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version 1.11, 2003/07/27 13:18:46 version 1.17, 2004/05/14 01:25:03
Line 1 
Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.10 2003/05/20 23:25:28 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 DO NOT EDIT THIS FILE   oxphc.texi
 */  */
 /*&C-texi  /*&C
 @node SM1 Functions,,, Top  @node SM1 Functions,,, Top
   
 */  */
 /*&jp-texi  /*&ja
 @chapter SM1 $BH!?t(B  @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}  $B$3$N@a$G$O(B sm1 $B$N(B ox $B%5!<%P(B @code{ox_sm1_forAsir}
Line 33  $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE
Line 33  $X$ $B$OJ?LL$KFs$D$N7j$r$"$1$?6u4V$G$"$k$N$G(B, $BE
 $B<!85$rEz$($k(B.  $B<!85$rEz$($k(B.
 @end tex  @end tex
 */  */
 /*&eg-texi  /*&en
 @chapter SM1 Functions  @chapter SM1 Functions
   
 This chapter describes  interface functions for  This chapter describes  interface functions for
Line 68  Hence, the dimension of the first de Rham cohomology g
Line 68  Hence, the dimension of the first de Rham cohomology g
 cohomology groups.  cohomology groups.
 @end tex  @end tex
 */  */
 /*&C-texi  /*&C
 @example  @example
   
 @include opening.texi  @include opening.texi
Line 77  cohomology groups.
Line 77  cohomology groups.
 [1,2]  [1,2]
 @end example  @end example
 */  */
 /*&C-texi  /*&C
 @noindent  @noindent
 The author of @code{sm1} : Nobuki Takayama, @code{takayama@@math.sci.kobe-u.ac.jp} @*  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} @*  The author of sm1 packages : Toshinori Oaku, @code{oaku@@twcu.ac.jp} @*
Line 87  Grobner Deformations of Hypergeometric Differential Eq
Line 87  Grobner Deformations of Hypergeometric Differential Eq
 See the appendix.  See the appendix.
 */  */
   
 /*&C-texi  /*&C
 @menu  @menu
 * ox_sm1_forAsir::  * ox_sm1_forAsir::
 * sm1.start::  * sm1.start::
Line 109  See the appendix.
Line 109  See the appendix.
 * sm1.rank::  * sm1.rank::
 * sm1.auto_reduce::  * sm1.auto_reduce::
 * sm1.slope::  * sm1.slope::
 * sm1.gb_d::  
 * sm1.syz_d::  
 * sm1.ahg::  * sm1.ahg::
 * sm1.bfunction::  * sm1.bfunction::
 * sm1.generalized_bfunction::  * sm1.generalized_bfunction::
Line 119  See the appendix.
Line 117  See the appendix.
 @end menu  @end menu
 */  */
   
 /*&jp-texi  /*&ja
 @section @code{ox_sm1_forAsir} $B%5!<%P(B  @section @code{ox_sm1_forAsir} $B%5!<%P(B
 */  */
 /*&eg-texi  /*&en
 @section @code{ox_sm1_forAsir} Server  @section @code{ox_sm1_forAsir} Server
 */  */
   
 /*&eg-texi  /*&en
 @node ox_sm1_forAsir,,, SM1 Functions  @node ox_sm1_forAsir,,, SM1 Functions
 @subsection @code{ox_sm1_forAsir}  @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir  @findex ox_sm1_forAsir
Line 157  See the appendix.
Line 155  See the appendix.
 to build your own server by reading @code{sm1} macros.  to build your own server by reading @code{sm1} macros.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @node ox_sm1_forAsir,,, SM1 Functions  @node ox_sm1_forAsir,,, SM1 Functions
 @subsection @code{ox_sm1_forAsir}  @subsection @code{ox_sm1_forAsir}
 @findex ox_sm1_forAsir  @findex ox_sm1_forAsir
Line 191  to build your own server by reading @code{sm1} macros.
Line 189  to build your own server by reading @code{sm1} macros.
 */  */
   
   
 /*&jp-texi  /*&ja
 @section $BH!?t0lMw(B  @section $BH!?t0lMw(B
 */  */
 /*&eg-texi  /*&en
 @section Functions  @section Functions
 */  */
   
