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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.36 and 1.52

version 1.36, 2010/02/05 07:45:48 version 1.52, 2016/05/18 11:52:56
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 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.35 2009/12/09 04:58:29 takayama Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.51 2016/05/14 07:55:16 nakayama Exp $
 \input texinfo  \input texinfo
 @iftex  @iftex
 @catcode`@#=6  @catcode`@#=6
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 @title $B<B83E*;EMM$N4X?t(B  @title $B<B83E*;EMM$N4X?t(B
 @subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B  @subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B
 @subtitle 1.0 $BHG(B  @subtitle 1.0 $BHG(B
 @subtitle 2008 $BG/(B 1 $B7n(B  @subtitle 2014 $BG/(B 12 $B7n(B
   
 @author  by Risa/Asir committers  @author  by Risa/Asir committers
 @page  @page
 @vskip 0pt plus 1filll  @vskip 0pt plus 1filll
 Copyright @copyright{} Risa/Asir committers  Copyright @copyright{} Risa/Asir committers
 2004. All rights reserved.  2004--2010. All rights reserved.
 @end titlepage  @end titlepage
   
 @comment --- $B$*$^$8$J$$(B ---  @comment --- $B$*$^$8$J$$(B ---
Line 134  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
Line 134  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
 * dcurrenttime::  * dcurrenttime::
 * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module)::  * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module)::
 * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option)::  * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option)::
   * tk_pfn.rkn::
   * tk_pfn.graph::
   * tk_rk.runge_kutta_4::
   * tk_rk.runge_kutta_4_linear::
   * tk_rk.zonal::
   * getpid::
 @end menu  @end menu
   
 @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B  @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B
Line 1834  builtin/dp.c 1.49
Line 1840  builtin/dp.c 1.49
 @table @var  @table @var
 @item gentrace  @item gentrace
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.
 @item gentsyz  @item gensyz
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.
 @item nora  @item nora
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.
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 @comment ****************************************************************  @comment ****************************************************************
   
 @itemize @bullet  @itemize @bullet
 @item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B asirgui.exe $B$N$"$k%U%)%k%@$*$h$S(B $B4D6-JQ?t(B TEMP $B$,Dj5A$5$l$F$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B.  @item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B $B4D6-JQ?t(B TEMP $B$G;XDj$5$l$?%U%)%k%@$K$3$N%U%!%$%k$,:n@.$5$l$k(B.
 @item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main window $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B.  @item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main window $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B.
 @item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B.  @item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B.
   @item http://www.math.kobe-u.ac.jp/Asir/Add-ons $B$K$F(B winfep.exe $B$rG[I[$7$F$$$k(B. winfep $B$G$O$"$i$+$8$a%U%!%$%k$KF~NO%9%/%j%W%H$r=q$$$F$*$$$F(B, asirgui $B$G0l9T$E$D<B9T$5$;$k$3$H$,$G$-$k(B. winfep $B$O%W%l%<%s%F!<%7%g%sMQ$N%=%U%H%&%(%"$G$"$k(B. $B$3$l$O(B asirgui.hnd $B$rMxMQ$7$F$$$k(B.
 @end itemize  @end itemize
   
 @example  @example
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 @item $B$3$N5!G=$O(B 2006-12-5, 2007-02-13 $B$K2C$($i$l$?(B.  @item $B$3$N5!G=$O(B 2006-12-5, 2007-02-13 $B$K2C$($i$l$?(B.
 @item @code{OpenXM_contrib2/windows/asir32gui/asir32gui.clw} 1.11  @item @code{OpenXM_contrib2/windows/asir32gui/asir32gui.clw} 1.11
 @item @code{OpenXM_contrib2/windows/asir32gui/asir32guiview.cpp}  1.15, 1.1.6  @item @code{OpenXM_contrib2/windows/asir32gui/asir32guiview.cpp}  1.15, 1.1.6
   @item winfep $B$O(B 2010-01-20 $B:"$KBh0lHG$,(B commit $B$5$l$?(B.
   @item @code{OpenXM_contrib2/windows/winfep}  1.1
 @end itemize  @end itemize
   
   
Line 2017  ChangeLog
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 @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.  @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.
 @item  @item
 @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B.  $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.  @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B.  $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.
 @item  
 $B$3$l$i$N4X?t$O(B UNIX $BHG$K$N$_<BAu$5$l$F$$$k(B.  
 @end itemize  @end itemize
   
 @example  @example
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 @end itemize  @end itemize
   
   
   @node getpid,,, $B%7%9%F%`(B
   @subsection @code{getpid}
   @findex getpid
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item getpid()
   @end table
   
   @table @var
   @item return
   $B@0?t(B
   @end table
   
   @itemize @bullet
   @item asir $B$N%W%m%;%9HV9f$rLa$9(B.
   @item $B%W%m%;%9HV9f$O(B asir, ox_asir $BEy$GFHN)$7$?%W%m%;%9$KBP$7$F%7%9%F%`Fb$G0l0U$G$"$k(B.
   @end itemize
   
   @example
   [219] getpid();
   3214
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B ox_work_dir() $B4X?t$,0l0U$J:n6H%U%!%$%kL>$rF@$k$?$a$K;H$o$l$F$$$k(B.
   src/asir-contrib/packages/src/misc/rr 1.3,
   asir2000/builtin/file.c 1.28, rat.c 1.5,
   asir2000/parse/puref.c 1.9 $B$r;2>H(B (2013/02/15, 18).
   @end itemize
   
   
   @node loadpath,,, $B%7%9%F%`(B
   @subsection @code{loadpath}
   @findex loadpath
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item ctrl(``loadpath''[,list])
   @end table
   
   @table @var
   @item list
   $BJ8;zNs(B($B%Q%9(B)$B$N%j%9%H(B
   @item return
   $BJ8;zNs(B($B%Q%9(B)$B$N%j%9%H(B, $B$^$?$O?t(B(list$B$,M?$($i$l$?$H$-(B)
   @end table
   
   @itemize @bullet
   @item asir $B$NAH$_9~$_4X?t(B ctrl $B$N%9%$%C%A$N$R$H$D$G$"$k(B.
   @item asir $B$N%m!<%I%Q%9$N=PNO$^$?$O@_Dj$r9T$&(B.
   @end itemize
   
   @example
   [0] L=ctrl("loadpath");
   [/home/you/OpenXM/lib/asir-contrib,/home/you/OpenXM/lib/asir,.]
   [1] ctrl("loadpath", cons(getenv("HOME")+"/lib",L));
   0
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B 2014-5-12 $B$K%3%_%C%H$5$l$?(B.
   $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/ctrl.c (1.41) $B$G$"$k(B.
   @end itemize
   
   
   @node sysinfo,,, $B%7%9%F%`(B
   @subsection @code{sysinfo}
   @findex sysinfo
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item sysinfo()
   @end table
   
   @table @var
   @item return
   $BJ8;zNs$N%j%9%H(B
   @end table
   
   @itemize @bullet
   @item asir $B$NF0:n$7$F$$$k%*%Z%l!<%F%#%s%0%7%9%F%`$N>pJs$rJV$9(B.
   @item $B%j%9%H$N3F@.J,$O(B, OS$B%?%$%W(B, $B%+!<%M%kL>(B, OS$BL>(B, CPU$B%?%$%W(B, OS$B%P!<%8%g%s(B, $B40A4$J>pJs(B, $B%m%1!<%k$G$"$k(B.
   @item OS$B%?%$%W$O(B unix, macosx, windows $B$N$$$:$l$+$G$"$k(B.
   @item unix $B$*$h$S(B macosx $B$K$*$$$F$O(B, $B%7%9%F%`%3!<%k$*$h$S(B uname $B%3%^%s%I$K$h$j>pJs$r<hF@$7$F$$$k(B.
   windows $B$G$O(B, GetVersionEx() $B$J$I$N(B Win32 API $B$,MQ$$$i$l$F$$$k(B.
   @end itemize
   
   @example
   [0] sysinfo();
   [windows,WindowsNT,Windows7,x86_64,6.1.7601,WindowsNT 6.1.7601 Windows7 Service Pack 1 x86_64,ja]
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B 2014-5-14 $B$K%3%_%C%H$5$l$?(B.
   $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/ctrl.c (1.42) $B$G$"$k(B.
   @end itemize
   
   
 @comment ****************************************************************  @comment ****************************************************************
   
   
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Line 2729  ChangeLog
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
 @item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W})  @item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W})
 :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9!#(B  :: D $B2C72(B M = D / @var{Id} ($B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id}) $B$KBP$7$F(B,
   $B=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9(B.
 @end table  @end table
   
