===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v
retrieving revision 1.9
retrieving revision 1.10
diff -u -p -r1.9 -r1.10
--- OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw	2020/02/25 02:21:53	1.9
+++ OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw	2020/10/27 02:44:16	1.10
@@ -1,4 +1,4 @@
-/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.8 2019/09/13 05:21:33 takayama Exp $ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.9 2020/02/25 02:21:53 takayama Exp $ */
 
 /*&C
 @c DO NOT EDIT THIS FILE   
@@ -1165,6 +1165,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
 @item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})
 @item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})
+@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
 ::  
 @end table
 
@@ -1196,6 +1197,8 @@ sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
 are for distributed polynomials.
 @item When the arguments are two, the function mod_reduction is called. It uses the ring
 structure saved in the global variable ring_var in the ox_sm1 server.
+@item The return value of reduction_verbose is of the form
+[r,c0,[c1,...,cm],[g1,...gm],init,order] where init is the initial of r and order is the order structure used.
 @end itemize
 */
 /*&ja
@@ -1206,6 +1209,7 @@ structure saved in the global variable ring_var in the
 @item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
 @item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})
 @item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})
+@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})
 ::  
 @end table
 
@@ -1240,6 +1244,8 @@ sm1.reduction_d(P,F,G) および sm1.reduction_noH_
 @item 引数が２つの時は mod_reduction 関数が呼ばれる. これは ox_sm1 の大域変数 
 ring_var 変数に保存された ring において簡約を行う. auto_reduce(1) が自動でセットされる.
 gb を参照.
+@item reduction_verbose の戻り値は
+[r,c0,[c1,...,cm],[g1,...gm],init,order] ここで init は 順序 order による r の initial.
 @end itemize
 */
 /*&C
@@ -1258,6 +1264,27 @@ gb を参照.
 [[0,0,0],-1,[[x^2+1,0,0],[1,0,0]],[[-x^2-x-1,x+1,0],[x^2+1,0,-1]]]
 @end example
 */
+
+/*&C
+@example
+XM_debug=0$
+sm1.auto_reduce(1)$
+F=[x*y-1,x^2+y^2-4]$
+Weight_vec=[[x,10,y,1]]$  
+printf("\n\nsyz----\n")$
+S=sm1.syz([F,[x,y],Weight_vec]);  // When Weight_vec is given, the TOP order is used.
+// If the Weight_vec is not given, the POT order (e.g., (1,0,0)<(0,1,0)<(0,0,1)) with grlex is used.
+Sgb=sm1.gb([S[0],[x,y],Weight_vec]);
+R0=[x+y,x^2*y+x];
+P=R0[0]*F[0]+R0[1]*F[1];
+R=sm1.reduction_verbose([R0,Sgb[0],[x,y],Weight_vec]);
+
+printf("\nMinimal representation=%a\n",R[0])$
+printf("The initial of minimal rep=%a\n",R[4])$
+printf("Order=%a\n",R[5][1][1])$
+@end example
+*/
+
 /*&en
 @table @t
 @item Reference