===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave,v
retrieving revision 1.2
retrieving revision 1.7
diff -u -p -r1.2 -r1.7
--- OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2001/07/11 06:23:16	1.2
+++ OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2003/05/04 08:37:40	1.7
@@ -1,10 +1,12 @@
-/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.1 2001/07/11 01:00:23 takayama Exp $ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.6 2002/08/23 08:16:13 takayama Exp $ */
 
 /*&C-texi
 @c DO NOT EDIT THIS FILE   oxphc.texi
 */
+/*&C-texi
+@node SM1 Functions,,, Top
+*/
 /*&jp-texi
-@node SM1 $BH!?t(B,,, Top
 @chapter SM1 $BH!?t(B
 
 $B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir}
@@ -31,7 +33,6 @@ $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE
 @end tex
 */
 /*&eg-texi
-@node SM1 Functions,,, Top
 @chapter SM1 Functions
 
 This chapter describes  interface functions for
@@ -69,12 +70,7 @@ 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]
@@ -89,6 +85,33 @@ Grobner Deformations of Hypergeometric Differential Eq
 1999, Springer.
 See the appendix.
 */
+
+/*
+@menu
+* ox_sm1_forAsir::
+* sm1_start::
+* sm1::
+* sm1_push_int0::
+* sm1_gb::
+* sm1_deRham::
+* sm1_hilbert::
+* hilbert_polynomial::
+* sm1_genericAnn::
+* sm1_wTensor0::
+* sm1_reduction::
+* sm1_xml_tree_to_prefix_string::
+* sm1_syz::
+* sm1_mul::
+* sm1_distraction::
+* sm1_gkz::
+* sm1_appell1::
+* sm1_appell4::
+* sm1_rank::
+* sm1_auto_reduce::
+* sm1_slope::
+@end menu
+*/
+
 /*&jp-texi
 @section @code{ox_sm1_forAsir} $B%5!<%P(B
 */ 
@@ -97,9 +120,6 @@ See the appendix.
 */ 
 
 /*&eg-texi
-@menu
-* ox_sm1_forAsir::
-@end menu
 @node ox_sm1_forAsir,,, Top
 @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir
@@ -131,9 +151,6 @@ to build your own server by reading @code{sm1} macros.
 @end itemize
 */
 /*&jp-texi
-@menu
-* ox_sm1_forAsir::
-@end menu
 @node ox_sm1_forAsir,,, Top
 @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir
@@ -190,9 +207,6 @@ def sm1_check_server(P) {
 
 /*&eg-texi
 @c sort-sm1_start
-@menu
-* sm1_start::
-@end menu
 @node sm1_start,,, SM1 Functions
 @subsection @code{sm1_start}
 @findex sm1_start
@@ -233,10 +247,7 @@ differential operators in default. (cf. @code{Sm1_ord_
 */
 /*&jp-texi
 @c sort-sm1_start
-@menu
-* sm1_start::
-@end menu
-@node sm1_start,,, SM1 $BH!?t(B
+@node sm1_start,,, SM1 Functions
 @subsection @code{sm1_start}
 @findex sm1_start
 @table @t
@@ -337,9 +348,6 @@ def sm1push(P,F) {
 
 /*&eg-texi
 @c sort-sm1
-@menu
-* sm1::
-@end menu
 @node sm1,,, SM1 Functions
 @subsection @code{sm1}
 @findex sm1
@@ -363,10 +371,7 @@ to execute the command string @var{s}.
 @end itemize
 */
 /*&jp-texi
-@menu
-* sm1::
-@end menu
-@node sm1,,, SM1 $BH!?t(B
+@node sm1,,, SM1 Functions
 @subsection @code{sm1}
 @findex sm1
 @table @t
@@ -407,13 +412,13 @@ 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
 */
 
@@ -523,9 +528,6 @@ def sm1_push_int0_R(A,P) {
 
 /*&eg-texi
 @c sort-sm1_push_int0
-@menu
-* sm1_push_int0::
-@end menu
 @node sm1_push_int0,,, SM1 Functions
 @subsection @code{sm1_push_int0}
 @findex sm1_push_int0
@@ -564,10 +566,7 @@ Note that @code{ox_push_cmo(@var{p},1234)} send the bi
 */
 /*&jp-texi
 @c sort-sm1_push_int0
-@menu
-* sm1_push_int0::
-@end menu
-@node sm1_push_int0,,, SM1 $BH!?t(B
+@node sm1_push_int0,,, SM1 Functions
 @subsection @code{sm1_push_int0}
 @findex sm1_push_int0
 @table @t
@@ -759,16 +758,13 @@ def sm1_isListOfVar(A) {
 
