===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/hol.sm1,v
retrieving revision 1.24
retrieving revision 1.28
diff -u -p -r1.24 -r1.28
--- OpenXM/src/kan96xx/Doc/hol.sm1	2005/06/23 03:23:26	1.24
+++ OpenXM/src/kan96xx/Doc/hol.sm1	2012/10/12 01:20:29	1.28
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.23 2005/06/16 08:40:04 takayama Exp $
+% $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.27 2012/09/16 01:53:08 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.
@@ -535,11 +535,11 @@ message-quiet
     %%% Enf of the preprocess
 
     groebnerOptions gb.options mergeGroebnerOptions /groebnerOptions set
-    gb.verbose { (groenberOptions = ) messagen groebnerOptions message } { } ifelse
+    gb.verbose { (groebnerOptions = ) messagen groebnerOptions message } { } ifelse
     termorder {
       f { {. dehomogenize} map } map /f set
       [(UseCriterion1) 1] system_variable
-      [f groenberOptions] groebner_sugar 0 get /gg set
+      [f groebnerOptions] groebner_sugar 0 get /gg set
       [(UseCriterion1) 0] system_variable
     }{
       f { {. dehomogenize} map} map /f set
@@ -817,6 +817,10 @@ message-quiet
   $Example 7: [ [( (x Dx)^2 + (y Dy)^2 + 1) ( x y Dx Dy -1)] (x,y) $
   $     [ [ (Dx) 1 ] ] ] [(gbCheck) 1] setAttributeList gb getAttributeList ::$
   (  )
+  $Example 8: /gb.options [(StopDegree) 11] def Onverbose $
+  $ [ [(x^10+y^10-1) (x^5*y^5 -1)] (x,y) $
+  $     [ [ (x) 1 ] ]]  gb pmat ; $
+  (  )
   (cf. gb, groebner, groebner_sugar, syz. )
 ]] putUsages
 
@@ -960,7 +964,11 @@ message-quiet
        ggall 0 gtmp put
     }{  } ifelse
 
-    gg getRing (oxRingStructure) dc /gb.oxRingStructure set
+    gg length 0 eq {  % there is no syzygy
+       ggall getRing (oxRingStructure) dc /gb.oxRingStructure set
+    }{
+     gg getRing (oxRingStructure) dc /gb.oxRingStructure set
+    } ifelse
 
     /arg1 [gg dehomogenize ggall] def
   ] pop
@@ -1064,6 +1072,10 @@ message-quiet
   (Example 5: [((x1+x2+x3)(x1 x2 + x2 x3 + x1 x3) - t x1 x2 x3 ) )
   (            (t,x1,x2,x3) -1 -2] annfs :: )
   (           Note that the example 4 uses huge memory space.)
+  (   )
+  (Note: This implementation is stable but obsolete. )
+  (As to faster implementation, we refer to ann0 and ann of Risa/Asir )
+  (Visit  http://www.math.kobe-u.ac.jp/Asir )
 ]] putUsages
 ( annfs ) messagen-quiet
 /annfs.verbose fs.verbose def