 @comment --- $B0z?t$N4JC1$J@bL@(B ---  @comment --- $B0z?t$N4JC1$J@bL@(B ---
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Line 2747  ChangeLog
   
 @itemize @bullet  @itemize @bullet
 @item  @item
 @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B  @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
 ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)  ($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
 @item  @item
 $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B  $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B.
 $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B  $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B,
 x,y $B$K$D$$$F@)8B$r9T$&!#(B  x,y $B$K$D$$$F@)8B$r9T$&(B.
 @end itemize  @end itemize
   
 $B0J2<$O!"%$%G%"%k(B  $B0J2<$O(B, $B%$%G%"%k(B
 @iftex  @iftex
 @tex  @tex
 $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $  $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $
 @end tex  @end tex
 $B$N(B  $B$H$*$$$?;~(B, D $B2C72(B
 @tex  @tex $M = D / I$ @end tex
 $x$  $B$N(B
 @end tex  @tex $x$ @end tex
 @end iftex  @end iftex
 @ifinfo  @ifinfo
 I = D . @{ x dx -1, y dy - 1 @} $B$N(B x  I = D . @{ x dx -1, y dy - 1 @} $B$H$*$$$?;~(B,
   D $B2C72(B M = D / I $B$N(B x
 @end ifinfo  @end ifinfo
 $B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B  $B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B.
 @example  @example
 [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);  [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
 -- generic_bfct_and_gr :0.001sec(0.001629sec)  -- generic_bfct_and_gr :0.001sec(0.001629sec)
Line 2653  B_@{S0@} length : 2
Line 2779  B_@{S0@} length : 2
 -- fctr(BF) + base :0.000999sec(0.0005109sec)  -- fctr(BF) + base :0.000999sec(0.0005109sec)
 [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]  [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]
 @end example  @end example
   $BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B,
   $B@)8B2C72$N4pDl(B
   @iftex
   @tex $\partial_x^1, \partial_x^0$ @end tex
   $B$r0UL#$7(B,
   $BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B
   @tex $(y \partial_y - 1, 0), (0, y\partial_y-1), (-1,0)$ @end tex
   @end iftex
   @ifinfo
   dx^1, dx^0
   $B$r0UL#$7(B,
   $BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B
   (y dy - 1, 0), (0, ydy-1), (-1,0)
   @end ifinfo
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
   
 @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B  @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
 @subsection @code{nk_restriction.restriction_ideal}  @subsection @code{nk_restriction.restriction_ideal}
 @comment --- $B:w0zMQ%-!<%o!<%I(B  @comment --- $B:w0zMQ%-!<%o!<%I(B
Line 2663  B_@{S0@} length : 2
Line 2803  B_@{S0@} length : 2
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
 @item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})  @item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
 :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9!#(B  :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9(B.
 @end table  @end table
   
 @comment --- $B0z?t$N4JC1$J@bL@(B ---  @comment --- $B0z?t$N4JC1$J@bL@(B ---
Line 2680  B_@{S0@} length : 2
Line 2820  B_@{S0@} length : 2
   
 @itemize @bullet  @itemize @bullet
 @item  @item
 @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B  @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
 ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)  ($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B)
 @item  @item
 $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B  $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B.
 $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B  $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B,
 x,y $B$K$D$$$F@)8B$r9T$&!#(B  x,y $B$K$D$$$F@)8B$r9T$&(B.
 @end itemize  @end itemize
   
 $B0J2<$O!"%$%G%"%k(B  $B0J2<$O(B, $B%$%G%"%k(B
 @iftex  @iftex
 @tex  @tex $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ @end tex
 $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $  
 @end tex  
 $B$N(B  $B$N(B
 @tex  @tex $x$ @end tex
 $x$  
 @end tex  
 @end iftex  @end iftex
 @ifinfo  @ifinfo
 I = D . @{ x dx -1, y dy - 1 @} $B$N(B x  I = D . @{ x dx -1, y dy - 1 @} $B$N(B x
Line 2721  B_@{S0@} length : 2
Line 2857  B_@{S0@} length : 2
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
 @item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W})  @item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W})
 :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9!#(B  :: D $B2C72(B M = D / @var{Id} ($B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id}) $B$KBP$7$F(B, $B=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9(B.
 @end table  @end table
   
 @comment --- $B0z?t$N4JC1$J@bL@(B ---  @comment --- $B0z?t$N4JC1$J@bL@(B ---
Line 2741  B_@{S0@} length : 2
Line 2877  B_@{S0@} length : 2
 @comment --- @bullet $B$O9uE@IU$-(B ---  @comment --- @bullet $B$O9uE@IU$-(B ---
 @itemize @bullet  @itemize @bullet
 @item  @item
 @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B  @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
 ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)  ($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B)
 @item  @item
 $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B  $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B.
 $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B  $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B,
 x,y $B$K$D$$$F@QJ,$r9T$&!#(B  x,y $B$K$D$$$F@QJ,$r9T$&(B.
 @end itemize  @end itemize
   
 $B0J2<$O!"%$%G%"%k(B  $B0J2<$O(B, $B%$%G%"%k(B
 @iftex  @iftex
 @tex  @tex $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\}$ @end tex
 $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $  $B$H$*$$$?;~(B, D $B2C72(B
 @end tex  @tex $M = D / I$ @end tex
 $B$N(B  $B$N(B
 @tex  @tex $t$ @end tex
 $t$  
 @end tex  
 @end iftex  @end iftex
 @ifinfo  @ifinfo
 I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t  I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @}
   $B$H$*$$$?;~(B, D $B2C72(B M = D / I $B$N(B t
 @end ifinfo  @end ifinfo
 $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])  $B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6])
 @example  @example
 [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],  [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],
 [dt,dx],[1,0]);  [dt,dx],[1,0]);
Line 2773  B_@{S0@} length : 2
Line 2908  B_@{S0@} length : 2
 -- fctr(BF) + base :0.001sec(0.0006731sec)  -- fctr(BF) + base :0.001sec(0.0006731sec)
 [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]]  [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]]
 @end example  @end example
   $BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B,
   $B@QJ,2C72$N4pDl(B
   @iftex
   @tex $t^1, t^0$ @end tex
   @end iftex
   @ifinfo
   t^1, t^0
   @end ifinfo
   $B$r0UL#$7(B,
   $BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@QJ,2C72$O(B
   @iftex
   @tex $(4 x \partial_x^2 + 6 \partial_x, 0), (0, -4 x \partial_x^2 - 6 \partial_x),
   (0, -2 x \partial_x), (0, 2 \partial_x)$ @end tex
   @end iftex
   @ifinfo
   (4 x dx^2 + 6 dx, 0), (0, -4 x dx^2 - 6 dx),
   (0, -2 x dx), (0, 2 dx)
   @end ifinfo
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
 @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B  @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
 @subsection @code{nk_restriction.integration_ideal}  @subsection @code{nk_restriction.integration_ideal}
Line 2782  B_@{S0@} length : 2
Line 2936  B_@{S0@} length : 2
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
 @item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})  @item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W})
 :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9!#(B  :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9(B.
 @end table  @end table
   
 @comment --- $B0z?t$N4JC1$J@bL@(B ---  @comment --- $B0z?t$N4JC1$J@bL@(B ---
Line 2802  B_@{S0@} length : 2
Line 2956  B_@{S0@} length : 2
 @comment --- @bullet $B$O9uE@IU$-(B ---  @comment --- @bullet $B$O9uE@IU$-(B ---
 @itemize @bullet  @itemize @bullet
 @item  @item
 @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B  @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
 ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)  ($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B)
 @item  @item
 $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B  $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B.
 $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B  $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B,
 x,y $B$K$D$$$F@QJ,$r9T$&!#(B  x,y $B$K$D$$$F@QJ,$r9T$&(B.
 @end itemize  @end itemize
   
 $B0J2<$O!"%$%G%"%k(B  $B0J2<$O(B, $B%$%G%"%k(B
 @iftex  @iftex
 @tex  @tex
 $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $  $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $
 @end tex  @end tex
 $B$N(B  $B$N(B
 @tex  @tex $t$ @end tex
 $t$  
 @end tex  
 @end iftex  @end iftex
 @ifinfo  @ifinfo
 I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t  I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t
 @end ifinfo  @end ifinfo
 $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6])  $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6])
 @example  @example
 [1431]  nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x],  [1431]  nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x],
 [dt,dx],[1,0]);  [dt,dx],[1,0]);
Line 2834  B_@{S0@} length : 2
Line 2986  B_@{S0@} length : 2
 -- fctr(BF) + base :0.001sec(0.001091sec)  -- fctr(BF) + base :0.001sec(0.001091sec)
 -- integration_ideal_internal :0.002sec(0.001879sec)  -- integration_ideal_internal :0.002sec(0.001879sec)
 [2*x*dx+1]  [2*x*dx+1]
 [1432]  
 @end example  @end example
   
