===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave,v
retrieving revision 1.10
retrieving revision 1.17
diff -u -p -r1.10 -r1.17
--- OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2003/05/20 23:25:28	1.10
+++ OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2004/05/14 01:25:03	1.17
@@ -1,12 +1,13 @@
-/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.9 2003/05/19 05:15:52 takayama Exp $ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.16 2004/03/05 19:05:11 ohara Exp $ */
 
-/*&C-texi
+/*&C
 @c DO NOT EDIT THIS FILE   oxphc.texi
 */
-/*&C-texi
+/*&C
 @node SM1 Functions,,, Top
+
 */
-/*&jp-texi
+/*&ja
 @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}
@@ -32,7 +33,7 @@ $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE
 $B<!85$rEz$($k(B.
 @end tex
 */
-/*&eg-texi
+/*&en
 @chapter SM1 Functions
 
 This chapter describes  interface functions for
@@ -67,7 +68,7 @@ Hence, the dimension of the first de Rham cohomology g
 cohomology groups.
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 
 @include opening.texi
@@ -76,7 +77,7 @@ cohomology groups.
 [1,2]
 @end example
 */
-/*&C-texi
+/*&C
 @noindent
 The author of @code{sm1} : Nobuki Takayama, @code{takayama@@math.sci.kobe-u.ac.jp} @*
 The author of sm1 packages : Toshinori Oaku, @code{oaku@@twcu.ac.jp} @*
@@ -86,7 +87,7 @@ Grobner Deformations of Hypergeometric Differential Eq
 See the appendix.
 */
 
-/*
+/*&C
 @menu
 * ox_sm1_forAsir::
 * sm1.start::
@@ -95,7 +96,6 @@ See the appendix.
 * sm1.gb::
 * sm1.deRham::
 * sm1.hilbert::
-* hilbert_polynomial::
 * sm1.genericAnn::
 * sm1.wTensor0::
 * sm1.reduction::
@@ -109,18 +109,23 @@ See the appendix.
 * sm1.rank::
 * sm1.auto_reduce::
 * sm1.slope::
+* sm1.ahg::
+* sm1.bfunction::
+* sm1.generalized_bfunction::
+* sm1.restriction::
+* sm1.saturation::
 @end menu
 */
 
-/*&jp-texi
+/*&ja
 @section @code{ox_sm1_forAsir} $B%5!<%P(B
 */ 
-/*&eg-texi
+/*&en
 @section @code{ox_sm1_forAsir} Server
 */ 
 
-/*&eg-texi
-@node ox_sm1_forAsir,,, Top
+/*&en
+@node ox_sm1_forAsir,,, SM1 Functions
 @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir
 @table @t
@@ -150,8 +155,8 @@ See the appendix.
 to build your own server by reading @code{sm1} macros.
 @end itemize
 */
-/*&jp-texi
-@node ox_sm1_forAsir,,, Top
+/*&ja
+@node ox_sm1_forAsir,,, SM1 Functions
 @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir
 @table @t
@@ -184,14 +189,14 @@ to build your own server by reading @code{sm1} macros.
 */
 
 
-/*&jp-texi
+/*&ja
 @section $BH!?t0lMw(B
 */ 
-/*&eg-texi
+/*&en
 @section Functions
 */ 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.start
 @node sm1.start,,, SM1 Functions
 @subsection @code{sm1.start}
@@ -233,7 +238,7 @@ The descriptor can be obtained by the function
 @code{sm1.get_Sm1_proc()}.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.start
 @node sm1.start,,, SM1 Functions
 @subsection @code{sm1.start}
@@ -274,7 +279,7 @@ The descriptor can be obtained by the function
 $B$3$N<1JLHV9f$O4X?t(B @code{sm1.get_Sm1_proc()} $B$G$H$j$@$9$3$H$,$G$-$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [260] ord([da,a,db,b]);
 [da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w, 
@@ -290,14 +295,14 @@ a*da+1                  
 a*da
 @end example
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},
     @code{ord}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},
@@ -307,7 +312,7 @@ a*da
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1
 @node sm1.sm1,,, SM1 Functions
 @subsection @code{sm1.sm1}
@@ -332,7 +337,7 @@ to execute the command string @var{s}.
 (In the next example, the descriptor number is 0.)
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @node sm1.sm1,,, SM1 Functions
 @subsection @code{sm1.sm1}
 @findex sm1.sm1
@@ -356,7 +361,7 @@ to execute the command string @var{s}.
  ($B<!$NNc$G$O(B, $B<1JLHV9f(B 0)
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [261] sm1.sm1(0," ( (x-1)^2 ) . ");
 0
@@ -369,13 +374,13 @@ x^2-2*x+1
 @end example
 */
 
