| version 1.34, 2009/05/16 04:56:32 |
version 1.47, 2013/02/18 07:18:32 |
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| %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.33 2009/05/16 03:13:07 ohara Exp $ |
%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.46 2012/09/18 11:41:18 takayama Exp $ |
| \input texinfo |
\input texinfo |
| @iftex |
@iftex |
| @catcode`@#=6 |
@catcode`@#=6 |
|
|
| @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 2013 $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 |
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| * 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):: |
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* tk_pfn.rkn:: |
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* tk_pfn.graph:: |
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* tk_rk.runge_kutta_4:: |
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* tk_rk.runge_kutta_4_linear:: |
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* tk_rk.zonal:: |
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* 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 |
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| Line 1840 builtin/dp.c 1.49 |
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| @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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| |
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| @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$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B. |
@item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B asirgui.exe $B$N$"$k%U%)%k%@$*$h$S(B $B4D6-JQ?t(B TEMP $B$,Dj5A$5$l$F$$$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 winodw $B$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 |
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@item winfep $B$O(B 2010-01-20 $B:"$KBh0lHG$,(B commit $B$5$l$?(B. |
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@item @code{OpenXM_contrib2/windows/winfep} 1.1 |
| @end itemize |
@end itemize |
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| @end itemize |
@end itemize |
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@node getpid,,, $B%7%9%F%`(B |
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@subsection @code{getpid} |
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@findex getpid |
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@comment --- $B4X?t$N4JC1$J@bL@(B --- |
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@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B --- |
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@table @t |
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@item getpid() |
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@end table |
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@table @var |
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@item return |
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$B@0?t(B |
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@end table |
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@itemize @bullet |
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@item asir $B$N%W%m%;%9HV9f$rLa$9(B. |
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@item $B%W%m%;%9HV9f$O(B asir, ox_asir $BEy$GFHN)$7$?%W%m%;%9$KBP$7$F%7%9%F%`Fb$G0l0U=P$"$k(B. |
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@end itemize |
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@example |
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[219] getpid() |
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3214 |
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@end example |
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@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 |
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@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit. |
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@noindent |
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ChangeLog |
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@itemize @bullet |
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@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. |
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src/asir-contrib/packages/src/misc/rr 1.3, |
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asir2000/builtin/file.c 1.28, rat.c 1.5, |
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asir2000/parse/puref.c 1.9 $B$r;2>H(B (2013/02/15, 18). |
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@end itemize |
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| @comment **************************************************************** |
@comment **************************************************************** |
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| Line 2837 B_@{S0@} length : 2 |
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| Line 2884 B_@{S0@} length : 2 |
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| [1432] |
[1432] |
| @end example |
@end example |
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@node nk_restriction.ann_mul,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
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@subsection @code{nk_restriction.ann_mul} |
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@comment --- $B:w0zMQ%-!<%o!<%I(B |
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@findex nk_restriction.ann_mul |
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@comment --- $B4X?t$N4JC1$J@bL@(B --- |
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@table @t |
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@item nk_restriction.ann_mul(@var{I}, @var{J}, @var{VL}, @var{DVL}) |
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:: @var{f} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{I}, |
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@var{g} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$r(B @var{J} $B$H$7$?$H$-(B, |
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@var{fg} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$rJV$9(B. |
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@end table |
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@comment --- $B0z?t$N4JC1$J@bL@(B --- |
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@table @var |
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@item I |
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$B%$%G%"%k$N@8@.85$N%j%9%H(B |
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@item J |
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$B%$%G%"%k$N@8@.85$N%j%9%H(B |
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@item VL |
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$BJQ?t$N%j%9%H(B |
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@item DVL |
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$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B) |
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@end table |
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@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B --- |
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@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B --- |
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@comment --- @bullet $B$O9uE@IU$-(B --- |
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@itemize @bullet |
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@item test_ann_mul(), test_ann_mul2(), test_ann_mul3() $B$r;2>H(B. |
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@end itemize |
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@node nk_restriction (option) ,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option) |
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@subsection @code{nk_restriction (option)} |
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@comment --- $B:w0zMQ%-!<%o!<%I(B |
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@findex nk_restriction (option) |
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@comment --- $B4X?t$N4JC1$J@bL@(B --- |
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@table @t |
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@item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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@item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord}) |
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@item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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@item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord}) |
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:: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B |
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@end table |
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@comment --- $B0z?t$N4JC1$J@bL@(B --- |
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@table @var |
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@item @var{n} |
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0 $B$^$?$O(B 1 |
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@item @var{p} |
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$B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B) |
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@item @var{m} |