 @node nk_restriction,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option)  @node nk_restriction.ann_mul,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
   @subsection @code{nk_restriction.ann_mul}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ann_mul
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.ann_mul(@var{I}, @var{J}, @var{VL}, @var{DVL})
   :: @var{f} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{I},
   @var{g} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$r(B @var{J} $B$H$7$?$H$-(B,
   @var{fg} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item I
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item J
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item test_ann_mul(), test_ann_mul2(), test_ann_mul3() $B$r;2>H(B.
   @end itemize
   
   
   @node nk_restriction (option) ,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option)
 @subsection @code{nk_restriction (option)}  @subsection @code{nk_restriction (option)}
 @comment --- $B:w0zMQ%-!<%o!<%I(B  @comment --- $B:w0zMQ%-!<%o!<%I(B
 @findex nk_restriction (option)  @findex nk_restriction (option)
Line 2845  B_@{S0@} length : 2
Line 3029  B_@{S0@} length : 2
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
 @item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})  @item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
 @item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})  @item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord})
 @item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})  @item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
 @item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})  @item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord})
 :: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B  :: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B
 @end table  @end table
   
Line 2859  B_@{S0@} length : 2
Line 3043  B_@{S0@} length : 2
 $B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B)  $B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B)
 @item @var{m}  @item @var{m}
 $B@0?t(B  $B@0?t(B
   @item @var{b}
   0, 1, 2, 3 $B$N$$$:$l$+(B
   @item @var{ord}
   $B=E$_(B0$B$NJQ?t$KBP$9$k9`=g=x(B
 @end table  @end table
   
 @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---  @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
Line 2899  restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s
Line 3087  restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s
   
 @item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B  @item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B
 $B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B.  $B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B.
   
   @item @var{b} $B$K$h$j(B, $B2C72$N%0%l%V%J4pDl7W;;$K@F<!2=(B, trace $B%"%k%4%j%:%`(B
   $B$rMQ$$$k$+$I$&$+;XDj$G$-$k(B.
   $B$?$@$7(B, $B@F<!2=$"$j$G7W;;$G$-$k$N$O(B Risa/Asir $B%P!<%8%g%s(B 20100415 $B0J9_$G$"$k(B.
   
   0: $B@F<!2=$J$7(B, trace $B$J$7(B
   
   1: $B@F<!2=$J$7(B, trace $B$"$j(B
   
   2: $B@F<!2=$"$j(B, trace $B$J$7(B ($B%G%U%)%k%H(B)
   
   3: $B@F<!2=$"$j(B, trace $B$"$j(B
   
   @item @var{ord} $B$,;XDj$5$l$k$H(B, $B=PNO$N@QJ,(B, $B@)8B%$%G%"%k$O(B, $B$=$N9`=g=x$K(B
   $B4X$9$k%0%l%V%J4pDl$H$J$k(B. $B2C72$N%0%l%V%J4pDl7W;;$N(B POT $B=g=x$N(B tie breaker
   $B$H$7$F;HMQ$5$l$k$N$G7W;;8zN($KBg$-$J1F6A$rM?$($k2DG=@-$,$"$k(B.
   $B%G%U%)%k%H$O(B 0, $B$D$^$jA4<!?t5U<!=q<0=g=x$G$"$k(B.
   
   $B$3$N%*%W%7%g%s$O(B @var{param} $B$HF1;~MxMQ$G$-$J$$(B. ($B8e$KBP1~M=Dj(B.)
 @end itemize  @end itemize
   
 $B0J2<$O(B,  $B0J2<$O(B,
Line 2959  $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
Line 3166  $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
 $B$G$"$k$3$H$r0UL#$9$k(B.  $B$G$"$k$3$H$r0UL#$9$k(B.
 @end ifinfo  @end ifinfo
   
   @node nk_restriction.trans_inhomo,,, D $B2C72$N@QJ,%$%G%"%k$NHs@F<!ItJ,$K4X$9$k4X?t(B
   @subsection @code{nk_restriction.trans_inhomo}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.trans_inhomo
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.trans_inhomo(@var{P}, @var{INT}, @var{VL}, @var{DVL}, @var{W})
   :: D $B2C72$N@)8B%$%G%"%k(B, $B@QJ,%$%G%"%k$N@8@.85$KBP$9$kHs@F<!ItJ,$N>pJs$+$i(B, $BG$0U$N85$KBP$9$kHs@F<!ItJ,$r7W;;$9$k4X?t(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item P
   $B@QJ,%$%G%"%k$N85(B, $B$^$?$O@)8B%$%G%"%k$N85(B
   @item INT
   nk_restriction.integration_ideal( ... |inhomo=1); $B$^$?$O(B
   
   nk_restriction.restriction_ideal( ... |inhomo=1); $B$N=PNO(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item @var{VL}, @var{DVL}, @var{W} $B$O(B @var{INT} $B$N7W;;$KMQ$$$?$b$N$r$=$N$^$^;HMQ$7$J$1$l$P$J$i$J$$(B.
   @item $B$b$7(B, @var{P} $B$,(B @var{INT[0]} $B$G@8@.$5$l$k@QJ,(B, $B@)8B%$%G%"%k$N85$G$J$$>l9g$O%(%i!<%a%C%;!<%8$,I=<($5$l$k(B.
   @end itemize
   
   @node nk_restriction.ost_integration_ideal,,, D $B2C72$N@QJ,%$%G%"%k(B
   @subsection @code{nk_restriction.ost_integration_ideal}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ost_integration_ideal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   $B@QJ,NN0h$,6h4V$ND>@Q$G$"$k$h$&$J@QJ,$NK~$?$9(B
   $B%[%m%N%_%C%/@F<!HyJ,J}Dx<07O$rJV$9(B (Oaku-Shiraki-Takayama, 2003).
   @table @t
   @item nk_restriction.ost_integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}, @var{LB}, @var{UB})
   :: Heaviside $B4X?t$H$N@Q$NK~$?$9HyJ,J}Dx<07O$N7W;;$K%7%g!<%H%+%C%HK!$rMQ$$$k(B.
   @item nk_restriction.ost_integration_ideal2(@var{Id}, @var{VL}, @var{DVL}, @var{W}, @var{LB}, @var{UB})
   :: Heaviside $B4X?t$H$N@Q$NK~$?$9HyJ,J}Dx<07O$N7W;;$K@)8B%$%G%"%k$rMQ$$$k(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @item LB
   $B@QJ,6h4V$N2<C<$rI=$9%j%9%H(B
   @item UB
   $B@QJ,6h4V$N>eC<$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item $B2<C<(B, $B>eC<$KL58BBg$r;XDj$9$k$H$-$O(B, $BJ8;zNs(B  "inf", "+inf", "-inf" $B$rMQ$$$k(B.
   @end itemize
   
   $B0J2<$O(B, Oaku-Shiraki-Takayama (2003) $B$NNc(B5.1$B$r7W;;$7$?$b$N$G$"$k(B.
   @iftex
   @tex
   $ \int_0^\infty \exp((-t^3+t)x) dt $
   @end tex
   $B$NHo@QJ,4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   @tex
   $ I = \langle \partial_t +(3t^2-1)x, \partial_x+t^3-t \rangle $
   @end tex
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end iftex
   @ifinfo
   \int_0^$B!g(B exp((-t^3+t)x) dt
   $B$NHs@QJ,4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   I = < dt +(3t^2-1)x, dx+t^3-t >
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end ifinfo
   @example
   [1871] Id=[dt+(3*t^2-1)*x, dx+t^3-t]$
   [1872] VL=[t,x]$
   [1873] DVL=[dt,dx]$
   [1874] W=[1,0]$
   [1875] nk_restriction.ost_integration_ideal(Id,VL,DVL,W,[0],["inf"]);
   -- nd_weyl_gr :0.008sec(0.006768sec)
   -- weyl_minipoly :0.004001sec(0.003029sec)
   -- generic_bfct_and_gr :0.012sec(0.0129sec)
   generic bfct : [[1,1],[s,1],[s-2,1]]
   S0 : 2
   B_{S0} length : 3
   -- fctr(BF) + base :0.008sec(0.007395sec)
   -- integration_ideal_internal :0.012sec + gc : 0.016sec(0.04311sec)
   [-27*x^3*dx^3-54*x^2*dx^2+(4*x^3+3*x)*dx+4*x^2-3,27*x^2*dx^4+135*x*dx^3+(-4*x^2+105)*dx^2-16*x*dx-8]
   
   
   [1876] nk_restriction.ost_integration_ideal2(Id,VL,DVL,W,[0],["inf"]);
   ($BN,(B)
   [27*x^3*dx^3+54*x^2*dx^2+(-4*x^3-3*x)*dx-4*x^2+3,-27*x^2*dx^4-135*x*dx^3+(4*x^2-105)*dx^2+16*x*dx+8]
   @end example
   $B$3$N=PNO$O(B, $B@QJ,$rNm2=$9$k%[%m%N%_%C%/7O$G$"$k(B.
   