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. 
 @end table
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}. 
@@ -383,7 +388,7 @@ x^2-2*x+1
 */
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.push_int0
 @node sm1.push_int0,,, SM1 Functions
 @subsection @code{sm1.push_int0}
@@ -421,7 +426,7 @@ Note that @code{ox_push_cmo(@var{p},1234)} send the bi
 @item In other cases,  @code{ox_push_cmo} is called without data conversion.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.push_int0
 @node sm1.push_int0,,, SM1 Functions
 @subsection @code{sm1.push_int0}
@@ -477,13 +482,13 @@ x*dx+1
 [1,2]
 @end example
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{ox_push_cmo}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item Reference
     @code{ox_push_cmo}
@@ -492,10 +497,9 @@ x*dx+1
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.gb
 @node sm1.gb,,, SM1 Functions
-@node sm1.gb_d,,, SM1 Functions
 @subsection @code{sm1.gb}
 @findex sm1.gb
 @findex sm1.gb_d
@@ -550,10 +554,9 @@ List
    the polynomials are dehomogenized (,i.e., h is set to 1).
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.gb
 @node sm1.gb,,, SM1 Functions
-@node sm1.gb_d,,, SM1 Functions
 @subsection @code{sm1.gb}
 @findex sm1.gb
 @findex sm1.gb_d
@@ -601,13 +604,13 @@ List
     $BLa$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
+/*&C
 @example
 [293] sm1.gb([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);
 [[x*dx+y*dy-1,y^2*dy^2+2],[x*dx,y^2*dy^2]]
 @end example
 */
-/*&eg-texi
+/*&en
 In the example above,
 @tex the set $\{ x \partial_x + y \partial_y -1,
                  y^2 \partial_y^2+2\}$ 
@@ -618,7 +621,7 @@ The set $\{x \partial_x, y^2 \partial_y\}$ is the lead
 (the initial monominals) of the Gr\"obner basis.
 @end tex
 */
-/*&jp-texi
+/*&ja
 $B>e$NNc$K$*$$$F(B,
 @tex $B=89g(B $\{ x \partial_x + y \partial_y -1,
                  y^2 \partial_y^2+2\}$ 
@@ -630,13 +633,13 @@ graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
 $BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B.
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 [294] sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]);
 [[dx+dy^3-4*dy,-dy^4+4*dy^2-1],[dx,-dy^4]]
 @end example
 */
-/*&eg-texi
+/*&en
 In the example above, two monomials 
 @tex
 $m = x^a y^b \partial_x^c \partial_y^d$ and 
@@ -649,7 +652,7 @@ compared by the reverse lexicographic order
 (i.e., if $50c+2d+a = 50c'+2d'+a'$, then use the reverse lexicogrpahic order).
 @end tex
 */
-/*&jp-texi
+/*&ja
 $B>e$NNc$K$*$$$FFs$D$N%b%N%_%"%k(B
 @tex
 $m = x^a y^b \partial_x^c \partial_y^d$ $B$*$h$S(B
@@ -663,14 +666,14 @@ $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 $B$5$l$k(B).
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 [294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1);
       map(print,F[2][0])$
       map(print,F[2][1])$
 @end example
 */
-/*&C-texi
+/*&C
 @example
 [595]
    sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"],
@@ -697,13 +700,13 @@ $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 @end example
 */
 
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm1.reduction}, @code{sm1.rat_to_p}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.reduction}, @code{sm1.rat_to_p}
@@ -712,7 +715,7 @@ $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.deRham
 @node sm1.deRham,,, SM1 Functions
 @subsection @code{sm1.deRham}
@@ -757,7 +760,7 @@ mode. So, it is strongly recommended to execute the co
 @code{ox_shutdown(sm1.get_Sm1_proc());} to interrupt and restart the server.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.deRham
 @node sm1.deRham,,, SM1 Functions
 @subsection @code{sm1.deRham}
@@ -801,7 +804,7 @@ mode. So, it is strongly recommended to execute the co
   $B$r0l;~(B shutdown $B$7$F%j%9%?!<%H$7$?J}$,0BA4$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [332] sm1.deRham([x^3-y^2,[x,y]]);
 [1,1,0]
@@ -809,7 +812,7 @@ mode. So, it is strongly recommended to execute the co
 [1,2]
 @end example
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm1.start}, @code{deRham} (sm1 command)
@@ -819,7 +822,7 @@ mode. So, it is strongly recommended to execute the co
     Journal of pure and applied algebra 139 (1999), 201--233.
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.start}, @code{deRham} (sm1 command)
@@ -833,7 +836,7 @@ mode. So, it is strongly recommended to execute the co
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.hilbert
 @node sm1.hilbert,,, SM1 Functions
 @subsection @code{sm1.hilbert}
@@ -875,7 +878,7 @@ List
    polynomials in @code{sm1} is  slower than in @code{asir}.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.hilbert
 @node sm1.hilbert,,, SM1 Functions
 @subsection @code{sm1.hilbert}
@@ -914,7 +917,7 @@ List
 @end itemize
 */
 
