| version 1.34, 2009/05/16 04:56:32 |
version 1.57, 2018/10/17 00:33:49 |
|
|
| %% $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 1.56 2018/03/28 07:44:06 takayama Exp $ |
| \input texinfo |
\input texinfo-ja |
| @iftex |
@iftex |
| @catcode`@#=6 |
@catcode`@#=6 |
| @def@fref#1{@xrefX[#1,,@code{#1},,,]} |
@def@fref#1{@xrefX[#1,,@code{#1},,,]} |
|
|
| @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 2018 $BG/(B 3 $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--2018. All rights reserved. |
| @end titlepage |
@end titlepage |
| |
|
| @comment --- $B$*$^$8$J$$(B --- |
@comment --- $B$*$^$8$J$$(B --- |
| Line 83 ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe |
|
| Line 83 ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe |
|
| @comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc |
@comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc |
| @comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B. |
@comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B. |
| @menu |
@menu |
| * quotetotex:: |
* asir-port.sh asir-install.sh:: |
| * quotetotex_env:: |
* asirgui.hnd:: |
| * objtoquote:: |
* chdir pwd:: |
| * copyright:: |
* copyright:: |
| * string_to_tb:: |
* dcurrenttime:: |
| * tb_to_string:: |
|
| * write_to_tb:: |
|
| * dp_gr_main:: |
* dp_gr_main:: |
| * asir-port.sh:: |
|
| * asir-install.sh:: |
|
| * get_struct_name:: |
|
| * get_element_names:: |
|
| * get_element_at:: |
|
| * put_element_at:: |
|
| * dp_initial_term:: |
* dp_initial_term:: |
| * dp_order:: |
* dp_order:: |
| * dp_weyl_gr_main:: |
* dp_weyl_gr_main:: |
| * list:: |
* eval_quote:: |
| * mapat:: |
* f_res:: |
| * set_print_function:: |
* fj_simplify.simplify:: |
| * small_jacobi:: |
|
| * flatten_quote:: |
* flatten_quote:: |
| * printf:: |
* function:: |
| * fprintf:: |
* get_struct_name get_element_names get_element_at put_element_at:: |
| * sprintf:: |
* getpid:: |
| * quote_to_funargs:: |
|
| * funargs_to_quote:: |
|
| * get_function_name:: |
|
| * remove_paren:: |
|
| * set_secure_mode:: |
|
| * set_secure_flag:: |
|
| * initialize_static_variable:: |
* initialize_static_variable:: |
| * eval_quote:: |
* list:: |
| |
* mapat:: |
| |
* 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):: |
| |
* noro_matrix.rr:: |
| |
* nqt_comp:: |
| * nqt_match:: |
* nqt_match:: |
| * nqt_match_rewrite:: |
* nqt_match_rewrite:: |
| |
* objtoquote:: |
| |
* ot_hgm_ahg.cbase:: |
| |
* ot_hgm_ahg.get_mat2:: |
| |
* ot_hgm_ahg.hgm_ahg_contiguity:: |
| |
* pari setbprec setround todouble mpfr_gamma mpfr_floor mpfr_round:: |
| |
* printf fprintf sprintf:: |
| |
* qt_is_var qt_is_coef:: |
| * qt_normalize:: |
* qt_normalize:: |
| |
* qt_rewrite:: |
| * qt_set_coef:: |
* qt_set_coef:: |
| * qt_set_ord:: |
* qt_set_ord:: |
| * qt_set_weight:: |
* qt_set_weight:: |
| * nqt_comp:: |
* quote_to_funargs funargs_to_quote remove_paren get_function_name:: |
| * qt_is_var:: |
* quotetotex quotetotex_env:: |
| * qt_is_ceof:: |
* set_print_function:: |
| * qt_rewrite:: |
* set_secure_flag set_secure_mode:: |
| * asirgui.hnd:: |
* small_jacobi:: |
| * noro_matrix.rr: |
* string_to_tb tb_to_string write_to_tb:: |
| * f_res:: |
* tk_fd.abc2ahg:: |
| * chdir:: |
* tk_fd.ahvec_abc:: |
| * pwd:: |
* tk_hgpoly.hgpoly:: |
| * dcurrenttime:: |
* tk_hgpoly.optip:: |
| * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module):: |
* tk_jack.zonal:: |
| * nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option):: |
* tk_pfn.graph:: |
| |
* tk_pfn.rkn:: |
| |
* tk_rk.runge_kutta_4:: |
| |
* tk_rk.runge_kutta_4_linear:: |
| @end menu |
@end menu |
| |
|
| @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B |
@node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B |
|
|
| @end itemize |
@end itemize |
| |
|
| |
|
| @node quote_to_funargs,,, $B%/%*!<%H(B |
@node quote_to_funargs funargs_to_quote remove_paren get_function_name,,, $B%/%*!<%H(B |
| @subsection @code{quote_to_funargs}, @code{funargs_to_quote}, @code{remove_paren} |
@subsection @code{quote_to_funargs}, @code{funargs_to_quote}, @code{remove_paren}, @code{get_function_name} |
| @findex quote_to_funargs |
@findex quote_to_funargs |
| @findex funargs_to_quote |
@findex funargs_to_quote |
| @findex remove_paren |
@findex remove_paren |
| |
@findex get_function_name |
| |
|
| @table @t |
@table @t |
| @item quote_to_funargs(@var{q}) |
@item quote_to_funargs(@var{q}) |
|
|
| @item |
@item |
| 2004-6-26 $B$N7W;;Be?t%;%_%J!<$K$*$$$F(B, $BCf@n$5$s$,(B simplifier $B$K$D$$$F$$$m$$$mLdBjDs5/(B |
2004-6-26 $B$N7W;;Be?t%;%_%J!<$K$*$$$F(B, $BCf@n$5$s$,(B simplifier $B$K$D$$$F$$$m$$$mLdBjDs5/(B |
| $B$r$7$?(B ($B7W;;Be?t%;%_%J!<%S%G%*;2>H(B). |
$B$r$7$?(B ($B7W;;Be?t%;%_%J!<%S%G%*;2>H(B). |
| @item parse/quote.c $B$N(B {\tt strcut fid_spec fid_spec_tab[] } |
@item parse/quote.c $B$N(B strcut fid_spec fid_spec_tab[] |
| $B$NItJ,$K=q$$$F$"$k7A<0$K(B @code{funargs_to_quote} $B$OJQ49$9$k(B. |
$B$NItJ,$K=q$$$F$"$k7A<0$K(B @code{funargs_to_quote} $B$OJQ49$9$k(B. |
| @end itemize |
@end itemize |
| |
|
|
|
| @end itemize |
@end itemize |
| @comment **************************************************************** |
@comment **************************************************************** |
| |
|
| @node qt_is_var,,, $B%/%*!<%H(B |
@node qt_is_var qt_is_coef,,, $B%/%*!<%H(B |
| @subsection @code{qt_is_var}, @code{qt_is_coef} |
@subsection @code{qt_is_var}, @code{qt_is_coef} |
| @findex qt_is_var |
@findex qt_is_var |
| @findex qt_is_coef |
@findex qt_is_coef |
|
|
| @end itemize |
@end itemize |
| |
|
| |
|
| @node sprintf,,, $BJ8;zNs=hM}(B |
@node printf fprintf sprintf,,, $BJ8;zNs=hM}(B |
| @subsection @code{printf}, @code{fprintf}, @code{sprintf} |
@subsection @code{printf}, @code{fprintf}, @code{sprintf} |
| |
@findex printf |
| |
@findex fprintf |
| @findex sprintf |
@findex sprintf |
| |
|
| @table @t |
@table @t |
| Line 1834 builtin/dp.c 1.49 |
|
| Line 1838 builtin/dp.c 1.49 |
|
| @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. |
| Line 1887 builtin/dp.c 1.49 |
|
| Line 1891 builtin/dp.c 1.49 |
|
| |
|
| @comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
@comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
| @comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
| @node asir-install.sh,,, $B%7%9%F%`(B |
@node asir-port.sh asir-install.sh,,, $B%7%9%F%`(B |
| @subsection @code{asir-port.sh}, @code{asir-install.sh} |
@subsection @code{asir-port.sh}, @code{asir-install.sh} |
| @findex asir-port.sh |
@findex asir-port.sh |
| @findex asir-install.sh |
@findex asir-install.sh |
|
|
| @comment **************************************************************** |
@comment **************************************************************** |
| |
|
| @itemize @bullet |
@itemize @bullet |
| @item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B asirgui.exe $B$N$"$k%U%)%k%@$*$h$S(B $B4D6-JQ?t(B TEMP $B$,Dj5A$5$l$F$$$l$P$3$N%U%!%$%k$,:n@.$5$l$k(B. |
