      /gbasis arg2  def
+      /flist  arg1  def
+      [(Homogenize) 0] system_variable
+      flist gbasis ecartd.reduction /arg1 set
+   ] pop
+   popEnv
+   popVariables
+   arg1
+ } def
+ [(ecartd.reduction_noh)
+ [ (f basis ecartd.reduction_noh 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 and)
+   (it should not contain the variable h.  cf. dehomogenize)
+   $h[0,1](D)-homogenization is NOT used.$
+   (cf. reduction, ecartd.gb, ecartd.reduction )
+   $Example:$
+   $ [[( 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]]] /ggg set $
+   $ (Dx+Dy) ggg ecartd.reduction_noh :: $
  ]] putUsages
  /ecart.stdOrder {

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