-/*&C-texi
+/*&C
 @example
 
 [346] load("katsura")$
@@ -944,13 +947,13 @@ List
 @end example
 */
 
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm1.start}, @code{sm1.gb}, @code{longname}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.start}, @code{sm1.gb}, @code{longname}
@@ -958,7 +961,7 @@ List
 */
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.genericAnn
 @node sm1.genericAnn,,, SM1 Functions
 @subsection @code{sm1.genericAnn}
@@ -987,7 +990,7 @@ List
     @var{f} is a polynomial in the variables @code{rest}(@var{v}).
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.genericAnn
 @node sm1.genericAnn,,, SM1 Functions
 @subsection @code{sm1.genericAnn}
@@ -1017,19 +1020,19 @@ List
     @var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [595] sm1.genericAnn([x^3+y^3+z^3,[s,x,y,z]]);
 [-x*dx-y*dy-z*dz+3*s,z^2*dy-y^2*dz,z^2*dx-x^2*dz,y^2*dx-x^2*dy]
 @end example
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm1.start}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.start}
@@ -1038,7 +1041,7 @@ List
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.wTensor0
 @node sm1.wTensor0,,, SM1 Functions
 @subsection @code{sm1.wTensor0}
@@ -1079,7 +1082,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @c sort-sm1.wTensor0
 @node sm1.wTensor0,,, SM1 Functions
 @subsection @code{sm1.wTensor0}
@@ -1119,7 +1122,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 $B0lHL$K(B, $B=PNO$O<+M32C72(B D^r $B$NItJ,2C72$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [258]  sm1.wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]);
 [[-y*x*dx-y*x*dy+4*x+y],[5*x*dx^2+5*x*dx+2*y*dy^2+(-2*y-6)*dy+3],
@@ -1130,7 +1133,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.reduction
 @node sm1.reduction,,, SM1 Functions
 @subsection @code{sm1.reduction}
@@ -1168,7 +1171,7 @@ sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
 are for distributed polynomials.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @node sm1.reduction,,, SM1 Functions
 @subsection @code{sm1.reduction}
 @findex sm1.reduction
@@ -1207,7 +1210,7 @@ sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @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],[y^4-4*y^2+1,x+y^3-4*y]]
@@ -1215,13 +1218,13 @@ sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 [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
+/*&en
 @table @t
 @item Reference
     @code{sm1.start}, @code{d_true_nf}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm1.start}, @code{d_true_nf}
@@ -1229,7 +1232,7 @@ sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 */
 
 
-/*&eg-texi
+/*&en
 @node sm1.xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1.xml_tree_to_prefix_string}
 @findex sm1.xml_tree_to_prefix_string
@@ -1257,7 +1260,7 @@ asir has not yet understood this CMO.
 command search path.)
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @node sm1.xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1.xml_tree_to_prefix_string}
 @findex sm1.xml_tree_to_prefix_string
@@ -1284,7 +1287,7 @@ String
 ($B$?$H$($P(B, /usr/local/jdk1.1.8/bin $B$r%3%^%s%I%5!<%A%Q%9$KF~$l$k$J$I(B.)
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [263] load("om");
 1
@@ -1301,13 +1304,13 @@ Trying to connect to the server... Done.
 basic_plus(basic_times(basic_power(x,4),1),basic_times(basic_power(x,0),-1))
 @end example
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{om_*}, @code{OpenXM/src/OpenMath},  @code{eval_str}
@@ -1317,10 +1320,9 @@ basic_plus(basic_times(basic_power(x,4),1),basic_times
 
 
 
