===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave,v
retrieving revision 1.1
retrieving revision 1.5
diff -u -p -r1.1 -r1.5
--- OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2001/07/11 01:00:23	1.1
+++ OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2002/08/11 08:39:47	1.5
@@ -1,4 +1,4 @@
-/*$OpenXM$ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.4 2002/07/14 13:14:37 takayama Exp $ */
 
 /*&C-texi
 @c DO NOT EDIT THIS FILE   oxphc.texi
@@ -69,12 +69,7 @@ cohomology groups.
 /*&C-texi
 @example
 
-This is Risa/Asir, Version 20000126.
-Copyright (C) FUJITSU LABORATORIES LIMITED.
-1994-1999. All rights reserved.
-xm version 20000202. Copyright (C) OpenXM Developing Team. 2000.
-ox_help(0); ox_help("keyword"); ox_grep("keyword"); for help message 
-Loading ~/.asirrc
+@include opening.texi
 
 [283] sm1_deRham([x*(x-1),[x]]);
 [1,2]
@@ -407,13 +402,13 @@ def sm1(P,F) {
 /*&jp-texi
 @table @t
 @item $B;2>H(B
-    @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}. 
+    @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}. 
 @end table
 */
 /*&eg-texi
 @table @t
 @item Reference
-    @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}. 
+    @code{sm1_start}, @code{ox_push_int0}, @code{sm1_push_poly0}, @code{Sm1_proc}. 
 @end table
 */
 
@@ -768,7 +763,7 @@ def sm1_isListOfVar(A) {
 @findex sm1_gb
 @findex sm1_gb_d
 @table @t
-@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p})
+@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r})
 ::  computes the Grobner basis of @var{f} in the ring of differential
 operators with the variable @var{v}.
 @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})
@@ -780,7 +775,7 @@ The result will be returned as a list of distributed p
 @table @var
 @item return
 List
-@item p
+@item p, q, r
 Number
 @item f, v, w
 List
@@ -808,6 +803,14 @@ List
    When a non-term order is given, the Grobner basis is computed in 
    the homogenized Weyl algebra  (See Section 1.2 of the book of SST).
    The homogenization variable h is automatically added.
+@item
+   When the optional variable @var{q} is set, @code{sm1_gb} returns,
+   as the third return value, a list of
+   the Grobner basis and the initial ideal
+   with sums of monomials sorted by the given order.
+   Each polynomial is expressed as a string temporally for now.
+   When the optional variable @var{r} is set to one,
+   the polynomials are dehomogenized (,i.e., h is set to 1).
 @end itemize
 */
 /*&jp-texi
@@ -821,7 +824,7 @@ List
 @findex sm1_gb
 @findex sm1_gb_d
 @table @t
-@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p})
+@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q},dehomogenize=@var{r})
 ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B.
 @item sm1_gb_d([@var{f},@var{v},@var{w}]|proc=@var{p})
 ::  @var{v} $B>e$NHyJ,:nMQAG4D$K$*$$$F(B @var{f} $B$N%0%l%V%J4pDl$r7W;;$9$k(B. $B7k2L$rJ,;6B?9`<0$N%j%9%H$GLa$9(B.
@@ -830,7 +833,7 @@ List
 @table @var
 @item return
 $B%j%9%H(B
-@item p
+@item p, q, r
 $B?t(B
 @item f, v, w
 $B%j%9%H(B
@@ -856,6 +859,12 @@ List
 @item
    Term order $B$G$J$$=g=x$,M?$($i$l$?>l9g$O(B, $BF1<!2=%o%$%kBe?t$G%0%l%V%J4pDl$,7W;;$5$l$k(B (SST $B$NK\$N(B Section 1.2 $B$r8+$h(B).
 $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B.
+@item $B%*%W%7%g%J%kJQ?t(B @var{q} $B$,%;%C%H$5$l$F$$$k$H$-$O(B,
+    3 $BHVL\$NLa$jCM$H$7$F(B, $B%0%l%V%J4pDl$*$h$S%$%K%7%!%k$N%j%9%H$,(B
+    $BM?$($i$l$?=g=x$G%=!<%H$5$l$?%b%N%_%"%k$NOB$H$7$FLa$5$l$k(B.
+    $B$$$^$N$H$3$m$3$NB?9`<0$O(B, $BJ8;zNs$GI=8=$5$l$k(B.
+    $B%*%W%7%g%J%kJQ?t(B @var{r} $B$,%;%C%H$5$l$F$$$k$H$-$O(B,
+    $BLa$jB?9`<0$O(B dehomogenize $B$5$l$k(B ($B$9$J$o$A(B h $B$K(B 1 $B$,BeF~$5$l$k(B).
 @end itemize
 */
 /*&C-texi
@@ -922,6 +931,13 @@ $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 */
 /*&C-texi
 @example
+[294] F=sm1_gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1);
+      map(print,F[2][0])$
+      map(print,F[2][1])$
+@end example
+*/
+/*&C-texi
+@example
 [595]
    sm1_gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"],
              [x,y],[[dx,1,x,-1],[dy,1]]]);
@@ -1102,7 +1118,7 @@ mode. So, it is strongly recommended to execute the co
 @table @t
 @item Reference
     @code{sm1_start}, @code{deRham} (sm1 command)
-@item Reference paper
+@item Algorithm:
     Oaku, Takayama, An algorithm for de Rham cohomology groups of the
     complement of an affine variety via D-module computation, 
     Journal of pure and applied algebra 139 (1999), 201--233.
@@ -1112,7 +1128,7 @@ mode. So, it is strongly recommended to execute the co
 @table @t
 @item $B;2>H(B
     @code{sm1_start}, @code{deRham} (sm1 command)
-@item $B;29MO@J8(B
+@item Algorithm:
     Oaku, Takayama, An algorithm for de Rham cohomology groups of the
     complement of an affine variety via D-module computation, 
     Journal of pure and applied algebra 139 (1999), 201--233.
@@ -2889,16 +2905,19 @@ of the system of differential equations @var{ii}
 along the hyperplane specified by
 the V filtration @var{v_filtration}.
 @item @var{v} is a list of variables.
-@item As to the algorithm,
-see "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
-How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
-Note that the signs of the slopes are negative, but the absolute values
-of the slopes are returned.
 @item The return value is a list of lists.
 The first entry of each list is the slope and the second entry
 is the weight vector for which the microcharacteristic variety is
 not bihomogeneous.
 @end itemize
+
+@noindent
+Algorithm:
+see "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
+How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
+Note that the signs of the slopes are negative, but the absolute values
+of the slopes are returned.
+
 */
 
