===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/hol.sm1,v
retrieving revision 1.19
retrieving revision 1.20
diff -u -p -r1.19 -r1.20
--- OpenXM/src/kan96xx/Doc/hol.sm1	2004/06/03 08:10:44	1.19
+++ OpenXM/src/kan96xx/Doc/hol.sm1	2004/06/10 06:01:50	1.20
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.18 2004/05/15 12:00:48 takayama Exp $
+% $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.19 2004/06/03 08:10:44 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.
@@ -1864,6 +1864,43 @@ message-quiet
   arg1
 } def
 
+/gb.reduction_noh {
+  /arg2 set
+  /arg1 set
+  [/in-gb.reduction_noh /gbasis /flist /ans /gbasis2
+  ] pushVariables
+  [(CurrentRingp) (KanGBmessage) (Homogenize)] pushEnv
+  [
+     /gbasis arg2  def
+     /flist  arg1  def
+     gbasis 0 get tag 6 eq { }
+     { (gb.reduction_noh: 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
+     [(Homogenize) 0] system_variable
+     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 )]
@@ -1894,6 +1931,20 @@ message-quiet
   $ [[( 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
+
+[(gb.reduction_noh)
+[ (f basis gb.reduction_noh 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.)
+  (cf. gb.reduction, gb )
+  $Example:$
+  $ [[( 2*Dx + 1 ) ( 2*Dy + 1 )] $
+  $   (x,y) [[(Dx) 1 (Dy) 1]]] /ggg set $
+  $ ((1-x-y)^2*Dx*Dy) ggg gb.reduction_noh :: $
 ]] putUsages
 
 ( ) message-quiet ;