 /*&eg-texi  /*&en
 @c sort-sm1.start  @c sort-sm1.start
 @node sm1.start,,, SM1 Functions  @node sm1.start,,, SM1 Functions
 @subsection @code{sm1.start}  @subsection @code{sm1.start}
Line 240  The descriptor can be obtained by the function
Line 238  The descriptor can be obtained by the function
 @code{sm1.get_Sm1_proc()}.  @code{sm1.get_Sm1_proc()}.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.start  @c sort-sm1.start
 @node sm1.start,,, SM1 Functions  @node sm1.start,,, SM1 Functions
 @subsection @code{sm1.start}  @subsection @code{sm1.start}
Line 281  The descriptor can be obtained by the function
Line 279  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.  $B$3$N<1JLHV9f$O4X?t(B @code{sm1.get_Sm1_proc()} $B$G$H$j$@$9$3$H$,$G$-$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [260] ord([da,a,db,b]);  [260] ord([da,a,db,b]);
 [da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w,  [da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w,
Line 297  a*da+1                  
Line 295  a*da+1                  
 a*da  a*da
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},      @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},
     @code{ord}      @code{ord}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},      @code{ox_launch}, @code{sm1.push_int0}, @code{sm1.push_poly0},
Line 314  a*da
Line 312  a*da
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1  @c sort-sm1
 @node sm1.sm1,,, SM1 Functions  @node sm1.sm1,,, SM1 Functions
 @subsection @code{sm1.sm1}  @subsection @code{sm1.sm1}
Line 339  to execute the command string @var{s}.
Line 337  to execute the command string @var{s}.
 (In the next example, the descriptor number is 0.)  (In the next example, the descriptor number is 0.)
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @node sm1.sm1,,, SM1 Functions  @node sm1.sm1,,, SM1 Functions
 @subsection @code{sm1.sm1}  @subsection @code{sm1.sm1}
 @findex sm1.sm1  @findex sm1.sm1
Line 363  to execute the command string @var{s}.
Line 361  to execute the command string @var{s}.
  ($B<!$NNc$G$O(B, $B<1JLHV9f(B 0)   ($B<!$NNc$G$O(B, $B<1JLHV9f(B 0)
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [261] sm1.sm1(0," ( (x-1)^2 ) . ");  [261] sm1.sm1(0," ( (x-1)^2 ) . ");
 0  0
Line 376  x^2-2*x+1
Line 374  x^2-2*x+1
 @end example  @end example
 */  */
   