-/*&eg-texi
+/*&en
 @c sort-sm1.syz
 @node sm1.syz,,, SM1 Functions
-@node sm1.syz_d,,, SM1 Functions
 @subsection @code{sm1.syz}
 @findex sm1.syz
 @findex sm1.syz_d
@@ -1347,7 +1349,7 @@ Here @var{s} is the syzygy of @var{f} in the ring of d
 operators with the variable @var{v}. 
 @var{g} is a Groebner basis of @var{f} with the weight vector @var{w},
 and @var{m} is a matrix that translates the input matrix @var{f} to the Gr\"obner
-basis @var {g}.
+basis @var{g}.
 @var{t} is the syzygy of the Gr\"obner basis @var{g}.
 In summary, @var{g} = @var{m} @var{f} and
 @var{s} @var{f} = 0 hold as matrices.
@@ -1361,10 +1363,9 @@ In summary, @var{g} = @var{m} @var{f} and
    The homogenization variable h is automatically added.
 @end itemize
 */
-/*&jp-texi
+/*&ja
 @c sort-sm1.syz
 @node sm1.syz,,, SM1 Functions
-@node sm1.syz_d,,, SM1 Functions
 @subsection @code{sm1.syz}
 @findex sm1.syz
 @findex sm1.syz_d
@@ -1404,7 +1405,7 @@ syzygy $B$G$"$k(B.
 $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [293] sm1.syz([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);
 [[[y*x*dy*dx-2,-x*dx-y*dy+1]],    generators of the syzygy
@@ -1413,7 +1414,7 @@ syzygy $B$G$"$k(B.
  [[y*x*dy*dx-2,-x*dx-y*dy+1]]]]
 @end example
 */
-/*&C-texi
+/*&C
 @example
 [294]sm1.syz([[x^2*dx^2+x*dx+y^2*dy^2+y*dy-4,x*y*dx*dy-1],[x,y],[[dx,-1,x,1]]]);
 [[[y*x*dy*dx-1,-x^2*dx^2-x*dx-y^2*dy^2-y*dy+4]], generators of the syzygy
@@ -1426,7 +1427,7 @@ syzygy $B$G$"$k(B.
 
 
 
-/*&eg-texi
+/*&en
 @node sm1.mul,,, SM1 Functions
 @subsection @code{sm1.mul}
 @findex sm1.mul
@@ -1452,7 +1453,7 @@ List
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.mul,,, SM1 Functions
 @subsection @code{sm1.mul}
 @findex sm1.mul
@@ -1480,7 +1481,7 @@ List
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 [277] sm1.mul(dx,x,[x]);
@@ -1496,7 +1497,7 @@ x+2*y
 	
  
 
-/*&eg-texi
+/*&en
 @node sm1.distraction,,, SM1 Functions
 @subsection @code{sm1.distraction}
 @findex sm1.distraction
@@ -1527,7 +1528,7 @@ See Saito, Sturmfels, Takayama : Grobner Deformations 
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.distraction,,, SM1 Functions
 
 @subsection @code{sm1.distraction}
@@ -1558,7 +1559,7 @@ See Saito, Sturmfels, Takayama : Grobner Deformations 
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 [280] sm1.distraction([x*dx,[x],[x],[dx],[x]]);
@@ -1574,14 +1575,14 @@ x^2+3*x+2
 @end example
 */
 
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{distraction2(sm1)}, 
 @end table
 */
 
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{distraction2(sm1)}, 
@@ -1590,7 +1591,7 @@ x^2+3*x+2
 
 
 
-/*&eg-texi
+/*&en
 @node sm1.gkz,,, SM1 Functions
 @subsection @code{sm1.gkz}
 @findex sm1.gkz
@@ -1615,7 +1616,7 @@ List
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.gkz,,, SM1 Functions
 @subsection @code{sm1.gkz}
 @findex sm1.gkz
@@ -1638,7 +1639,7 @@ List
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1654,7 +1655,7 @@ List
 
 
 
-/*&eg-texi
+/*&en
 @node sm1.appell1,,, SM1 Functions
 @subsection @code{sm1.appell1}
 @findex sm1.appell1
@@ -1678,10 +1679,13 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
 where @var{a} =(a,c,b1,...,bn).
 When n=2, the Lauricella function is called the Appell function F_1.
 The parameters a, c, b1, ..., bn may be rational numbers.
+@item It does not call sm1 function appell1. As a concequence,
+when parameters are rational or symbolic, this function also works
+as well as integral parameters.
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.appell1,,, SM1 Functions
 @subsection @code{sm1.appell1}
 @findex sm1.appell1
@@ -1705,10 +1709,12 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,c,b1,...,bn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.
+@item sm1 $B$N4X?t(B appell1 $B$r$h$V$o$1$G$J$$$N$G(B, $B%Q%i%a!<%?$,M-M}?t$dJ8;z<0$N>l9g$b(B
+$B@5$7$/F0$/(B.
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1727,7 +1733,7 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
  [x1*dx1*dx2,-x1^2*dx1^2,-x2^2*dx1*dx2,-x1*x2^2*dx2^2]]
 
