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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.46 and 1.49

version 1.46, 2012/09/18 11:41:18 version 1.49, 2014/12/14 01:06:44
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 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.45 2012/02/26 01:25:30 takayama Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.48 2014/05/29 13:18:18 ohara 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 2012 $BG/(B 9 $B7n(B  @subtitle 2014 $BG/(B 12 $B7n(B
   
 @author  by Risa/Asir committers  @author  by Risa/Asir committers
 @page  @page
Line 139  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
Line 139  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
 * tk_rk.runge_kutta_4::  * tk_rk.runge_kutta_4::
 * tk_rk.runge_kutta_4_linear::  * tk_rk.runge_kutta_4_linear::
 * tk_rk.zonal::  * 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 1950  ChangeLog
Line 1951  ChangeLog
 @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$$$k(B.  @item http://www.math.kobe-u.ac.jp/Asir/Add-ons $B$K$F(B winfep.exe $B$rG[I[$7$F$$$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$$$k(B.
Line 2025  ChangeLog
Line 2026  ChangeLog
 @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.  @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.
 @item  @item
 @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B.  $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.  @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B.  $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.
 @item  
 $B$3$l$i$N4X?t$O(B UNIX $BHG$K$N$_<BAu$5$l$F$$$k(B.  
 @end itemize  @end itemize
   
 @example  @example
Line 2094  ChangeLog
Line 2093  ChangeLog
 @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 ****************************************************************
   
   
Line 3564  holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7
Line 3680  holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7
 @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.  @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.
 @end itemize  @end itemize
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  @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
   
   
   @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  template
 @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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