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}.      @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}.
 @end table  @end table
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}.      @code{sm1.start}, @code{ox_push_int0}, @code{sm1.push_poly0}, @code{sm1.get_Sm1_proc()}.
Line 390  x^2-2*x+1
Line 388  x^2-2*x+1
 */  */
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.push_int0  @c sort-sm1.push_int0
 @node sm1.push_int0,,, SM1 Functions  @node sm1.push_int0,,, SM1 Functions
 @subsection @code{sm1.push_int0}  @subsection @code{sm1.push_int0}
Line 428  Note that @code{ox_push_cmo(@var{p},1234)} send the bi
Line 426  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.  @item In other cases,  @code{ox_push_cmo} is called without data conversion.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.push_int0  @c sort-sm1.push_int0
 @node sm1.push_int0,,, SM1 Functions  @node sm1.push_int0,,, SM1 Functions
 @subsection @code{sm1.push_int0}  @subsection @code{sm1.push_int0}
Line 484  x*dx+1
Line 482  x*dx+1
 [1,2]  [1,2]
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{ox_push_cmo}      @code{ox_push_cmo}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item Reference  @item Reference
     @code{ox_push_cmo}      @code{ox_push_cmo}
Line 499  x*dx+1
Line 497  x*dx+1
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.gb  @c sort-sm1.gb
 @node sm1.gb,,, SM1 Functions  @node sm1.gb,,, SM1 Functions
 @node sm1.gb_d,,, SM1 Functions  
 @subsection @code{sm1.gb}  @subsection @code{sm1.gb}
 @findex sm1.gb  @findex sm1.gb
 @findex sm1.gb_d  @findex sm1.gb_d
Line 557  List
Line 554  List
    the polynomials are dehomogenized (,i.e., h is set to 1).     the polynomials are dehomogenized (,i.e., h is set to 1).
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.gb  @c sort-sm1.gb
 @node sm1.gb,,, SM1 Functions  @node sm1.gb,,, SM1 Functions
 @node sm1.gb_d,,, SM1 Functions  
 @subsection @code{sm1.gb}  @subsection @code{sm1.gb}
 @findex sm1.gb  @findex sm1.gb
 @findex sm1.gb_d  @findex sm1.gb_d
Line 608  List
Line 604  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).      $BLa$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  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [293] sm1.gb([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);  [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]]  [[x*dx+y*dy-1,y^2*dy^2+2],[x*dx,y^2*dy^2]]
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 In the example above,  In the example above,
 @tex the set $\{ x \partial_x + y \partial_y -1,  @tex the set $\{ x \partial_x + y \partial_y -1,
                  y^2 \partial_y^2+2\}$                   y^2 \partial_y^2+2\}$
Line 625  The set $\{x \partial_x, y^2 \partial_y\}$ is the lead
Line 621  The set $\{x \partial_x, y^2 \partial_y\}$ is the lead
 (the initial monominals) of the Gr\"obner basis.  (the initial monominals) of the Gr\"obner basis.
 @end tex  @end tex
 */  */
 /*&jp-texi  /*&ja
 $B>e$NNc$K$*$$$F(B,  $B>e$NNc$K$*$$$F(B,
 @tex $B=89g(B $\{ x \partial_x + y \partial_y -1,  @tex $B=89g(B $\{ x \partial_x + y \partial_y -1,
                  y^2 \partial_y^2+2\}$                   y^2 \partial_y^2+2\}$
Line 637  graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
Line 633  graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
 $BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B.  $BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B.
 @end tex  @end tex
 */  */
 /*&C-texi  /*&C
 @example  @example
 [294] sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]);  [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]]  [[dx+dy^3-4*dy,-dy^4+4*dy^2-1],[dx,-dy^4]]
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 In the example above, two monomials  In the example above, two monomials
 @tex  @tex
 $m = x^a y^b \partial_x^c \partial_y^d$ and  $m = x^a y^b \partial_x^c \partial_y^d$ and
Line 656  compared by the reverse lexicographic order
Line 652  compared by the reverse lexicographic order
 (i.e., if $50c+2d+a = 50c'+2d'+a'$, then use the reverse lexicogrpahic order).  (i.e., if $50c+2d+a = 50c'+2d'+a'$, then use the reverse lexicogrpahic order).
 @end tex  @end tex
 */  */
 /*&jp-texi  /*&ja
 $B>e$NNc$K$*$$$FFs$D$N%b%N%_%"%k(B  $B>e$NNc$K$*$$$FFs$D$N%b%N%_%"%k(B
 @tex  @tex
 $m = x^a y^b \partial_x^c \partial_y^d$ $B$*$h$S(B  $m = x^a y^b \partial_x^c \partial_y^d$ $B$*$h$S(B
Line 670  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
Line 666  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 $B$5$l$k(B).  $B$5$l$k(B).
 @end tex  @end tex
 */  */
 /*&C-texi  /*&C
 @example  @example
 [294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1);  [294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1);
       map(print,F[2][0])$        map(print,F[2][0])$
       map(print,F[2][1])$        map(print,F[2][1])$
 @end example  @end example
 */  */
 /*&C-texi  /*&C
 @example  @example
 [595]  [595]
    sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"],     sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"],
Line 704  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
Line 700  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 @end example  @end example
 */  */
   