 [283] sm1.rank(sm1.appell1([1/2,3,5,-1/3]));
-1
+3
 
 [285] Mu=2$ Beta = 1/3$
 [287] sm1.rank(sm1.appell1([Mu+Beta,Mu+1,Beta,Beta,Beta]));
@@ -1738,7 +1744,7 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
 
 */
 
-/*&eg-texi
+/*&en
 @node sm1.appell4,,, SM1 Functions
 @subsection @code{sm1.appell4}
 @findex sm1.appell4
@@ -1762,10 +1768,13 @@ F_4(a,b,c1,c2,...,cn;x1,...,xn)
 where @var{a} =(a,b,c1,...,cn).
 When n=2, the Lauricella function is called the Appell function F_4.
 The parameters a, b, c1, ..., cn may be rational numbers.
+@item @item It does not call sm1 function appell4. As a concequence,
+when parameters are rational or symbolic, this function also works
+as well as integral parameters.
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.appell4,,, SM1 Functions
 @subsection @code{sm1.appell4}
 @findex sm1.appell4
@@ -1789,10 +1798,12 @@ F_C(a,b,c1,c2,...,cn;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,b,c1,...,cn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.
+@item sm1 $B$N4X?t(B appell1 $B$r$h$V$o$1$G$J$$$N$G(B, $B%Q%i%a!<%?$,M-M}?t$dJ8;z<0$N>l9g$b(B
+$B@5$7$/F0$/(B.
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1812,7 +1823,7 @@ F_C(a,b,c1,c2,...,cn;x1,...,xn)
 
 
 
-/*&eg-texi
+/*&en
 @node sm1.rank,,, SM1 Functions
 @subsection @code{sm1.rank}
 @findex sm1.rank
@@ -1841,7 +1852,7 @@ holonomic. It is generally faster than @code{sm1.rank}
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.rank,,, SM1 Functions
 @subsection @code{sm1.rank}
 @findex sm1.rank
@@ -1869,7 +1880,7 @@ holonomic. It is generally faster than @code{sm1.rank}
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1892,7 +1903,7 @@ holonomic. It is generally faster than @code{sm1.rank}
 */
 
 
-/*&eg-texi
+/*&en
 @node sm1.auto_reduce,,, SM1 Functions
 @subsection @code{sm1.auto_reduce}
 @findex sm1.auto_reduce
@@ -1918,7 +1929,7 @@ Grobner bases.  This is the default.
 @end itemize
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.auto_reduce,,, SM1 Functions
 @subsection @code{sm1.auto_reduce}
 @findex sm1.auto_reduce
@@ -1946,7 +1957,7 @@ reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,%
 
   
 
-/*&eg-texi
+/*&en
 @node sm1.slope,,, SM1 Functions
 @subsection @code{sm1.slope}
 @findex sm1.slope
@@ -1991,7 +2002,7 @@ of the slopes are returned.
 
 */
 
-/*&jp-texi
+/*&ja
 @node sm1.slope,,, SM1 Functions
 @subsection @code{sm1.slope}
 @findex sm1.slope
@@ -2034,7 +2045,7 @@ Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, 
 Slope $B$N@dBPCM$rLa$9(B.
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -2053,13 +2064,13 @@ Slope $B$N@dBPCM$rLa$9(B.
 @end example
 
 */
-/*&eg-texi
+/*&en
 @table @t
 @item Reference
     @code{sm.gb}
 @end table
 */
-/*&jp-texi
+/*&ja
 @table @t
 @item $B;2>H(B
     @code{sm.gb}
@@ -2067,12 +2078,12 @@ Slope $B$N@dBPCM$rLa$9(B.
 */
 
 
-/*&eg-texi
-@include sm1-auto-en.texi
+/*&en
+@include sm1-auto.en
 */
 
-/*&jp-texi
-@include sm1-auto-ja.texi
+/*&ja
+@include sm1-auto.ja
 */