===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/exp/exp-ja.texi,v
retrieving revision 1.40
retrieving revision 1.49
diff -u -p -r1.40 -r1.49
--- OpenXM/src/asir-doc/exp/exp-ja.texi	2010/09/28 07:24:34	1.40
+++ OpenXM/src/asir-doc/exp/exp-ja.texi	2014/12/14 01:06:44	1.49
@@ -1,4 +1,4 @@
-%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.39 2010/07/16 07:55:06 nisiyama Exp $
+%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.48 2014/05/29 13:18:18 ohara Exp $
 \input texinfo
 @iftex
 @catcode`@#=6
@@ -38,7 +38,7 @@
 @title $B<B83E*;EMM$N4X?t(B
 @subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B
 @subtitle 1.0 $BHG(B
-@subtitle 2010 $BG/(B 2 $B7n(B
+@subtitle 2014 $BG/(B 12 $B7n(B
 
 @author  by Risa/Asir committers
 @page
@@ -134,7 +134,12 @@ ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
 * 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 (option)::
-* tk_pf.rkn::
+* tk_pfn.rkn::
+* tk_pfn.graph::
+* tk_rk.runge_kutta_4::
+* tk_rk.runge_kutta_4_linear::
+* tk_rk.zonal::
+* getpid::
 @end menu
 
 @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B
@@ -1835,7 +1840,7 @@ builtin/dp.c 1.49
 @table @var
 @item gentrace
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.
-@item gentsyz
+@item gensyz
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.
 @item nora
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.
@@ -1946,7 +1951,7 @@ ChangeLog
 @comment ****************************************************************
 
 @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$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B.
+@item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B $B4D6-JQ?t(B TEMP $B$G;XDj$5$l$?%U%)%k%@$K$3$N%U%!%$%k$,:n@.$5$l$k(B.
 @item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main window $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B.
 @item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B.
 @item http://www.math.kobe-u.ac.jp/Asir/Add-ons $B$K$F(B winfep.exe $B$rG[I[$7$F$$$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$$$k(B. 
@@ -2021,8 +2026,6 @@ ChangeLog
 @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B.
 @item
 @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B.  $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B.
-@item
-$B$3$l$i$N4X?t$O(B UNIX $BHG$K$N$_<BAu$5$l$F$$$k(B.
 @end itemize
 
 @example
@@ -2090,6 +2093,123 @@ ChangeLog
 @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 ****************************************************************
 
 
@@ -2841,7 +2961,40 @@ B_@{S0@} length : 2
 [1432]
 @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)}
 @comment --- $B:w0zMQ%-!<%o!<%I(B
 @findex nk_restriction (option)
@@ -2986,10 +3139,10 @@ $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
 $B$G$"$k$3$H$r0UL#$9$k(B.
 @end ifinfo
 
-@node nk_restriction,,, D $B2C72$N@QJ,%$%G%"%k$NHs@F<!ItJ,$K4X$9$k4X?t(B
+@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 trans_inhomo
+@findex nk_restriction.trans_inhomo
 
 @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t
@@ -3021,6 +3174,150 @@ nk_restriction.restriction_ideal( ... |inhomo=1); $B$
 @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
+
+
 @noindent
 ChangeLog
 @itemize @bullet
@@ -3028,6 +3325,7 @@ ChangeLog
 @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.
 @end itemize
 
 @node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B
@@ -3104,7 +3402,9 @@ ChangeLog
 
 @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, ...]
+$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.
@@ -3118,11 +3418,12 @@ ChangeLog
 @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.testgraph();
+[1590] tk_pfn.testgraph1();
 
 $B$3$3$G(B testgraph1() $B$O0J2<$N$H$*$j(B. 
 def testgraph1() {
@@ -3137,7 +3438,7 @@ def testgraph1() {
   Iv = [0.105994,-0.651603,-0.760628];
   Dom=[[0.5,1.5],[1.5,9]];
   Step = 0.5;
-  return graph(Pf,Dom,Iv,Step | fit=1);  
+  return tk_pfn.graph(Pf,Dom,Iv,Step | fit=1);  
 }
 
 
@@ -3153,8 +3454,116 @@ ChangeLog
 @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$$$k(B.
+taka_plot_auto $B$O2<J}8~$G(B y $B$,@5(B.
+
+@end example
+
+
+@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B
+@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
+@noindent
+ChangeLog
+@itemize @bullet
+@item 2010$BG/(B Pfaffian $B$N?tCM2r@O$N0Y$K:F@0Hw(B.
+@item @code{OpenXM/src/asir-contrib/packages/src/taka_runge_kutta.rr} 1.17
+@end itemize
+
+
+
 @node fj_simp.simplify,,, $B<B83E*;EMM$N4X?t(B
 @subsection @code{fj_simp.simplify}
 @findex fj_simp.simplify
@@ -3218,7 +3627,433 @@ Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification
 OpenXM/src/asir-contrib/packages/src/fj_simplify.rr
 @end itemize
 
-@comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.
+@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
+
+
+@comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  template
 @comment ****************************************************************
 @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.