 /*&eg-texi
 @c sort-sm1_gb
-@menu
-* sm1_gb::
-@end menu
 @node sm1_gb,,, SM1 Functions
 @node sm1_gb_d,,, SM1 Functions
 @subsection @code{sm1_gb}
 @findex sm1_gb
 @findex sm1_gb_d
 @table @t
-@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q})
+@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 +776,7 @@ The result will be returned as a list of distributed p
 @table @var
 @item return
 List
-@item p, q
+@item p, q, r
 Number
 @item f, v, w
 List
@@ -814,20 +810,19 @@ List
    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
 @c sort-sm1_gb
-@menu
-* sm1_gb::
-@end menu
-@node sm1_gb,,, SM1 $BH!?t(B
-@node sm1_gb_d,,, SM1 $BH!?t(B
+@node sm1_gb,,, SM1 Functions
+@node sm1_gb_d,,, SM1 Functions
 @subsection @code{sm1_gb}
 @findex sm1_gb
 @findex sm1_gb_d
 @table @t
-@item sm1_gb([@var{f},@var{v},@var{w}]|proc=@var{p},sorted=@var{q})
+@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.
@@ -836,7 +831,7 @@ List
 @table @var
 @item return
 $B%j%9%H(B
-@item p, q
+@item p, q, r
 $B?t(B
 @item f, v, w
 $B%j%9%H(B
@@ -866,6 +861,8 @@ List
     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
@@ -1014,9 +1011,6 @@ def sm1_pgb(A) {
 
 /*&eg-texi
 @c sort-sm1_deRham
-@menu
-* sm1_deRham::
-@end menu
 @node sm1_deRham,,, SM1 Functions
 @subsection @code{sm1_deRham}
 @findex sm1_deRham
@@ -1062,10 +1056,7 @@ mode. So, it is strongly recommended to execute the co
 */
 /*&jp-texi
 @c sort-sm1_deRham
-@menu
-* sm1_deRham::
-@end menu
-@node sm1_deRham,,, SM1 $BH!?t(B
+@node sm1_deRham,,, SM1 Functions
 @subsection @code{sm1_deRham}
 @findex sm1_deRham
 @table @t
@@ -1119,7 +1110,7 @@ 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.
@@ -1129,7 +1120,7 @@ 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.
@@ -1239,10 +1230,6 @@ def sm1_reduction_noH_d(F,G) {
 
 /*&eg-texi
 @c sort-sm1_hilbert
-@menu
-* sm1_hilbert::
-* hilbert_polynomial::
-@end menu
 @node sm1_hilbert,,, SM1 Functions
 @subsection @code{sm1_hilbert}
 @findex sm1_hilbert
@@ -1285,11 +1272,7 @@ List
 */
 /*&jp-texi
 @c sort-sm1_hilbert
-@menu
-* sm1_hilbert::
-* hilbert_polynomial::
-@end menu
-@node sm1_hilbert,,, SM1 $BH!?t(B
+@node sm1_hilbert,,, SM1 Functions
 @subsection @code{sm1_hilbert}
 @findex sm1_hilbert
 @findex hilbert_polynomial
@@ -1385,9 +1368,6 @@ def sm1_hilbert(A) {
 
 /*&eg-texi
 @c sort-sm1_genericAnn
-@menu
-* sm1_genericAnn::
-@end menu
 @node sm1_genericAnn,,, SM1 Functions
 @subsection @code{sm1_genericAnn}
 @findex sm1_genericAnn
@@ -1417,10 +1397,7 @@ List
 */
 /*&jp-texi
 @c sort-sm1_genericAnn
-@menu
-* sm1_genericAnn::
-@end menu
-@node sm1_genericAnn,,, SM1 $BH!?t(B
+@node sm1_genericAnn,,, SM1 Functions
 @subsection @code{sm1_genericAnn}
 @findex sm1_genericAnn
 @table @t
@@ -1487,9 +1464,6 @@ def sm1_tensor0(F) {
 
 /*&eg-texi
 @c sort-sm1_wTensor0
-@menu
-* sm1_wTensor0::
-@end menu
 @node sm1_wTensor0,,, SM1 Functions
 @subsection @code{sm1_wTensor0}
 @findex sm1_wTensor0
@@ -1531,10 +1505,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 
 /*&jp-texi
 @c sort-sm1_wTensor0
-@menu
-* sm1_wTensor0::
-@end menu
-@node sm1_wTensor0,,, SM1 $BH!?t(B
+@node sm1_wTensor0,,, SM1 Functions
 @subsection @code{sm1_wTensor0}
 @findex sm1_wTensor0
 @table @t
@@ -1593,9 +1564,6 @@ def sm1_wTensor0(F) {
 