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.reduction}, @code{sm1.rat_to_p}      @code{sm1.reduction}, @code{sm1.rat_to_p}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.reduction}, @code{sm1.rat_to_p}      @code{sm1.reduction}, @code{sm1.rat_to_p}
Line 719  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
Line 715  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.deRham  @c sort-sm1.deRham
 @node sm1.deRham,,, SM1 Functions  @node sm1.deRham,,, SM1 Functions
 @subsection @code{sm1.deRham}  @subsection @code{sm1.deRham}
Line 764  mode. So, it is strongly recommended to execute the co
Line 760  mode. So, it is strongly recommended to execute the co
 @code{ox_shutdown(sm1.get_Sm1_proc());} to interrupt and restart the server.  @code{ox_shutdown(sm1.get_Sm1_proc());} to interrupt and restart the server.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.deRham  @c sort-sm1.deRham
 @node sm1.deRham,,, SM1 Functions  @node sm1.deRham,,, SM1 Functions
 @subsection @code{sm1.deRham}  @subsection @code{sm1.deRham}
Line 808  mode. So, it is strongly recommended to execute the co
Line 804  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.    $B$r0l;~(B shutdown $B$7$F%j%9%?!<%H$7$?J}$,0BA4$G$"$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [332] sm1.deRham([x^3-y^2,[x,y]]);  [332] sm1.deRham([x^3-y^2,[x,y]]);
 [1,1,0]  [1,1,0]
Line 816  mode. So, it is strongly recommended to execute the co
Line 812  mode. So, it is strongly recommended to execute the co
 [1,2]  [1,2]
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.start}, @code{deRham} (sm1 command)      @code{sm1.start}, @code{deRham} (sm1 command)
Line 826  mode. So, it is strongly recommended to execute the co
Line 822  mode. So, it is strongly recommended to execute the co
     Journal of pure and applied algebra 139 (1999), 201--233.      Journal of pure and applied algebra 139 (1999), 201--233.
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.start}, @code{deRham} (sm1 command)      @code{sm1.start}, @code{deRham} (sm1 command)
Line 840  mode. So, it is strongly recommended to execute the co
Line 836  mode. So, it is strongly recommended to execute the co
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.hilbert  @c sort-sm1.hilbert
 @node sm1.hilbert,,, SM1 Functions  @node sm1.hilbert,,, SM1 Functions
 @subsection @code{sm1.hilbert}  @subsection @code{sm1.hilbert}
Line 882  List
Line 878  List
    polynomials in @code{sm1} is  slower than in @code{asir}.     polynomials in @code{sm1} is  slower than in @code{asir}.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.hilbert  @c sort-sm1.hilbert
 @node sm1.hilbert,,, SM1 Functions  @node sm1.hilbert,,, SM1 Functions
 @subsection @code{sm1.hilbert}  @subsection @code{sm1.hilbert}
Line 921  List
Line 917  List
 @end itemize  @end itemize
 */  */
   
 /*&C-texi  /*&C
 @example  @example
   
 [346] load("katsura")$  [346] load("katsura")$
Line 951  List
Line 947  List
 @end example  @end example
 */  */
   