   @node nk_restriction.ost_sum,,, D $B2C72$N@QJ,%$%G%"%k(B
   @subsection @code{nk_restriction.ost_sum}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ost_sum
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.ost_sum(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $BOB$NK~$?$9(B($B@F<!(B/$BHs@F<!(B)$B:9J,J}Dx<07O$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$k:9J,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item Oaku-Shiraki-Takayama (2003) $B$NBh(B6$B@a$N%"%k%4%j%:%`$N<BAu(B.
   @item $B%*%W%7%g%s(B inhomo $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$rM?$($k>pJs$bJV$9(B.
   @end itemize
   
   $B0J2<$O(B, Oaku-Shiraki-Takayama (2003) $B$NNc(B6.5$B$NHs@F<!ItJ,$^$G7W;;$7$?$b$N$G$"$k(B.
   @iftex
   @tex
   $ \sum_{k=a}^b {n \choose k} $
   @end tex
   $B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   @tex
   $ I = \langle (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) \rangle $
   @end tex
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end iftex
   @ifinfo
   \sum_{k=a}^b n_C_k
   $B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   I = < (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) >
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end ifinfo
   @example
   [1871] Id=[(n-k+1)*en-(n+1), (k+1)*ek-(n-k)]$
   [1872] VL=[k,n]$
   [1873] DVL=[ek,en]$
   [1874] W=[1,0]$
   [1875] nk_restriction.ost_sum(Id,VL,DVL,W|inhomo=1);
   -- nd_weyl_gr :0.006667sec(0.004057sec)
   -- weyl_minipoly :0sec(0.001163sec)
   -- generic_bfct_and_gr :0.01sec(0.007085sec)
   generic bfct : [[1,1],[s,1]]
   S0 : 0
   B_{S0} length : 1
   -- fctr(BF) + base :0.003333sec(0.001785sec)
   -- restriction_ideal_internal :0sec(0.002336sec)
   [[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]]
   @end example
   
   @subsection @code{nk_restriction.module_restriction}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.module_restriction
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.module_restriction(@var{M}, @var{VL}, @var{DVL}, @var{W})
   :: D $B2C72(B D^r/@var{M} (@var{M} $B$O(B D^r $B$NItJ,2C72(B) $B$N=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item M
   D $B<+M32C72(B D^r $B$NItJ,2C72(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
   @comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)}
   $B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@)8B$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B,
   @var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B.
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B.
   $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B
   x $B$K$D$$$F@)8B$r9T$&(B.
   @end itemize
   
   $B0J2<$O(B, D $B<+M32C72(B
   @iftex
   @tex $D^2$ @end tex
   $B$NItJ,2C72(B
   @tex
   $M = D \cdot \{(\partial_x, \partial_y), (\partial_y, \partial_x), (x,y) \}$
   @end tex
   $B$r$H$j(B, D $B2C72(B
   @tex $D^2 / M$ @end tex
   $B$N(B
   @tex $x$ @end tex
   @end iftex
   @ifinfo
   D^2 $B$NItJ,2C72(B M = D . @{ (dx, dy), (dy, dx), (x, y) @}
   $B$r$H$j(B, D $B2C72(B D^2 / M $B$N(B x
   @end ifinfo
   $B$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B.
   @example
   [2691] nk_restriction.module_restriction([[dx,dy],[dy,dx],[x,y]], [x,y], [dx,dy], [1,0]);
   ....
   bfunction :
   s
   [[1,1],[s,1]]
   integer roots :
   [0,0]
   Generators:
   [e1,e2]
   Relations:
   [-8*e2*dy,4*e2*dy^2,-4*e2*dy^3,4*e1*y*dy-4*e1,-4*e1*dy^2,-4*e2,-e2*y*dy^2+2*e2*dy,-e1*y*dy+e1,e1*y*dy-e1]
   [[0,-1],[-dy^2,0],[y*dy-1,0]]
   @end example
   $B@)8B2C72$O(B
   @iftex
   @tex $(0, -1), (-\partial_y^2, 0), (y \partial_y -1 , 0)$ @end tex
   @end iftex
   @ifinfo
   (0, -1), (-dy^2, 0), (y, dy-1, 0)
   @end ifinfo
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
   @subsection @code{nk_restriction.module_integration}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.module_integration
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.module_integration(@var{M}, @var{VL}, @var{DVL}, @var{W})
   :: D $B2C72(B D^r/M (@var{M} $B$O(B D^r $B$NItJ,2C72(B) $B$N=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item M
   D $B<+M32C72(B D^r $B$NItJ,2C72(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item
   @var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B.
   @comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)}
   $B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@QJ,$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B,
   @var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B.
   @item
   $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B.
   $BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B
   x $B$K$D$$$F@QJ,$r9T$&(B.
   @end itemize
   
   $B0J2<$O(B, D $B<+M32C72(B
   @iftex
   @tex $D^2$ @end tex
   $B$NItJ,2C72(B
   @tex $M = D \cdot \{(x, y), (y, x), (\partial_x, \partial_y) \}$ @end tex
   $B$r$H$j(B, D $B2C72(B
   @tex $D^2/M$ @end tex
   $B$N(B
   @tex $x$ @end tex
   @end iftex
   @ifinfo
   D^2 $B$NItJ,2C72(B M = D . @{ (x, y), (y, x), (dx, dy) @} $B$r$H$j(B,
   D $B2C72(B D^2 / M $B$N(B x
   @end ifinfo
   $B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k(B.
   @example
   [2702] nk_restriction.module_integration([[x,y],[y,x],[dx,dy]], [x,y], [dx,dy], [1,0]);
   ...
   bfunction :
   s
   [[1,1],[s,1]]
   integer roots :
   [0,0]
   Generators:
   [e1,e2]
   Relations:
   [-8*e2*y,-4*e2*y^2,-4*e2*y^3,-4*e1*y*dy-8*e1,-4*e1*y^2,-4*e2,-e2*y^2*dy-4*e2*y,e1*y*dy+2*e1,e1*y*dy+2*e1]
   [[0,-1],[y*dy+2,0],[-y^2,0]]
   @end example
   $B@QJ,2C72$O(B
   @iftex
   @tex $(0, -1), (y \partial_y + 2, 0), (-y^2, 0)$ @end tex
   @end iftex
   @ifinfo
   (0, -1), (y dy + 2, 0), (-y^2, 0)
   @end ifinfo
   $B$G@8@.$5$l$k$3$H$,$o$+$k(B.
   
 @noindent  @noindent
 ChangeLog  ChangeLog
 @itemize @bullet  @itemize @bullet
 @item  $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B.  @item  $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B.
 @item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B.  @item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B. 1.7--1.9 $B$r8+$h(B.
   @item 2010-05 $B$+$i(B 2010-07 $B$K$+$1$F(B 2 $B$D$N(B option (@code{ht}, @code{ord}) $B$H(B
   $B?7$?$J4X?t(B trans_inhomo() $B$,DI2C$5$l$?(B. 1.10--1.13 $B$r8+$h(B.
   @item 2011-08 $B$K(B ost_sum() $B$,DI2C$5$l$?(B. 1.20 $B$r8+$h(B.
   @item 2016-05 $B$K(B module_integration(), module_restriction() $B$,DI2C$5$l$?(B.
 @end itemize  @end itemize
   