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$B@0?t(B |
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@item @var{b} |
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0, 1, 2, 3 $B$N$$$:$l$+(B |
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@item @var{ord} |
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$B=E$_(B0$B$NJQ?t$KBP$9$k9`=g=x(B |
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@end table |
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@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B --- |
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@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B --- |
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@comment --- @bullet $B$O9uE@IU$-(B --- |
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@itemize @bullet |
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@item @var{n} $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$N7W;;$r9T$&(B. |
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restriction_ideal (integration_ideal) $B$K4X$7$F$O(B, $B%$%G%"%k(B @code{I} $B$N(B |
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@code{M} $BJQ?t$K$D$$$F$N@)8B(B($B@QJ,(B)$B%$%G%"%k(B @code{J} $B$H(B |
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@iftex |
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@tex |
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{\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} |
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@end tex |
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@end iftex |
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@ifinfo |
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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 |
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@end ifinfo |
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$B$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. |
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$B>\$7$$=PNO$N8+J}$K$D$$$F$O(B, $B2<$NNc$d%=!<%9$N(B @code{inhomo_part} $B$N(B |
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$B%3%a%s%H$r;2>H(B. |
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restriction, integration $B$KBP$9$k(B @code{inhomo} $B%*%W%7%g%s$O(B |
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restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s$H$7$F$N<B9TMQ$J$N$G(B, |
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$B%f!<%6$,L@<(E*$K;HMQ$9$k$3$H$O$J$$(B. |
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@item @var{param} $B$K;XDj$5$l$?JQ?t$O78?tBN$KB0$9$k$b$N$H$_$J$5$l$F7W;;$,9T$o$l$k(B. |
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$B$^$?(B, ``generic'' $B$G$"$k$3$H$,2>Dj$5$l$k(B. |
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$B$D$^$j(B, $B$3$l$i$NJQ?t$K0MB8$9$k$h$&$J(B generic b-$B4X?t$N:,$O(B, |
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$B:GBg@0?t:,$G$J$$$H$$$&$3$H$G$"$k(B. |
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@item @var{param} $B$,;XDj$5$l$k$H(B, generic b-$B4X?t$N7W;;$O(B noro $B$K$h$k(B |
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$B9bB.%"%k%4%j%:%`$G$O$J$/(B, $B>C5nK!$,MQ$$$i$l$k(B. |
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@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$b(B |
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$BMxMQ$G$-$k(B. |
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@item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B |
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$B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B. |
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@item @var{b} $B$K$h$j(B, $B2C72$N%0%l%V%J4pDl7W;;$K@F<!2=(B, trace $B%"%k%4%j%:%`(B |
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$B$rMQ$$$k$+$I$&$+;XDj$G$-$k(B. |
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$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. |
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0: $B@F<!2=$J$7(B, trace $B$J$7(B |
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1: $B@F<!2=$J$7(B, trace $B$"$j(B |
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2: $B@F<!2=$"$j(B, trace $B$J$7(B ($B%G%U%)%k%H(B) |
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3: $B@F<!2=$"$j(B, trace $B$"$j(B |
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@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 |
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$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 |
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$B$H$7$F;HMQ$5$l$k$N$G7W;;8zN($KBg$-$J1F6A$rM?$($k2DG=@-$,$"$k(B. |
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$B%G%U%)%k%H$O(B 0, $B$D$^$jA4<!?t5U<!=q<0=g=x$G$"$k(B. |
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$B$3$N%*%W%7%g%s$O(B @var{param} $B$HF1;~MxMQ$G$-$J$$(B. ($B8e$KBP1~M=Dj(B.) |
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@end itemize |
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$B0J2<$O(B, |
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@iftex |
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@tex |
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$ t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} $ |
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@end tex |
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$B$N(B annihilator |
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@tex |
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$I = D \cdot \{ x(1-x) \partial_x^2+((1-t) \partial_t-(a+b+1)x+c-1) |
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\partial_x-ab, (1-t)x \partial_x+t(1-t) \partial_t+(2-c)t+b-1, |
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(xt-1) \partial_x+at \}$ |
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@end tex |
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$B$N(B |
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@tex |
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$t$ |
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@end tex |
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$B$K$D$$$F$N@QJ,%$%G%"%k(B |
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@tex |
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$J$ |
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@end tex |
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$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
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@end iftex |
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@ifinfo |
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t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} |
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$B$N(B annihilator |
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I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab, |
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(1-t)x dx+t(1-t)dt+(2-c)t+b-1, (xt-1)dx+at @} |
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$B$N(B t $B$K$D$$$F$N@QJ,%$%G%"%k(B J |
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$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
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@end ifinfo |
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@example |
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[1555] A=ndbf.ann_n([t,1-t,1-x*t])$ |
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[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 |
| |
|
| |
@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$$$H$-(B, $BHs@F<!ItJ,$rM?$($k>pJs$bJV$9(B. |
| |
@end itemize |
| |
|
| |
$B0J2<$O(B, Oaku-Shiraki-Takayama (2003) $B$NNc(B6.5$B$NHs@F<!ItJ,$^$G7W;;$7$?$b$N$G$"$k(B. |
| |
@iftex |
| |
@tex |
| |
$ \sum_{k=a}^b {n \choose k} $ |
| |
@end tex |
| |
$B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B |
| |
@tex |
| |
$ I = \langle (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) \rangle $ |
| |
@end tex |
| |
$B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B. |
| |
@end iftex |
| |
@ifinfo |
| |
\sum_{k=a}^b n_C_k |
| |
$B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B |
| |
I = < (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) > |
| |
$B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B. |
| |
@end ifinfo |
| |
@example |
| |
[1871] Id=[(n-k+1)*en-(n+1), (k+1)*ek-(n-k)]$ |
| |
[1872] VL=[k,n]$ |
| |
[1873] DVL=[ek,en]$ |
| |
[1874] W=[1,0]$ |
| |
[1875] nk_restriction.ost_sum(Id,VL,DVL,W|inhomo=1); |
| |
-- nd_weyl_gr :0.006667sec(0.004057sec) |
| |
-- weyl_minipoly :0sec(0.001163sec) |
| |
-- generic_bfct_and_gr :0.01sec(0.007085sec) |
| |
generic bfct : [[1,1],[s,1]] |
| |
S0 : 0 |
| |
B_{S0} length : 1 |
| |
-- fctr(BF) + base :0.003333sec(0.001785sec) |
| |
-- restriction_ideal_internal :0sec(0.002336sec) |
| |
[[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]] |
| |
@end example |
| |
|
| |
|
| @noindent |
@noindent |
| ChangeLog |
ChangeLog |
| @itemize @bullet |
@itemize @bullet |
| @item $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$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. 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 |
@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 |
| |
|
| |
@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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