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.start}, @code{sm1.gb}, @code{longname}      @code{sm1.start}, @code{sm1.gb}, @code{longname}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.start}, @code{sm1.gb}, @code{longname}      @code{sm1.start}, @code{sm1.gb}, @code{longname}
Line 965  List
Line 961  List
 */  */
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.genericAnn  @c sort-sm1.genericAnn
 @node sm1.genericAnn,,, SM1 Functions  @node sm1.genericAnn,,, SM1 Functions
 @subsection @code{sm1.genericAnn}  @subsection @code{sm1.genericAnn}
Line 994  List
Line 990  List
     @var{f} is a polynomial in the variables @code{rest}(@var{v}).      @var{f} is a polynomial in the variables @code{rest}(@var{v}).
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.genericAnn  @c sort-sm1.genericAnn
 @node sm1.genericAnn,,, SM1 Functions  @node sm1.genericAnn,,, SM1 Functions
 @subsection @code{sm1.genericAnn}  @subsection @code{sm1.genericAnn}
Line 1024  List
Line 1020  List
     @var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B.      @var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [595] sm1.genericAnn([x^3+y^3+z^3,[s,x,y,z]]);  [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]  [-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  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.start}      @code{sm1.start}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.start}      @code{sm1.start}
Line 1045  List
Line 1041  List
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.wTensor0  @c sort-sm1.wTensor0
 @node sm1.wTensor0,,, SM1 Functions  @node sm1.wTensor0,,, SM1 Functions
 @subsection @code{sm1.wTensor0}  @subsection @code{sm1.wTensor0}
Line 1086  the inputs @var{f} and @var{g} are left ideals of D.
Line 1082  the inputs @var{f} and @var{g} are left ideals of D.
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @c sort-sm1.wTensor0  @c sort-sm1.wTensor0
 @node sm1.wTensor0,,, SM1 Functions  @node sm1.wTensor0,,, SM1 Functions
 @subsection @code{sm1.wTensor0}  @subsection @code{sm1.wTensor0}
Line 1126  the inputs @var{f} and @var{g} are left ideals of D.
Line 1122  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.  $B0lHL$K(B, $B=PNO$O<+M32C72(B D^r $B$NItJ,2C72$G$"$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [258]  sm1.wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]);  [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],  [[-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],
Line 1137  the inputs @var{f} and @var{g} are left ideals of D.
Line 1133  the inputs @var{f} and @var{g} are left ideals of D.
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.reduction  @c sort-sm1.reduction
 @node sm1.reduction,,, SM1 Functions  @node sm1.reduction,,, SM1 Functions
 @subsection @code{sm1.reduction}  @subsection @code{sm1.reduction}
Line 1175  sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
Line 1171  sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
 are for distributed polynomials.  are for distributed polynomials.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @node sm1.reduction,,, SM1 Functions  @node sm1.reduction,,, SM1 Functions
 @subsection @code{sm1.reduction}  @subsection @code{sm1.reduction}
 @findex sm1.reduction  @findex sm1.reduction
Line 1214  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
Line 1210  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.  $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [259] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);  [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]]  [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
Line 1222  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
Line 1218  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]]  [0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm1.start}, @code{d_true_nf}      @code{sm1.start}, @code{d_true_nf}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm1.start}, @code{d_true_nf}      @code{sm1.start}, @code{d_true_nf}
Line 1236  sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
Line 1232  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  @node sm1.xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1.xml_tree_to_prefix_string}  @subsection @code{sm1.xml_tree_to_prefix_string}
 @findex sm1.xml_tree_to_prefix_string  @findex sm1.xml_tree_to_prefix_string
Line 1264  asir has not yet understood this CMO.
Line 1260  asir has not yet understood this CMO.
 command search path.)  command search path.)
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @node sm1.xml_tree_to_prefix_string,,, SM1 Functions  @node sm1.xml_tree_to_prefix_string,,, SM1 Functions
 @subsection @code{sm1.xml_tree_to_prefix_string}  @subsection @code{sm1.xml_tree_to_prefix_string}
 @findex sm1.xml_tree_to_prefix_string  @findex sm1.xml_tree_to_prefix_string
Line 1291  String
Line 1287  String
 ($B$?$H$($P(B, /usr/local/jdk1.1.8/bin $B$r%3%^%s%I%5!<%A%Q%9$KF~$l$k$J$I(B.)  ($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  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [263] load("om");  [263] load("om");
 1  1
Line 1308  Trying to connect to the server... Done.
Line 1304  Trying to connect to the server... Done.
 basic_plus(basic_times(basic_power(x,4),1),basic_times(basic_power(x,0),-1))  basic_plus(basic_times(basic_power(x,4),1),basic_times(basic_power(x,0),-1))
 @end example  @end example
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str}      @code{om_*}, @code{OpenXM/src/OpenMath}, @code{eval_str}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{om_*}, @code{OpenXM/src/OpenMath},  @code{eval_str}      @code{om_*}, @code{OpenXM/src/OpenMath},  @code{eval_str}
Line 1324  basic_plus(basic_times(basic_power(x,4),1),basic_times
Line 1320  basic_plus(basic_times(basic_power(x,4),1),basic_times
   
   
   