 @node $B$=$NB>(B,,, $B<B83E*;EMM$N4X?t(B  @node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B
 @section $B$=$NB>(B  @section $B$=$NB>(B($BL$J,N`(B)
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  @node tk_pfn.rkn,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_pfn.rkn}
   @findex tk_pfn.rkn
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_pfn.rkn(@var{F},@var{X},@var{Y},@var{Xs},@var{Ys},@var{Ht},@var{H})
   :: Pfaffian $BJ}Dx<0$KBP$9$k(B Runge-Kutta $BK!(B
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B  $BFHN)JQ?t$H2r$NAH(B
   @item F, X, Y, Xs, Ys, Ht, H
   @var{F} $B$O(B Pfaffian $BJ}Dx<0$N78?t9TNs%j%9%H(B.
   @var{X} $B$OFHN)JQ?t%j%9%H(B.
   @var{Y} $B$O=>B0JQ?t%j%9%H(B.
   @var{Xs} $BFHN)JQ?t$N=PH/CM%j%9%H(B.
   @var{Ys} $B$O=PH/;~$N=>B0JQ?t$NCM%j%9%H(B.
   @var{Xt} $B$ODd;_$9$kFHN)JQ?t$NCM%j%9%H(B.
   @var{H} $B$OHy>/?t(B.
   @end table
   
   @itemize @bullet
   @item $B$3$N4X?t$OO"N)(BPfaffian$BJ}Dx<0(B dY/d X[i] = F[i] Y $B$r?tCME*$K2r$/(B.
   @item $BG$0U$N(B holonomic system $B$O(B Pfaffian $BJ}Dx<0$KJQ49$G$-$k(B ([SST, Chap 1]).$B!!JQ49$K$O(B yang.rr $B%Q%C%1!<%8$rMQ$$$k(B.
   @item d F[i]/d X[j] + F[i] F[j] = d F[j]/d X[i] + F[j] F[i] = 0 $B$,G$0U$N(B i, j $B$KBP$7$F@.N)$7$F$$$k$3$H$,2r$,B8:_$9$kI,MW==J,>r7o$G$"$k(B. $B$3$N>r7o$,@.N)$7$J$$$H$-$K$3$N4X?t$rMQ$$$F2r$r7W;;$7$F$b$=$N2r$O56J*$G$"$k(B.
   @item X[i] $B$,F0$/HO0O$O<B?t$G$J$$$H$$$1$J$$(B.
   @item Xs[i] <= X[i] <= Xt[i] $B$^$?$O(B Xt[i] <= X[i] <= Xs[i] $B$G$"$k(B.
   @item $B0z?t$NM?$(J}$NNc$O%=!<%9%3!<%I(B (@code{OpenXM/lib/asir-contrib/tk_pfn.rr} )$B$N(B @code{tk_pfn.test1}, @code{tk_pfn.test2} $B$r;2>H(B.
   @item $B2<$NNc$N=PNO$O(B X=(1,3) $B$G$NCM$,(B Y=(-8,2,-6) $B$G$"$k$3$H$r0UL#$9$k(B.
   @item $B;29M(B. taka_runge_kutta.rr, yang.rr
   @end itemize
   
   @example
   [1355] import("tk_pfn.rr");
   [1590]  tk_pfn.test1();
   Value at (3,0.1)[8.99,6,-0.2]
   Value at (1,3)[-8,2,-6]
   [[[1,3],-8,2,-6],
    [[1,2.9],-7.41,2,-5.8],
    --- snip ---
    [[3,0.1],8.99,6,-0.2]]
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B 2009-12 $B$+$i(B 2010-01 $B$K$+$1$F:G=i$NHG$,=q$+$l$?(B.
   @item @code{OpenXM/src/asir-contrib/packages/src/tk_pfn.rr} 1.1, 1.2
   @item $B$3$N%b%8%e!<%k$NA0?H$O(B @code{tk_pf2.rr} $B$G$"$k(B. $B$3$l$OFHN)JQ?t$,(B 2 $B8D$N>l9g$G$"$k(B.
   @end itemize
   
   
   @node tk_pfn.graph,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_pfn.graph}
   @findex tk_pfn.graph
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_pfn.graph(@var{Pf},@var{Dom},@var{Iv},@var{Step})
   :: 2$BJQ?t(B Pfaffian $BJ}Dx<0$r(B Runge-Kutta $BK!$G2r$$$F%0%i%UI=<($9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B  $B%j%9%H$NMWAG$O0J2<$N7A<0(B [[x$B$NCM(B,y$B$NCM(B],Y_1$B$NCM(B,Y_2$B$NCM(B, ...].
   [x$B$NCM(B, y$B$NCM(B] $B$O(B [0,0],[0.2,0],[0.4,0], ... , [0,0.2],[0.2,0.2], ... $B$N$h$&$K(B
   y $B$NCM$,30B&%k!<%W(B, x $B$NCM$,FbB&%k!<%W$N7A<0$GA}$($k(B.
   @item Pf, Dom, Iv, Step
   @var{Pf} $B$O(B Pfaffian $BJ}Dx<0$N78?t9TNs%j%9%H(B.  $BFHN)JQ?t$O(B x, y $B$G8GDj(B.
   @var{Dom} $B%j%9%H(B. $B2r$/$Y$-NN0h(B.
   @var{Iv} $B%j%9%H(B. $BNN0h$N:8C<$G$N=i4|CM(B.
   @var{Step} $B9o$_I}(B.
   @end table
   
   @itemize @bullet
   @item tk_pf2.rr, mt_graph.rr $B$r(B import $B$7$F$*$/I,MW$,$"$k(B.
   @item $B$3$N4X?t$OO"N)(BPfaffian$BJ}Dx<0(B dY/dx = Pf[0] Y, dY/dy = Pf[1] Y $B$r?tCME*$K2r$$$F%0%i%UI=<($9$k(B.
   @item @var{Dom} $B$O(B [[xmin,xmax],[ymin,ymax]] $B$N7A<0(B.
   @item $BNc$O%=!<%9%3!<%I(B (@code{OpenXM/lib/asir-contrib/tk_pfn.rr} )$B$N(B @code{tk_pfn.testgraph1()}, @code{tk_pfn.testgraph2()} $B$r;2>H(B.
   @item option $B$H$7$F$O(B fit=1 $B$,$"$k(B. Z$B<4$rE,59D4@0$9$k(B.
   @item @var{Dom} $B$NC<$O%0%i%UI=<($N;~$K0lIt%+%C%H$5$l$k$N$GCm0U(B.
   @end itemize
   
   @example
   [1355] import("tk_pf2.rr"); import("mt_graph.rr"); import("tk_pfn.rr");
   [1590] tk_pfn.testgraph1();
   
   $B$3$3$G(B testgraph1() $B$O0J2<$N$H$*$j(B.
   def testgraph1() {
     /* tk_bess2.bess2pf(1/2); */
     Pf=  [[[ 0, (1)/(x), 0 ],
            [ -x, (2*x^2+1)/(x), -2*x ],
            [ -y, 0, 0 ]],
           [[ 0, 0, (1)/(y) ],
            [ -x, 0, 0 ],
            [ -x, (1/2)/(x), (-1/2)/(y) ]]];
     /* tk_bess2.bess2Iv(1/2,[0.5,1.5]); */
     Iv = [0.105994,-0.651603,-0.760628];
     Dom=[[0.5,1.5],[1.5,9]];
     Step = 0.5;
     return tk_pfn.graph(Pf,Dom,Iv,Step | fit=1);
   }
   
   
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B 2010-08 $B$K:G=i$NHG$,=q$+$l$?(B.
   @item @code{OpenXM/src/asir-contrib/packages/src/tk_pfn.rr} 1.8
   @end itemize
   
   @node tk_rk.runge_kutta_4,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_rk.runge_kutta_4}
   @findex tk_rk.runge_kutta_4
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_rk.runge_kutta_4(@var{Eq},@var{X},@var{Y},@var{X0},@var{Y0},@var{Terminal},@var{Step})
   :: 4$B<!$N(B Runge-Kutta $BK!$K$h$kHyJ,J}Dx<0$N?tCM6a;w2r(B
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B  $B%j%9%H$NMWAG$O0J2<$N7A<0(B [@var{X}$B$NCM(B,Y_1$B$NCM(B,Y_2$B$NCM(B, ...].
    @var{X} $B$NCM$O8:$C$F$$$/(B. $B$h$C$F%j%9%H$N@hF,$,(B @var{Terminal} $BIU6a$G$N(B @var{Y} $B$NCM(B.
   @item Eq, X, Y, Step
   @var{Eq} $B$O(B $BJ}Dx<0$N1&JU(B. $B%j%9%H(B. Y[0]'=Eq[0], Y[1]'=Eq[1], ... $B$G$"$k(B.
   @var{X} $BFHN)JQ?tL>(B.
   @var{Y} $B%j%9%H(B. $B=>B0JQ?t$N%j%9%H(B.
   @var{Step} $B9o$_I}(B.
   @item X0, Y0, Terminal
   @var{X0} $B=PH/E@$N(B @var{X} $B$NCM(B.
   @var{Y0} $B=PH/E@$G$N(B @var{Y} $B$N=i4|CM(B.
   @var{Terminal} @var{X} $B$N=*CeE@(B.
   @end table
   