@item asirgui (Windows $BHG(B) $B$r5/F0$9$k$H(B $B4D6-JQ?t(B TEMP $B$G;XDj$5$l$?%U%)%k%@$K$3$N%U%!%$%k$,:n@.$5$l$k(B. |
| @item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main winodw $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B. |
@item $BCf?H$O#1#0?J@0?t$G(B, asirgui $B$N(B main window $B$N%O%s%I%k$G$"$k(B. $B$3$N%O%s%I%k$"$F$K(B PostMessage $B$r$9$l$P(B, asuirgui $B$K%-!<%\!<%I$+$iF~NO$7$?$N$HF1MM$J8z2L$,F@$i$l$k(B. |
| @item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B. |
@item text editor $B$G:n@.(B, $BJ]B8$7$?%U%!%$%k$r(B text editor $BB&$+$i(B asirgui $B$KFI$_9~$^$;$?$j$9$k$?$a$KMxMQ2DG=(B. |
| |
@item http://www.math.kobe-u.ac.jp/Asir/Add-ons $B$K$F(B winfep.exe $B$rG[I[$7$F$$$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$$$k(B. |
| @end itemize |
@end itemize |
| |
|
| @example |
@example |
|
|
| @item $B$3$N5!G=$O(B 2006-12-5, 2007-02-13 $B$K2C$($i$l$?(B. |
@item $B$3$N5!G=$O(B 2006-12-5, 2007-02-13 $B$K2C$($i$l$?(B. |
| @item @code{OpenXM_contrib2/windows/asir32gui/asir32gui.clw} 1.11 |
@item @code{OpenXM_contrib2/windows/asir32gui/asir32gui.clw} 1.11 |
| @item @code{OpenXM_contrib2/windows/asir32gui/asir32guiview.cpp} 1.15, 1.1.6 |
@item @code{OpenXM_contrib2/windows/asir32gui/asir32guiview.cpp} 1.15, 1.1.6 |
| |
@item winfep $B$O(B 2010-01-20 $B:"$KBh0lHG$,(B commit $B$5$l$?(B. |
| |
@item @code{OpenXM_contrib2/windows/winfep} 1.1 |
| @end itemize |
@end itemize |
| |
|
| |
|
| @comment **************************************************************** |
@comment **************************************************************** |
| |
|
| @node chdir,,, $B%7%9%F%`(B |
@node chdir pwd,,, $B%7%9%F%`(B |
| @subsection @code{chdir}, @code{pwd} |
@subsection @code{chdir}, @code{pwd} |
| @findex chdir |
@findex chdir |
| @findex pwd |
@findex pwd |
|
|
| @code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B. |
@code{pwd} $B$O%+%l%s%H%G%#%l%/%H%j$rJ8;zNs$GJV$9(B. |
| @item |
@item |
| @code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B. $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B. |
@code{chdir} $B$O%+%l%s%H%G%#%l%/%H%j$r(B @var{directory} $B$KJQ99$9$k(B. $B@.8y$9$l$P(B 0 $B$r<:GT$9$l$P(B -1 $B$rJV$9(B. |
| @item |
|
| $B$3$l$i$N4X?t$O(B UNIX $BHG$K$N$_<BAu$5$l$F$$$k(B. |
|
| @end itemize |
@end itemize |
| |
|
| @example |
@example |
|
|
| @end itemize |
@end itemize |
| |
|
| |
|
| |
@node getpid,,, $B%7%9%F%`(B |
| |
@subsection @code{getpid} |
| |
@findex getpid |
| |
|
| |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| |
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B --- |
| |
@table @t |
| |
@item getpid() |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B@0?t(B |
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@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 |
| |
|
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@table @var |
| |
@item list |
| |
$BJ8;zNs(B($B%Q%9(B)$B$N%j%9%H(B |
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@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. |
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@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 |
| |
|
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|
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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 |
| |