 /*&eg-texi  /*&en
 @c sort-sm1.syz  @c sort-sm1.syz
 @node sm1.syz,,, SM1 Functions  @node sm1.syz,,, SM1 Functions
 @node sm1.syz_d,,, SM1 Functions  
 @subsection @code{sm1.syz}  @subsection @code{sm1.syz}
 @findex sm1.syz  @findex sm1.syz
 @findex sm1.syz_d  @findex sm1.syz_d
Line 1354  Here @var{s} is the syzygy of @var{f} in the ring of d
Line 1349  Here @var{s} is the syzygy of @var{f} in the ring of d
 operators with the variable @var{v}.  operators with the variable @var{v}.
 @var{g} is a Groebner basis of @var{f} with the weight vector @var{w},  @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  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}.  @var{t} is the syzygy of the Gr\"obner basis @var{g}.
 In summary, @var{g} = @var{m} @var{f} and  In summary, @var{g} = @var{m} @var{f} and
 @var{s} @var{f} = 0 hold as matrices.  @var{s} @var{f} = 0 hold as matrices.
Line 1368  In summary, @var{g} = @var{m} @var{f} and
Line 1363  In summary, @var{g} = @var{m} @var{f} and
    The homogenization variable h is automatically added.     The homogenization variable h is automatically added.
 @end itemize  @end itemize
 */  */
 /*&jp-texi  /*&ja
 @c sort-sm1.syz  @c sort-sm1.syz
 @node sm1.syz,,, SM1 Functions  @node sm1.syz,,, SM1 Functions
 @node sm1.syz_d,,, SM1 Functions  
 @subsection @code{sm1.syz}  @subsection @code{sm1.syz}
 @findex sm1.syz  @findex sm1.syz
 @findex sm1.syz_d  @findex sm1.syz_d
Line 1411  syzygy $B$G$"$k(B.
Line 1405  syzygy $B$G$"$k(B.
 $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B.  $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B.
 @end itemize  @end itemize
 */  */
 /*&C-texi  /*&C
 @example  @example
 [293] sm1.syz([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);  [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  [[[y*x*dy*dx-2,-x*dx-y*dy+1]],    generators of the syzygy
Line 1420  syzygy $B$G$"$k(B.
Line 1414  syzygy $B$G$"$k(B.
  [[y*x*dy*dx-2,-x*dx-y*dy+1]]]]   [[y*x*dy*dx-2,-x*dx-y*dy+1]]]]
 @end example  @end example
 */  */
 /*&C-texi  /*&C
 @example  @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]]]);  [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  [[[y*x*dy*dx-1,-x^2*dx^2-x*dx-y^2*dy^2-y*dy+4]], generators of the syzygy
Line 1433  syzygy $B$G$"$k(B.
Line 1427  syzygy $B$G$"$k(B.
   
   
   
 /*&eg-texi  /*&en
 @node sm1.mul,,, SM1 Functions  @node sm1.mul,,, SM1 Functions
 @subsection @code{sm1.mul}  @subsection @code{sm1.mul}
 @findex sm1.mul  @findex sm1.mul
Line 1459  List
Line 1453  List
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.mul,,, SM1 Functions  @node sm1.mul,,, SM1 Functions
 @subsection @code{sm1.mul}  @subsection @code{sm1.mul}
 @findex sm1.mul  @findex sm1.mul
Line 1487  List
Line 1481  List
 @end itemize  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
 [277] sm1.mul(dx,x,[x]);  [277] sm1.mul(dx,x,[x]);
Line 1503  x+2*y
Line 1497  x+2*y
   
   
   
 /*&eg-texi  /*&en
 @node sm1.distraction,,, SM1 Functions  @node sm1.distraction,,, SM1 Functions
 @subsection @code{sm1.distraction}  @subsection @code{sm1.distraction}
 @findex sm1.distraction  @findex sm1.distraction
Line 1534  See Saito, Sturmfels, Takayama : Grobner Deformations 
Line 1528  See Saito, Sturmfels, Takayama : Grobner Deformations 
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.distraction,,, SM1 Functions  @node sm1.distraction,,, SM1 Functions
   
 @subsection @code{sm1.distraction}  @subsection @code{sm1.distraction}
Line 1565  See Saito, Sturmfels, Takayama : Grobner Deformations 
Line 1559  See Saito, Sturmfels, Takayama : Grobner Deformations 
 @end itemize  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
 [280] sm1.distraction([x*dx,[x],[x],[dx],[x]]);  [280] sm1.distraction([x*dx,[x],[x],[dx],[x]]);
Line 1581  x^2+3*x+2
Line 1575  x^2+3*x+2
 @end example  @end example
 */  */
   