   @itemize @bullet
   @item taka_runge_kutta.rr $B$r(B import $B$7$F$*$/I,MW$,$"$k(B.
   @item $B$3$N4X?t$OO"N)>oHyJ,J}Dx<0(B Y[0]'=Eq[0], Y[1]'=Eq[1], ... $B$r?tCME*$K2r$/(B.
   @item $BNc$O%=!<%9%3!<%I(B (@code{OpenXM/lib/asir-contrib/src/taka_runge_kutta.rr} )$B$N(B
   @code{tk_rk.test4()} $B$r;2>H(B.
   @end itemize
   
   @example
   [1355] import("taka_runge_kutta.rr");
   [1590] tk_rk.test4();
   
   $B$3$3$G(B test4() $B$O0J2<$N$H$*$j(B. $B?6F0$NJ}Dx<0(B, y0'=y1, y1'=-y0 (y0''+y0=0). $BEz$O(B y0=cos(x)
   taka_plot_auto $B$O2<J}8~$G(B y $B$,@5(B.
   
   def test4() {
     A=runge_kutta_4([y1,-y0],x,[y0,y1],0,[1,0],3.14*2,0.1);
     taka_plot_auto(A);
     return(A);
   }
   
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$N4X?t$O(B 2000 $BG/Be$NA0H>$K:G=i$NHG$,=q$+$l$?(B. 2010$BG/(B Pfaffian $B$N?tCM2r@O$N0Y$K:FEY@0Hw(B
   @item @code{OpenXM/src/asir-contrib/packages/src/taka_runge_kutta.rr} 1.17
   @end itemize
   
   @node tk_rk.runge_kutta_4_linear,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_rk.runge_kutta_4_linear}
   @findex tk_rk.runge_kutta_4_linear
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_rk.runge_kutta_4_linear(@var{P},@var{X},@var{Y},@var{X0},@var{Y0},@var{Terminal},@var{Step})
   :: 4$B<!$N(B Runge-Kutta $BK!$K$h$kHyJ,J}Dx<0$N?tCM6a;w2r(B. $B@~7AJ}Dx<0@lMQ(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B  $B%j%9%H$NMWAG$O0J2<$N7A<0(B [@var{X}$B$NCM(B,Y_1$B$NCM(B,Y_2$B$NCM(B, ...].
    @var{X} $B$NCM$O8:$C$F$$$/(B. $B$h$C$F%j%9%H$N@hF,$,(B @var{Terminal} $BIU6a$G$N(B @var{Y} $B$NCM(B.
   @item P, X, Y, Step
   @var{P} $B$O(B $BJ}Dx<0$N1&JU(B. $B%j%9%H(B. Y'=P Y $B$G$"$k(B. $B=>B0JQ?t(B @var{Y} $B$OITMW(B.
   @var{X} $BFHN)JQ?tL>(B.
   @var{Y} $B%j%9%H(B. $B=>B0JQ?t$N%j%9%H(B. $B=>B0JQ?t$O<+F0@8@.$5$l$k(B. $B;H$o$l$F$$$J$$$N$G6u%j%9%H$G$h$$(B.
   @var{Step} $B9o$_I}(B.
   @item X0, Y0, Terminal
   @var{X0} $B=PH/E@$N(B @var{X} $B$NCM(B.
   @var{Y0} $B=PH/E@$G$N(B @var{Y} $B$N=i4|CM(B.
   @var{Terminal} @var{X} $B$N=*CeE@(B.
   @end table
   
   @itemize @bullet
   @item taka_runge_kutta.rr $B$r(B import $B$7$F$*$/I,MW$,$"$k(B.
   @end itemize
   
   @example
   [1355] import("taka_runge_kutta.rr");
   [1590] A=tk_rk.runge_kutta_4_linear([[0,1],[-1,0]],x,[ ], 0, [1,0], 3.14*2, 0.1);
   [1591] taka_plot_auto(A);
   
   $B?6F0$NJ}Dx<0(B, y0'=y1, y1'=-y0 (y0''+y0=0). $BEz$O(B y0=cos(x) $B$r2r$$$F$$$k(B.
   taka_plot_auto $B$O2<J}8~$G(B y $B$,@5(B.
   
   @end example
   
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item 2010$BG/(B Pfaffian $B$N?tCM2r@O$N0Y$K:F@0Hw(B.
   @item @code{OpenXM/src/asir-contrib/packages/src/taka_runge_kutta.rr} 1.17
   @end itemize
   
   
   
   @node fj_simp.simplify,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{fj_simp.simplify}
   @findex fj_simp.simplify
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item fj_simp.simplify(@var{arg1})
   :: arg1 $B$r4JC12=$9$k(B.
   @end table
   
   @table @var
   @item return
   $BB?9`<0(B, $BM-M}<0(B $B$^$?$O(B quote
   @item arg1
   $BB?9`<0(B $B$^$?$O(B $BM-M}<0(B
   @end table
   
   @itemize @bullet
   @item
   $B8=:_$N%P!<%8%g%s$G$O(B fj_simp.simplify $B$G$J$/(B, $BC1$K(B simplify $B$H$h$V(B.
   @item
   $B$3$N4X?t$O(B
   Joel S. Cohen, Computer Algebra and Symbolic Computation,
   http://web.cs.du.edu/~jscohen/MathematicalMethods/index.htm
   $B$K5-=R$5$l$F$$$k(B Automatic simplification algorithm $B$H(B
   B.F.Caviness, R.J.Fateman, Simplification of Radical Expressions (1976)
   $B$K5-=R$5$l$F$$$k(B radcan $B%"%k%4%j%:%`$N<BAu$G$"$k(B.
   @item
   $BJ#AGB?CM4X?t$H$7$F$O(B (x*y)^a = x^a*x^b $B$O0lHL$K$O@.N)$7$J$$$N$G(B, $B7k2L$rJ#AG4X?t$K;H$&$H$-$O(B
   $BCm0U$,I,MW$G$"$k(B. (x^a = exp(a*log(x)) $B$J$N$G(B)
   @end itemize
   
   @example
   load("fj_simplify.rr");
   [1434] simplify((x^(1/2))^3);
   ((x)^(3/2))
   [1435] simplify((2^(1/2))^2);
   2
   [1436] simplify((2+2^(1/2))^3);
   14*((2)^(1/2))+20
   [1437] simplify(exp(x)*exp(-x+y));
   ((@@e)^(y))
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{quote}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B>-MhE*$K$O(B module $B2=$7$F(B fj_simp module $B$K4^$a$kM=Dj(B.
   poly_simplify $B$+$i(B fj_simp.simplify $B$r8F$V(B.
   @item
   Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification $B$N5!G=(B.
   @item
   $B$3$N4X?t$O(B 2010.01 $B$K(B M.Fujimoto $B$K$h$j:G=i$NHG$,=q$+$l$?(B.
   OpenXM/src/asir-contrib/packages/src/fj_simplify.rr
   @end itemize
   
   @node tk_jack.zonal,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_jack.zonal}
   @findex tk_jack.zonal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_jack.zonel(@var{p},@var{n})
   :: $BJ,3d(B p $B$KBP$9$k(B n $BJQ?t$N(B zonal $BB?9`<0$r=PNO$9$k(B.
   @end table
   
   @table @var
   @item return
   $BB?9`<0(B. x_1, x_2, ... $B$,JQ?t(B.
   @item p
   $B?t$N%j%9%H(B. p=[p0,p1,...] $B$N;~(B p0>=p1>=...>0.
   @item n
   $B<+A3?t(B
   @end table
   
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B
   Koev-Edelman $B$K$h$k(B Pieri $B7?8x<0$rMQ$$$?(B Jack symmetric function $B$N7W;;(B
   $B%"%k%4%j%:%`$N<BAu$G$"$k(B.
   $B>\$7$/$O(B Wikipedia $B1Q8lHG(B Jack symmetric function $B$N9`$r;2>H(B.
   @item zonal(P,N) = jack(P,N,2) $B$G$"$k(B.
   @end itemize
   
   @example
   load("tk_jack.rr");
   [1434] tk_jack.zonal([3,2,1],3);
   (112*x_3*x_2^2+112*x_3^2*x_2)*x_1^3+(112*x_3*x_2^3+168*x_3^2*x_2^2+112*x_3^3*x_2)*x_1^2+(112*x_3^2*x_2^3+112*x_3^3*x_2^2)*x_1
   [1435] tk_jack.zonal([1,1],3);
   (2*x_2+2*x_3)*x_1+2*x_3*x_2
   [1436]  tk_jack.jack([1,1],3,2);
   (2*x_2+2*x_3)*x_1+2*x_3*x_2
   @end example
   