 /*&eg-texi
 @c sort-sm1_reduction
-@menu
-* sm1_reduction::
-@end menu
 @node sm1_reduction,,, SM1 Functions
 @subsection @code{sm1_reduction}
 @findex sm1_reduction
@@ -1623,7 +1591,7 @@ division algorithm to @var{f}. The set of variables is
 @code{sm1_reduction_noH} is for the Weyl algebra.
 @item The return value is of the form
 [r,c0,[c1,...,cm],[g1,...gm]] where @var{g}=[g1, ..., gm] and
-r/c0 + c1 g1 + ... + cm gm = 0.
+c0 f + c1 g1 + ... + cm gm = r.
 r/c0 is the normal form.
 @item The function reduction reduces reducible terms that appear
 in lower order terms.
@@ -1633,10 +1601,7 @@ are for distributed polynomials.
 @end itemize
 */
 /*&jp-texi
-@menu
-* sm1_reduction::
-@end menu
-@node sm1_reduction,,, SM1 $BH!?t(B
+@node sm1_reduction,,, SM1 Functions
 @subsection @code{sm1_reduction}
 @findex sm1_reduction
 @table @t
@@ -1664,8 +1629,8 @@ are for distributed polynomials.
 $B>JN,$7$F$b$h$$(B.
 @code{sm1_reduction_noH} $B$O(B, Weyl algebra $BMQ(B.
 @item $BLa$jCM$O<!$N7A$r$7$F$$$k(B:
-[r,c0,[c1,...,cm],[g1,...gm]] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,
-r/c0 + c1 g1 + ... + cm gm = 0
+[r,c0,[c1,...,cm],g] $B$3$3$G(B @var{g}=[g1, ..., gm] $B$G$"$j(B,
+c0 f + c1 g1 + ... + cm gm = r
 $B$,$J$j$?$D(B.
 r/c0 $B$,(B normal form $B$G$"$k(B.
 @item $B$3$NH!?t$O(B, $BDc<!9`$K$"$i$o$l$k(B reducible $B$J9`$b4JC12=$9$k(B.
@@ -1677,9 +1642,9 @@ sm1_reduction_d(P,F,G) $B$*$h$S(B sm1_reduction_noH_
 /*&C-texi
 @example
 [259] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);
-[x^2+y^2-4,1,[0,0],[x+y^3-4*y,y^4-4*y^2+1]]
+[x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
 [260] sm1_reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);
-[0,1,[-y^2+4,-x+y^3-4*y],[x+y^3-4*y,y^4-4*y^2+1]]
+[0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]
 @end example
 */
 /*&eg-texi
@@ -1730,9 +1695,6 @@ def sm1_reduction_noH(A) {
 }
 
 /*&eg-texi
-@menu
-* sm1_xml_tree_to_prefix_string::
-@end menu
 @node sm1_xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1_xml_tree_to_prefix_string}
 @findex sm1_xml_tree_to_prefix_string
@@ -1761,10 +1723,7 @@ command search path.)
 @end itemize
 */
 /*&jp-texi
-@menu
-* sm1_xml_tree_to_prefix_string::
-@end menu
-@node sm1_xml_tree_to_prefix_string,,, SM1 $BH!?t(B
+@node sm1_xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1_xml_tree_to_prefix_string}
 @findex sm1_xml_tree_to_prefix_string
 @table @t
@@ -1887,9 +1846,6 @@ def sm1_res_div(A) {
 
 /*&eg-texi
 @c sort-sm1_syz
-@menu
-* sm1_syz::
-@end menu
 @node sm1_syz,,, SM1 Functions
 @node sm1_syz_d,,, SM1 Functions
 @subsection @code{sm1_syz}
@@ -1934,11 +1890,8 @@ In summary, @var{g} = @var{m} @var{f} and
 */
 /*&jp-texi
 @c sort-sm1_syz
-@menu
-* sm1_syz::
-@end menu
-@node sm1_syz,,, SM1 $BH!?t(B
-@node sm1_syz_d,,, SM1 $BH!?t(B
+@node sm1_syz,,, SM1 Functions
+@node sm1_syz_d,,, SM1 Functions
 @subsection @code{sm1_syz}
 @findex sm1_syz
 @findex sm1_syz_d
@@ -2033,9 +1986,6 @@ def sm1_mul(A,B,V) {
 }
 
 /*&eg-texi
-@menu
-* sm1_mul::
-@end menu
 @node sm1_mul,,, SM1 Functions
 @subsection @code{sm1_mul}
 @findex sm1_mul
@@ -2062,10 +2012,7 @@ List
 */
 
 /*&jp-texi
-@menu
-* sm1_mul::
-@end menu
-@node sm1_mul,,, SM1 $BH!?t(B
+@node sm1_mul,,, SM1 Functions
 @subsection @code{sm1_mul}
 @findex sm1_mul
 @table @t
@@ -2229,9 +2176,6 @@ def sm1_distraction(A) {
 }
 