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{distraction2(sm1)},      @code{distraction2(sm1)},
 @end table  @end table
 */  */
   
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{distraction2(sm1)},      @code{distraction2(sm1)},
Line 1597  x^2+3*x+2
Line 1591  x^2+3*x+2
   
   
   
 /*&eg-texi  /*&en
 @node sm1.gkz,,, SM1 Functions  @node sm1.gkz,,, SM1 Functions
 @subsection @code{sm1.gkz}  @subsection @code{sm1.gkz}
 @findex sm1.gkz  @findex sm1.gkz
Line 1622  List
Line 1616  List
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.gkz,,, SM1 Functions  @node sm1.gkz,,, SM1 Functions
 @subsection @code{sm1.gkz}  @subsection @code{sm1.gkz}
 @findex sm1.gkz  @findex sm1.gkz
Line 1645  List
Line 1639  List
 @end itemize  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
   
Line 1661  List
Line 1655  List
   
   
   
 /*&eg-texi  /*&en
 @node sm1.appell1,,, SM1 Functions  @node sm1.appell1,,, SM1 Functions
 @subsection @code{sm1.appell1}  @subsection @code{sm1.appell1}
 @findex sm1.appell1  @findex sm1.appell1
Line 1685  F_D(a,b1,b2,...,bn,c;x1,...,xn)
Line 1679  F_D(a,b1,b2,...,bn,c;x1,...,xn)
 where @var{a} =(a,c,b1,...,bn).  where @var{a} =(a,c,b1,...,bn).
 When n=2, the Lauricella function is called the Appell function F_1.  When n=2, the Lauricella function is called the Appell function F_1.
 The parameters a, c, b1, ..., bn may be rational numbers.  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  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.appell1,,, SM1 Functions  @node sm1.appell1,,, SM1 Functions
 @subsection @code{sm1.appell1}  @subsection @code{sm1.appell1}
 @findex sm1.appell1  @findex sm1.appell1
Line 1712  F_D(a,b1,b2,...,bn,c;x1,...,xn)
Line 1709  F_D(a,b1,b2,...,bn,c;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,  $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,c,b1,...,bn).  @var{a} =(a,c,b1,...,bn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.  $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(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  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
   
Line 1734  F_D(a,b1,b2,...,bn,c;x1,...,xn)
Line 1733  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]]   [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]));  [283] sm1.rank(sm1.appell1([1/2,3,5,-1/3]));
 1  3
   
 [285] Mu=2$ Beta = 1/3$  [285] Mu=2$ Beta = 1/3$
 [287] sm1.rank(sm1.appell1([Mu+Beta,Mu+1,Beta,Beta,Beta]));  [287] sm1.rank(sm1.appell1([Mu+Beta,Mu+1,Beta,Beta,Beta]));
Line 1745  F_D(a,b1,b2,...,bn,c;x1,...,xn)
Line 1744  F_D(a,b1,b2,...,bn,c;x1,...,xn)
   
 */  */
   
 /*&eg-texi  /*&en
 @node sm1.appell4,,, SM1 Functions  @node sm1.appell4,,, SM1 Functions
 @subsection @code{sm1.appell4}  @subsection @code{sm1.appell4}
 @findex sm1.appell4  @findex sm1.appell4
Line 1769  F_4(a,b,c1,c2,...,cn;x1,...,xn)
Line 1768  F_4(a,b,c1,c2,...,cn;x1,...,xn)
 where @var{a} =(a,b,c1,...,cn).  where @var{a} =(a,b,c1,...,cn).
 When n=2, the Lauricella function is called the Appell function F_4.  When n=2, the Lauricella function is called the Appell function F_4.
 The parameters a, b, c1, ..., cn may be rational numbers.  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  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.appell4,,, SM1 Functions  @node sm1.appell4,,, SM1 Functions
 @subsection @code{sm1.appell4}  @subsection @code{sm1.appell4}
 @findex sm1.appell4  @findex sm1.appell4
Line 1796  F_C(a,b,c1,c2,...,cn;x1,...,xn)
Line 1798  F_C(a,b,c1,c2,...,cn;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,  $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,b,c1,...,cn).  @var{a} =(a,b,c1,...,cn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.  $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(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  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
   
