===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/exp/exp-ja.texi,v
retrieving revision 1.37
retrieving revision 1.46
diff -u -p -r1.37 -r1.46
--- OpenXM/src/asir-doc/exp/exp-ja.texi	2010/02/06 01:32:31	1.37
+++ OpenXM/src/asir-doc/exp/exp-ja.texi	2012/09/18 11:41:18	1.46
@@ -1,4 +1,4 @@
-%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.36 2010/02/05 07:45:48 nisiyama Exp $
+%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.45 2012/02/26 01:25:30 takayama 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 2012 $BG/(B 9 $B7n(B
 
 @author  by Risa/Asir committers
 @page
@@ -134,7 +134,11 @@ 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::
 @end menu
 
 @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B
@@ -1835,7 +1839,7 @@ 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.
@@ -2841,7 +2845,40 @@ 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)
@@ -2849,9 +2886,9 @@ B_@{S0@} length : 2
 @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t
 @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_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
 @end table
 
@@ -2863,6 +2900,10 @@ B_@{S0@} length : 2
 $B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B)
 @item @var{m}
 $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
 
 @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
@@ -2903,6 +2944,25 @@ restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s
 
 @item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B
 $B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B. 
+
+@item @var{b} $B$K$h$j(B, $B2C72$N%0%l%V%J4pDl7W;;$K@F<!2=(B, trace $B%"%k%4%j%:%`(B
+$B$rMQ$$$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
 
 $B0J2<$O(B,
@@ -2963,11 +3023,193 @@ $\{(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.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
+
+
 @noindent
 ChangeLog
 @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 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.
 @end itemize
 
 @node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B
@@ -3028,6 +3270,298 @@ ChangeLog
 @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
 
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.