 /*&eg-texi
-@menu
-* sm1_distraction::
-@end menu
 @node sm1_distraction,,, SM1 Functions
 @subsection @code{sm1_distraction}
 @findex sm1_distraction
@@ -2263,10 +2207,7 @@ See Saito, Sturmfels, Takayama : Grobner Deformations 
 */
 
 /*&jp-texi
-@menu
-* sm1_distraction::
-@end menu
-@node sm1_distraction,,, SM1 $BH!?t(B
+@node sm1_distraction,,, SM1 Functions
 
 @subsection @code{sm1_distraction}
 @findex sm1_distraction
@@ -2386,9 +2327,6 @@ def sm1_gkz(S) {
 
 
 /*&eg-texi
-@menu
-* sm1_gkz::
-@end menu
 @node sm1_gkz,,, SM1 Functions
 @subsection @code{sm1_gkz}
 @findex sm1_gkz
@@ -2414,10 +2352,7 @@ List
 */
 
 /*&jp-texi
-@menu
-* sm1_gkz::
-@end menu
-@node sm1_gkz,,, SM1 $BH!?t(B
+@node sm1_gkz,,, SM1 Functions
 @subsection @code{sm1_gkz}
 @findex sm1_gkz
 @table @t
@@ -2499,9 +2434,6 @@ def sm1aux_x(I) {
 
 
 /*&eg-texi
-@menu
-* sm1_appell1::
-@end menu
 @node sm1_appell1,,, SM1 Functions
 @subsection @code{sm1_appell1}
 @findex sm1_appell1
@@ -2529,10 +2461,7 @@ The parameters a, c, b1, ..., bn may be rational numbe
 */
 
 /*&jp-texi
-@menu
-* sm1_appell1::
-@end menu
-@node sm1_appell1,,, SM1 $BH!?t(B
+@node sm1_appell1,,, SM1 Functions
 @subsection @code{sm1_appell1}
 @findex sm1_appell1
 @table @t
@@ -2614,9 +2543,6 @@ def sm1_appell4(S) {
 }
 
 /*&eg-texi
-@menu
-* sm1_appell4::
-@end menu
 @node sm1_appell4,,, SM1 Functions
 @subsection @code{sm1_appell4}
 @findex sm1_appell4
@@ -2644,10 +2570,7 @@ The parameters a, b, c1, ..., cn may be rational numbe
 */
 
 /*&jp-texi
-@menu
-* sm1_appell4::
-@end menu
-@node sm1_appell4,,, SM1 $BH!?t(B
+@node sm1_appell4,,, SM1 Functions
 @subsection @code{sm1_appell4}
 @findex sm1_appell4
 @table @t
@@ -2711,9 +2634,6 @@ def sm1_rrank(A) {
 
 
 /*&eg-texi
-@menu
-* sm1_rank::
-@end menu
 @node sm1_rank,,, SM1 Functions
 @subsection @code{sm1_rank}
 @findex sm1_rank
@@ -2743,10 +2663,7 @@ holonomic. It is generally faster than @code{sm1_rank}
 */
 
 /*&jp-texi
-@menu
-* sm1_rank::
-@end menu
-@node sm1_rank,,, SM1 $BH!?t(B
+@node sm1_rank,,, SM1 Functions
 @subsection @code{sm1_rank}
 @findex sm1_rank
 @table @t
@@ -2804,9 +2721,6 @@ def sm1_auto_reduce(T) {
 }
 
 /*&eg-texi
-@menu
-* sm1_auto_reduce::
-@end menu
 @node sm1_auto_reduce,,, SM1 Functions
 @subsection @code{sm1_auto_reduce}
 @findex sm1_auto_reduce
@@ -2833,10 +2747,7 @@ Grobner bases.  This is the default.
 */
 
 /*&jp-texi
-@menu
-* sm1_auto_reduce::
-@end menu
-@node sm1_auto_reduce,,, SM1 $BH!?t(B
+@node sm1_auto_reduce,,, SM1 Functions
 @subsection @code{sm1_auto_reduce}
 @findex sm1_auto_reduce
 @table @t
@@ -2874,9 +2785,6 @@ def sm1_slope(II,V,FF,VF) {
 
 
 /*&eg-texi
-@menu
-* sm1_slope::
-@end menu
 @node sm1_slope,,, SM1 Functions
 @subsection @code{sm1_slope}
 @findex sm1_slope
@@ -2906,23 +2814,23 @@ 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
-@menu
-* sm1_slope::
-@end menu
-@node sm1_slope,,, SM1 $BH!?t(B
+@node sm1_slope,,, SM1 Functions
 @subsection @code{sm1_slope}
 @findex sm1_slope
 @table @t
@@ -2950,16 +2858,18 @@ 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
@@ -2992,6 +2902,15 @@ 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
 */