Line 1819  F_C(a,b,c1,c2,...,cn;x1,...,xn)
Line 1823  F_C(a,b,c1,c2,...,cn;x1,...,xn)
   
   
   
 /*&eg-texi  /*&en
 @node sm1.rank,,, SM1 Functions  @node sm1.rank,,, SM1 Functions
 @subsection @code{sm1.rank}  @subsection @code{sm1.rank}
 @findex sm1.rank  @findex sm1.rank
Line 1848  holonomic. It is generally faster than @code{sm1.rank}
Line 1852  holonomic. It is generally faster than @code{sm1.rank}
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.rank,,, SM1 Functions  @node sm1.rank,,, SM1 Functions
 @subsection @code{sm1.rank}  @subsection @code{sm1.rank}
 @findex sm1.rank  @findex sm1.rank
Line 1876  holonomic. It is generally faster than @code{sm1.rank}
Line 1880  holonomic. It is generally faster than @code{sm1.rank}
 @end itemize  @end itemize
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
   
Line 1899  holonomic. It is generally faster than @code{sm1.rank}
Line 1903  holonomic. It is generally faster than @code{sm1.rank}
 */  */
   
   
 /*&eg-texi  /*&en
 @node sm1.auto_reduce,,, SM1 Functions  @node sm1.auto_reduce,,, SM1 Functions
 @subsection @code{sm1.auto_reduce}  @subsection @code{sm1.auto_reduce}
 @findex sm1.auto_reduce  @findex sm1.auto_reduce
Line 1925  Grobner bases.  This is the default.
Line 1929  Grobner bases.  This is the default.
 @end itemize  @end itemize
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.auto_reduce,,, SM1 Functions  @node sm1.auto_reduce,,, SM1 Functions
 @subsection @code{sm1.auto_reduce}  @subsection @code{sm1.auto_reduce}
 @findex sm1.auto_reduce  @findex sm1.auto_reduce
Line 1953  reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,%
Line 1957  reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,%
   
   
   
 /*&eg-texi  /*&en
 @node sm1.slope,,, SM1 Functions  @node sm1.slope,,, SM1 Functions
 @subsection @code{sm1.slope}  @subsection @code{sm1.slope}
 @findex sm1.slope  @findex sm1.slope
Line 1998  of the slopes are returned.
Line 2002  of the slopes are returned.
   
 */  */
   
 /*&jp-texi  /*&ja
 @node sm1.slope,,, SM1 Functions  @node sm1.slope,,, SM1 Functions
 @subsection @code{sm1.slope}  @subsection @code{sm1.slope}
 @findex sm1.slope  @findex sm1.slope
Line 2041  Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, 
Line 2045  Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, 
 Slope $B$N@dBPCM$rLa$9(B.  Slope $B$N@dBPCM$rLa$9(B.
 */  */
   
 /*&C-texi  /*&C
   
 @example  @example
   
Line 2060  Slope $B$N@dBPCM$rLa$9(B.
Line 2064  Slope $B$N@dBPCM$rLa$9(B.
 @end example  @end example
   
 */  */
 /*&eg-texi  /*&en
 @table @t  @table @t
 @item Reference  @item Reference
     @code{sm.gb}      @code{sm.gb}
 @end table  @end table
 */  */
 /*&jp-texi  /*&ja
 @table @t  @table @t
 @item $B;2>H(B  @item $B;2>H(B
     @code{sm.gb}      @code{sm.gb}
Line 2074  Slope $B$N@dBPCM$rLa$9(B.
Line 2078  Slope $B$N@dBPCM$rLa$9(B.
 */  */
   
   
 /*&eg-texi  /*&en
 @include sm1-auto-en.texi  @include sm1-auto.en
 */  */
   
 /*&jp-texi  /*&ja
 @include sm1-auto-ja.texi  @include sm1-auto.ja
 */  */
   
   
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