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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.35 and 1.38

version 1.35, 2009/12/09 04:58:29 version 1.38, 2010/02/10 05:49:58
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 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.34 2009/05/16 04:56:32 ohara Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.37 2010/02/06 01:32:31 takayama Exp $
 \input texinfo  \input texinfo
 @iftex  @iftex
 @catcode`@#=6  @catcode`@#=6
Line 38 
Line 38 
 @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 2010 $BG/(B 2 $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_pf.rkn::
 @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 1948  ChangeLog
Line 1949  ChangeLog
 @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$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B.  @item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B asirgui.exe $B$N$"$k%U%)%k%@$*$h$S(B $B4D6-JQ?t(B TEMP $B$,Dj5A$5$l$F$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B.
 @item $BCf?H$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
Line 1988  ChangeLog
Line 1990  ChangeLog
 @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 2837  B_@{S0@} length : 2
Line 2841  B_@{S0@} length : 2
 [1432]  [1432]
 @end example  @end example
   
   @node nk_restriction,,, 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)
   
   @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.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
   @item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m})
   :: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item @var{n}
   0 $B$^$?$O(B 1
   @item @var{p}
   $B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B)
   @item @var{m}
   $B@0?t(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item @var{n} $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$N7W;;$r9T$&(B.
   
   restriction_ideal (integration_ideal) $B$K4X$7$F$O(B, $B%$%G%"%k(B @code{I} $B$N(B
   @code{M} $BJQ?t$K$D$$$F$N@)8B(B($B@QJ,(B)$B%$%G%"%k(B @code{J} $B$H(B
   
   @iftex
   @tex
   {\tt J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1])} $\in$ {\tt I}
   @end tex
   @end iftex
   @ifinfo
   J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1]) \in I
   @end ifinfo
   
   $B$rK~$?$9Hs@F<!ItJ,$r9=@.$9$k>pJs(B @code{IH} $B$H$N%Z%"(B @code{[J,IH]} $B$r=PNO$9$k(B.
   $B>\$7$$=PNO$N8+J}$K$D$$$F$O(B, $B2<$NNc$d%=!<%9$N(B @code{inhomo_part} $B$N(B
   $B%3%a%s%H$r;2>H(B.
   
   restriction, integration $B$KBP$9$k(B @code{inhomo} $B%*%W%7%g%s$O(B
   restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s$H$7$F$N<B9TMQ$J$N$G(B,
   $B%f!<%6$,L@<(E*$K;HMQ$9$k$3$H$O$J$$(B.
   
   @item @var{param} $B$K;XDj$5$l$?JQ?t$O78?tBN$KB0$9$k$b$N$H$_$J$5$l$F7W;;$,9T$o$l$k(B.
   $B$^$?(B, ``generic'' $B$G$"$k$3$H$,2>Dj$5$l$k(B.
   $B$D$^$j(B, $B$3$l$i$NJQ?t$K0MB8$9$k$h$&$J(B generic b-$B4X?t$N:,$O(B,
   $B:GBg@0?t:,$G$J$$$H$$$&$3$H$G$"$k(B.
   
   @item @var{param} $B$,;XDj$5$l$k$H(B, generic b-$B4X?t$N7W;;$O(B noro $B$K$h$k(B
   $B9bB.%"%k%4%j%:%`$G$O$J$/(B, $B>C5nK!$,MQ$$$i$l$k(B.
   @var{param} $B$K6u%j%9%H$r;XDj$9$k$3$H$G(B, b-$B4X?t$N7W;;J}K!$N%U%i%0$H$7$F$b(B
   $BMxMQ$G$-$k(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.
   @end itemize
   
   $B0J2<$O(B,
   @iftex
   @tex
   $ t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} $
   @end tex
   $B$N(B annihilator
   @tex
   $I = D \cdot \{ x(1-x) \partial_x^2+((1-t) \partial_t-(a+b+1)x+c-1)
    \partial_x-ab, (1-t)x \partial_x+t(1-t) \partial_t+(2-c)t+b-1,
    (xt-1) \partial_x+at \}$
   @end tex
   $B$N(B
   @tex
   $t$
   @end tex
   $B$K$D$$$F$N@QJ,%$%G%"%k(B
   @tex
   $J$
   @end tex
   $B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3])
   @end iftex
   @ifinfo
   t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a}
   $B$N(B annihilator
   I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab,
    (1-t)x dx+t(1-t)dt+(2-c)t+b-1, (xt-1)dx+at @}
   $B$N(B t $B$K$D$$$F$N@QJ,%$%G%"%k(B J
   $B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3])
   @end ifinfo
   @example
   [1555] A=ndbf.ann_n([t,1-t,1-x*t])$
   [1556] I=map(subst,A,s0,b-1,s1,c-b-1,s2,-a);
   [(x^2-x)*dx^2+((t-1)*dt+(a+b+1)*x-c+1)*dx+b*a,(-t+1)*x*dx+(t^2-t)*dt+(-c+2)*t+b-1,(t*x-1)*dx+a*t]
   [1557] J=nk_restriction.integration_ideal(I,[t,x],[dt,dx],[1,0]|inhomo=1, param=[a,b,c]);
   -- nd_weyl_gr :0sec(0.001875sec)
   -- weyl_minipoly_by_elim :0.008001sec(0.006133sec)
   -- generic_bfct_and_gr :0.008001sec(0.006181sec)
   generic bfct : [[-1,1],[s,1],[s-a+c-1,1]]
   S0 : 0
   B_{S0} length : 1
   -- fctr(BF) + base :0sec(0.003848sec)
   -- integration_ideal_internal :0sec(0.07707sec)
   [[(x^2-x)*dx^2+((a+b+1)*x-c)*dx+b*a],[[[[dt,(-t+1)*dx]],1]]]
   @end example
   @iftex
   $B$3$N=PNO$O(B
   @tex
   $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
   - 1/1 \{ \partial_t (-t+1) \partial_x \} \in I$
   @end tex
   $B$G$"$k$3$H$r0UL#$9$k(B.
   @end iftex
   @ifinfo
   $B$3$N=PNO$O(B
   @{(x^2-x)dx^2+((a+b+1)x-c)dx+ab @} - 1/1 @{ dt (-t+1)dx @} \in I
   $B$G$"$k$3$H$r0UL#$9$k(B.
   @end ifinfo
   
 @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.
 @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)
   
   @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 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
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.
 @comment ****************************************************************  @comment ****************************************************************
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  Added in v.1.38
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