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Diff for /OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave between version 1.13 and 1.14

version 1.13, 2003/07/28 01:36:36 version 1.14, 2004/03/05 15:30:50
Line 1 
Line 1 
 /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.12 2003/07/28 01:17:39 takayama Exp $ */  /*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.13 2003/07/28 01:36:36 takayama Exp $ */
   
 /*&C-texi  /*&C-texi
 @c DO NOT EDIT THIS FILE   oxphc.texi  @c DO NOT EDIT THIS FILE   oxphc.texi
Line 7 
Line 7 
 @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 117  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 155  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 189  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 238  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 295  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 312  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 337  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 374  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 388  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 426  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 482  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 497  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
 @subsection @code{sm1.gb}  @subsection @code{sm1.gb}
Line 554  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
 @subsection @code{sm1.gb}  @subsection @code{sm1.gb}
Line 610  List
Line 610  List
 [[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 621  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 639  graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
Line 639  graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
 [[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 652  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 700  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
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 715  $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
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 760  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 812  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 822  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 836  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 878  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 947  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 961  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 990  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 1026  List
Line 1026  List
 [-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 1041  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 1082  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 1133  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 1171  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 1218  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 1232  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 1260  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 1304  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 1320  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
 @subsection @code{sm1.syz}  @subsection @code{sm1.syz}
Line 1363  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
 @subsection @code{sm1.syz}  @subsection @code{sm1.syz}
Line 1427  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 1453  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 1497  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 1528  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 1575  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 1591  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 1616  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 1655  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 1682  The parameters a, c, b1, ..., bn may be rational numbe
Line 1682  The parameters a, c, b1, ..., bn may be rational numbe
 @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 1739  F_D(a,b1,b2,...,bn,c;x1,...,xn)
Line 1739  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 1766  The parameters a, b, c1, ..., cn may be rational numbe
Line 1766  The parameters a, b, c1, ..., cn may be rational numbe
 @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 1813  F_C(a,b,c1,c2,...,cn;x1,...,xn)
Line 1813  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 1842  holonomic. It is generally faster than @code{sm1.rank}
Line 1842  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 1893  holonomic. It is generally faster than @code{sm1.rank}
Line 1893  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 1919  Grobner bases.  This is the default.
Line 1919  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 1947  reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(B. $B$3$A$i$,%
Line 1947  reduced $B%0%l%V%J4pDl$H$O$+$.$i$J$$(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 1992  of the slopes are returned.
Line 1992  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 2054  Slope $B$N@dBPCM$rLa$9(B.
Line 2054  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 2068  Slope $B$N@dBPCM$rLa$9(B.
Line 2068  Slope $B$N@dBPCM$rLa$9(B.
 */  */
   
   
 /*&eg-texi  /*&en
 @include sm1-auto-en.texi  @include sm1-auto-en.texi
 */  */
   
 /*&jp-texi  /*&ja
 @include sm1-auto-ja.texi  @include sm1-auto-ja.texi
 */  */
   
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  Added in v.1.14
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