   @table @t
   @item $B;2>H(B
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B wishart $BJ,I[$K=>$&BP>N9TNs$NBh0l8GM-CM$,(B x $B0J2<$G$"$k3NN($N7W;;$r(B
   holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7W;;$9$k(B C $B$N%W%m%0%i%`$,(B
   $BI,MW$G$"$C$?(B. $B$=$l$r(B debug $B$9$k$?$a$K$H$j$"$($:=q$$$?$b$N(B.
   @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.
   @end itemize
   
   @node ot_hgm_ahg.cbase,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.cbase}
   @findex ot_hgm_ahg.cbase
   
   @table @t
   @item cbase(@var{A})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(B Pfaffian $B$N4pDl$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   Pfaffian$B$N4pDl(B($BHyJ,:nMQAG$N%b%N%_%"%k(B)$B$N%j%9%H(B
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item A-$BD64v2?%$%G%"%k$N(B Q(x)[dx] $B$K$*$1$kI8=`4pDl$O(B Pfaffian $B$N4pDl$H$J$k$,(B, $B5U$O$+$J$i$:$7$b??$G$O$J$$(B.  $B8D?t$O$b$A$m$sF1$8$G$"$k(B.
   @item
   $B%"%k%4%j%:%`$O(B
   T.Hibi, K.Nishiyama, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103
   $B$K$h$k(B.
   $B$5$i$K%Q%i%a!<%?(B b $B$r?t$KFC<l2=$9$k3NN(;;K!$rMQ$$$F$$$k(B.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] ot_hgm_ahg.cbase([[1,1,1,1],[0,1,2,3]]);
   We use a probabilistic algorithm to determine the base.[dx2^2,dx3*dx2,dx3^2]
   
   [dx3,dx4,1]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{get_mat2}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2012  $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B.
   @item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog  ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B.
   @end itemize
   
   @node ot_hgm_ahg.get_mat2,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.get_mat2}
   @findex ot_hgm_ahg.get_mat2
   @comment get_mat2
   @table @t
   @item get_mat2(@var{A},@var{W},@var{Std},@var{Mset})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O(B H_A $B$N(B Pfaffian $B$N4pDl$r5a$a$k$?$a$N(B Sylvester $BK!(B $B$rE,MQ$9$k$?$a$N9TNs$r@8@.$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item W
   $B%j%9%H(B. toric ideal $B$N%0%l%V%J!<4pDl$r7W;;$9$k$?$a$N(B weight vector.
   $BB?J,$J$s$G$b$$$$$O$:(B.
   @item Std
   $B%j%9%H(B. Pfaffian $B$N4pDl(B.  cbase(A) $B$N=PNO$rMQ$$$k(B.
   @item Mset
   Sylvester $B7?9TNs$r:n$k$?$a$NHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item $B=PNO$r(B @var{P} $B$KBeF~$9$k$H(B,
   @var{P}[0]*@var{P}[2] - @var{P}[1]*@var{Std} $B$,(B modulo  H_A $B$G(B 0 $B$H$J$k(B.
   @var{P}[0] $B$H(B @var{P}[2] $B$r7k9g$7$?9TNs$,(B, sylvester $B9TNs(B ($BO@J8$N5-9f$G$N(B F').
   @var{P}[2], @var{Std} $B$,(B index $B%b%N%_%"%k$G$"$k(B.
   $BO@J8$G$N5-9f$G$O(B @var{P}[2] $B$O(B M_t,  @var{Std} $B$O(B S.
   @item
   $B%"%k%4%j%:%`$O(B
   K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method
   $B$K$h$k(B.  $BO@J8$N9TNs(B F'.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] A=[[1,1,1,1],[0,1,2,3]]$
   Std=ot_hgm_ahg.cbase(A)$
   W=[[dx1,1,dx2,1,dx3,1,dx4,1]]$
   Mset=[1,dx1,dx2,dx3,dx4]$
   [2192] ot_hgm_ahg.get_mat2(A,W,Std,Mset);
   
   $B>JN,(B
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{cbase}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2012  $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B.
   @item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog  ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B.
   @item
   $B%=!<%9(B ot_hgm_ahg.rr $B$N(B test3(), test3b(), test4(), test5(), test6(), test6c() $BEy$KMxMQNc$,$"$k(B.
   @item
   test3b() $B$G(B @var{Mset} $B$r0l<!<0A4It$K$7$?$b$N$,(B, $BO@J8$NNc(B.
   @end itemize
   
   @comment -------------------
   @comment  hgm_ahg_contiguity
   @comment -------------------
   @node ot_hgm_ahg.hgm_ahg_contiguity,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{ot_hgm_ahg.hgm_ahg_contiguity}
   @findex ot_hgm_ahg.hgm_ahg_contiguity
   
   @table @t
   @item hgm_ahg_contiguity(@var{A},@var{StdMon},@var{Line},@var{X0},@var{InitVal},@var{Start},@var{End})
   ::  @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(Bcontiguity relation
   $B$r(B Sylvester matrix $B$rMQ$$$F7W;;$7(B, $B$=$l$rMQ$$$FD64v2?4X?t$NCM$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   $B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$NCM(B F(End;X0) ??
   @item A
   $B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B.
   @item StdMon
   $B%j%9%H(B.  Pfaffian $B$N4pDl$rM?$($kHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B.
   @item Line
   $B%j%9%H(B  [ContiDir,Beta,Z].
   @item X0
   $B%j%9%H(B. x $BJQ?t$NCM(B.
   @item InitVal
   $B%j%9%H(B. $B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$N=i4|CM(B F(Start;X0)
   @item Start
   $B%j%9%H(B.   Z $B%Q%i%a!<%?$N=i4|CM(B??
   @item End
   $B%j%9%H(B.   Z $B%Q%i%a!<%?$N=*C<CM(B??
   @end table
   
   @itemize @bullet
   @item Todo, $B$3$N4X?t$N%$%s%?%U%'!<%9$OJQ99$5$l$kM=Dj(B.
   @item  X0 $B$OM-M}?t$N%j%9%H(B.
   @item ContiDir $B$O(B End-Start $B$HF1$8J}8~(B.
   @item Beta.  A$BD64v2?4X?t$N(B B $B%Q%i%a!<%?$N=i4|CM(B ??
   @item Z.  ContiDir $B$G$N0l<!85(B contiguity $B$rI=8=$9$k$?$a$NITDj85$NL>A0(B.
   @item $B%=!<%9Cf$NMxMQNc(B. test_fd_conti(), test_c111_conti()
   @item
   $B%"%k%4%j%:%`$*$h$SMxE@$O(B
   K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method
   $B;2>H(B.
   @end itemize
   
   @example
   [2190] import("ot_hgm_ahg.rr");
   1
   [2191] ot_hgm_ahg.test_fd_conti();
   (Todo, $B0z?t$,$I$&$J$k$+$NNc$r2C$($k(B.)
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{get_mat2}
   @ref{hgm_ahg_expected_value_contiguity}
   @ref{hgm_ahg}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B 2014-07-11 $B$K:G=i$NHG$,(B 1.10$BHG(B ot_hgm_ahg.rr $B$K(B commit $B$5$l$?(B.
   @item $B%$%s%?%U%'!<%9$,99?7$5$l$?HG$O(B, 1.??$BHG(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_hgpoly.optip
   @comment -------------------
   @node tk_hgpoly.optip,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_hgpoly.optip}
   @findex tk_hgpoly.optip
   
   @table @t
   @item hgpoly.optip(@var{A},@var{B},@var{W})
   ::  $B@0?t7W2hLdBj$r%0%l%V%J!<4pDl$rMQ$$$F2r$/(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $BHsIi@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item B
   $BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B
   @item W
   $BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @itemize @bullet
   @item  @var{A} U = @var{B} $B$rK~$?$9HsIi$N@0?t%Y%/%H%k(B U $B$NCf$G(B,
   $BFb@Q(B @var{W} U $B$r:G>.2=$9$k(B U $B$rLa$9(B.
   @end itemize
   
   @example
   [0] import("tk_hgpoly.rr");
   [2191] tk_hgpoly.optip([[1,1,1,1],[0,1,2,3]],[20,40],[1,1,1,0]);
   [6,1,0,13]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{feasible}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-12 $B$K(B commit $B$5$l$?(B.
   $B85HG$O(B h-mle/A-hg/Prog
   @end itemize
   