 /*&jp-texi
@@ -2933,16 +2952,18 @@ not bihomogeneous.
 $BHyJ,J}Dx<07O(B @var{ii} $B$N(B V filtration  @var{v_filtration}
 $B$G;XDj$9$kD6J?LL$K1h$C$F$N(B (geomeric) slope $B$r7W;;$9$k(B.
 @item @var{v} $B$OJQ?t$N%j%9%H(B.
-@item $B;HMQ$7$F$$$k%"%k%4%j%:%`$K$D$$$F$O(B,
+@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B.
+$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B
+microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B.
+@end itemize
+
+@noindent
+Algorithm:
 "A.Assi, F.J.Castro-Jimenez and J.M.Granger,
 How to calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
 $B$r$_$h(B.
 Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, $B$3$N%W%m%0%i%`$O(B,
 Slope $B$N@dBPCM$rLa$9(B.
-@item $BLa$jCM$O(B, $B%j%9%H$r@.J,$H$9$k%j%9%H$G$"$k(B.
-$B@.J,%j%9%H$NBh(B 1 $BMWAG$,(B slope, $BBh(B 2 $BMWAG$O(B, $B$=$N(B weight vector $B$KBP1~$9$k(B
-microcharacteristic variety $B$,(B bihomogeneous $B$G$J$$(B.
-@end itemize
 */
 
 /*&C-texi
@@ -2975,6 +2996,15 @@ microcharacteristic variety $B$,(B bihomogeneous $B
 @item $B;2>H(B
     @code{sm_gb}
 @end table
+*/
+
+
+/*&eg-texi
+@include sm1-auto-en.texi
+*/
+
+/*&jp-texi
+@include sm1-auto-ja.texi
 */