   @comment -------------------
   @comment  tk_hgpoly.hgpoly
   @comment -------------------
   @node tk_hgpoly.hgpoly,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_hgpoly.hgpoly}
   @findex tk_hgpoly.hgpoly
   @table @t
   @item hgpoly.hgpoly(@var{A},@var{B})
   ::  @var{A}, @var{B} $B$GDj5A$5$l$kD64v2?B?9`<0$r7W;;$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $BHsIi@0?t(B(todo, $B:FEY3NG'(B)$B$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B
   @item B
   $BHsIi@0?t$r@.J,$H$9$k%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item  $BLa$jCM$r(B F $B$H$9$k$H$-(B, F[0] $B$,D64v2?B?9`<0(B. $BJQ?t$O(B x_1, x_2, ...
   F[1] $B$O(B F[0] $B$NJ,;6I=8=B?9`<0(B.
   @end itemize
   
   @example
   [0] import("tk_hgpoly.rr");
   [2191] tk_hgpoly.hgpoly([[1,1,1,1],[0,1,2,3]],[2,2]);
   [x_3*x_1+1/2*x_2^2,(1/2)*<<0,2,0,0>>+(1)*<<1,0,1,0>>]
   @end example
   
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-12 $B$K(B commit $B$5$l$?(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_fd.abc2ahg
   @comment -------------------
   @node tk_fd.abc2ahg,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_fd.abc2ahg}
   @findex tk_fd.abc2ahg
   @table @t
   @item tk_fd.abc2ahg(@var{A},@var{B},@var{C})
   ::  F_D(@var{A}, @var{B},@var{C}) $B$r2r$K$b$D(B A-$BD64v2?J}Dx<07O$r5a$a$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B.
   @item A
   $B?t(B
   @item B
   $B?t$N%j%9%H(B
   @item C
   $B?t(B
   @end table
   
   @itemize @bullet
   @item $BLa$jCM%j%9%H$NBh#0@.J,$O(B A-$BD64v2?J}Dx<07O$rDj5A$9$k9TNs(B.
   $BBh#1@.J,$O(BA-$BD64v2?J}Dx<07O$N%Q%i%a!<%?&B(B.
   @end itemize
   
   @example
   [2191] tk_fd.abc2ahg(-3,[-4,-5],3);
   
   [[[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],[11,5,4,5]]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{abc2marginal}
   @ref{marginal2abc}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-12-13 $B$K(B tk_fd.rr $B$KDI2C$5$l$?(B.
   @end itemize
   
   @comment -------------------
   @comment  tk_fd.ahvec_abc
   @comment -------------------
   @node tk_fd.ahvec_abc,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_fd.ahvec_abc}
   @findex tk_fd.ahvec_abc
   @table @t
   @item tk_fd.ahvec_abc(@var{A},@var{B},@var{C},@var{Y} | all=1)
   ::   abc2marginal(@var{A}, @var{B},@var{C})  $B$r<~JUOB$K$b$D(B (2,m+1) $BJ,3dI=A4BN$K$D$$$F$N@55,2=Dj?t(B Z, $B$*$h$S(B Z $B$NJQ?t(B Y[1][0], ..., Y[1][m]
   (2$BHVL\$N9T(B)$B$K$D$$$F$NJPHyJ,$r7W;;$9$k(B.
   @end table
   
   @table @var
   @item return
   $B%j%9%H(B @var{Ans}
   @item A
   $B?t(B
   @item B
   $B?t$N%j%9%H(B. $BD9$5$O(B m.
   @item C
   $B?t(B
   @item Y
   (2,m+1) $BJQ?tCM$r$"$i$o$9%j%9%H$N%j%9%H(B.
   @end table
   
   @itemize @bullet
   @item
   @var{A}, @var{B}, @var{C}, $B$K8=$l$k?t$O@0?t$rM?$($k(B.
   @var{Y} $B$N@.J,$OM-M}?t$rM?$($k(B.
   @item
   @var{Ans}[2]*@var{Ans}[1] $B$,(B Z.
   @var{Ans}[2]*@var{Ans}[0][I] $B$,(B Z $B$N(B Y[1][I] $B$K$D$$$F$NJPHyJ,(B.
   @item
   $BO@J8(B
   1.Y.Goto, Contiguity relations of Lauricella's F_D revisited,  arxiv:1412.3256
   $B$GF3=P$5$l$F$$$k(B
   contiguity relation $B$rMQ$$$F7W;;$9$k(B.
   @end itemize
   
   @example
   [2449] marginal2abc([3,12],[6,3,3,3]);
   [-3,[-3,-3,-3],4]
   
   [2450] tk_fd.ahvec_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]);
   [[ 24041/1152 143551/11520 16973/1280 78827/5760 ],1/7776]
   
   [2451] expectation_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]);
   [721230/173593,430653/173593,458271/173593,67566/24799]
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{expectation_abc}
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B   2014-$B2F$K3+H/$5$l$?(B.
   @end itemize
   
   
   @node pari,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{pari}, @code{setbprec},@code{setround},@code{todouble},@code{mpfr_gamma},@code{mpfr_floor},@code{mpfr_round},
   @findex pari
   @findex setbprec
   @findex setround
   @findex todouble
   @findex mpfr_gamma
   @findex mpfr_floor
   @findex mpfr_round
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item pari(@var{arg1},@var{arg2},...)
   ::  MPFR $B$G(B pari $B$N4X?t$r(B emulate $B$9$k$+(B ox_pari $B%5!<%P!<$r8F$S=P$9(B.
   @itemx setbprec(@var{arg1})
   @itemx setround(@var{arg1})
      $B4]$a$NJ}K!$N;XDj(B. mpfr $B=`5r(B.
   @itemx todouble(@var{arg1})
   :: bigfloat $B7?$r(B double $B$KJQ49$9$k(B.
   @itemx mpfr_gamma(@var{arg1})
   :: gamma $B4X?t$N7W;;(B.
   @itemx mpfr_floor(@var{arg1})
   ::  floor $B$N7W;;(B.
   @itemx mpfr_round(@var{arg1})
   :: $B4]$a$N7W;;(B.
   @end table
   
   @table @var
   @item return
   $B8e=R(B.
   @item arg1, arg2
   $B8e=R(B.
   @end table
   
   @itemize @bullet
   @item 20150807 $B0J9_$N(B asir $B$G$O(B, bigfloat $B$,(B pari $B$G$O$J$/(B mpfr $B$rMQ$$$F7W;;$5$l$k(B.
   Todo, pari $B$O(B ox_pari $B$r8F$S=P$9$,(B, $B$^$@(B ox_pari $B$KL$<BAu$N5!G=$,B?$/$"$k(B.
   $B6h4V1i;;$X$NBP1~$O9T$C$F$$$J$$(B.
   @item
   pari(floor,@var{arg1}),
   pari(round,@var{arg1}),
   pari(gamma,@var{arg1})
   $B$O(B mpfr $B$G(B pari $B$r(B emulate $B$7$F$$$k$N$G(B, $BF0:n$,0[$J$k(B.
   $BFC$K(B gamma $B$OJ#AG?t$N0z?t$r<u$1<h$i$J$$(B.
   pari $B$N(B floor $B$O7e?t$,B-$j$J$/$J$k$H%(%i!<$G=*N;$7$?$,(B,
   $B$3$N(B floor $B$G$O(B setprec $B$G;XDj$7$?7e?t0JFb$J$i@5$7$/(B floor $B$rLa$9(B.
   Todo, ox_pari  $B$r;XDj$7$F8F$S=P$9J}K!(B.
   @end itemize
   
   @example
   [219] ctrl("bigfloat",1)$
   [220] setprec(100)$
   [221] pari(floor,1111111111111.1+1/10);
   1111111111111
   @end example
   
   @table @t
   @item $B;2>H(B
   @ref{pari}
   @end table
   
   @comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
   @comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
   @noindent
   ChangeLog
   @itemize @bullet
   @item $B$3$l$i$NBgJQ99$O(B 2015-08-03 $B$h$j(B 08-07 $B$N(B asir $B9g=I$G$*$3$J$o$l$?(B.
   $B$^$@:n6HCf(B.  Todo, asirgui $B$X$NBP1~(B. debug, ...
   @item $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B asir2000/builtin/bfaux.c,
   asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB??t(B.
   @end itemize
   
 @comment ****************************************************************  @comment ****************************************************************
 @comment --- $B"~"~"~"~(B  $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B  @comment --- $B"~"~"~"~(B  $B0J2<B>$N4X?t$K$D$$$F??;w$7$F5-=R$9$k(B. $B"~"~"~"~(B
 @comment $B?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.  @comment $B?7$7$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B.
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