@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. |
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@end itemize |
| |
|
| |
|
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@node sysinfo,,, $B%7%9%F%`(B |
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@subsection @code{sysinfo} |
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@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 --- |
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@table @t |
| |
@item sysinfo() |
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@end table |
| |
|
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@table @var |
| |
@item return |
| |
$BJ8;zNs$N%j%9%H(B |
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@end table |
| |
|
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@itemize @bullet |
| |
@item asir $B$NF0:n$7$F$$$k%*%Z%l!<%F%#%s%0%7%9%F%`$N>pJs$rJV$9(B. |
| |
@item $B%j%9%H$N3F@.J,$O(B, OS$B%?%$%W(B, $B%+!<%M%kL>(B, OS$BL>(B, CPU$B%?%$%W(B, OS$B%P!<%8%g%s(B, $B40A4$J>pJs(B, $B%m%1!<%k$G$"$k(B. |
| |
@item OS$B%?%$%W$O(B unix, macosx, windows $B$N$$$:$l$+$G$"$k(B. |
| |
@item unix $B$*$h$S(B macosx $B$K$*$$$F$O(B, $B%7%9%F%`%3!<%k$*$h$S(B uname $B%3%^%s%I$K$h$j>pJs$r<hF@$7$F$$$k(B. |
| |
windows $B$G$O(B, GetVersionEx() $B$J$I$N(B Win32 API $B$,MQ$$$i$l$F$$$k(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[0] sysinfo(); |
| |
[windows,WindowsNT,Windows7,x86_64,6.1.7601,WindowsNT 6.1.7601 Windows7 Service Pack 1 x86_64,ja] |
| |
@end example |
| |
|
| |
|
| |
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B |
| |
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit. |
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item $B$3$N4X?t$O(B 2014-5-14 $B$K%3%_%C%H$5$l$?(B. |
| |
$BJQ99$r$&$1$?%=!<%9%3!<%I$O(B builtin/ctrl.c (1.42) $B$G$"$k(B. |
| |
@end itemize |
| |
|
| |
|
| @comment **************************************************************** |
@comment **************************************************************** |
| |
|
| |
|
| @node $B8@8l(B,,, $B<B83E*;EMM$N4X?t(B |
@node $B8@8l(B,,, $B<B83E*;EMM$N4X?t(B |
| @section $B8@8l(B |
@section $B8@8l(B |
| |
|
| @node get_struct_name,,, $B8@8l(B |
@node get_struct_name get_element_names get_element_at put_element_at,,, $B8@8l(B |
| @subsection @code{get_struct_name}, @code{get_element_names}, @code{get_element_at}, @code{put_element_at} |
@subsection @code{get_struct_name}, @code{get_element_names}, @code{get_element_at}, @code{put_element_at} |
| @findex get_struct_name |
@findex get_struct_name |
| @findex get_element_names |
@findex get_element_names |
|
|
| @end itemize |
@end itemize |
| |
|
| |
|
| @node set_secure_flag,,, $B8@8l(B |
@node set_secure_flag set_secure_mode,,, $B8@8l(B |
| @subsection @code{set_secure_flag}, @code{set_secure_mode} |
@subsection @code{set_secure_flag}, @code{set_secure_mode} |
| @findex set_secure_flag |
@findex set_secure_flag |
| @findex set_secure_mode |
@findex set_secure_mode |
|
|
| |
|
| @comment **************************************************************** |
@comment **************************************************************** |
| |
|
| |
@node function,,, $B8@8l(B |
| |
@subsection @code{function} |
| |
@findex function |
| |
|
| |
@table @t |
| |
@item function $B@k8@$9$k$3$H$K$h$jH!?t7A<0$NITDj85$r@8@.$G$-$k(B. |
| |
@end table |
| |
|
| |
@comment --- $B@bL@(B --- |
| |
@table @t |
| |
@item function $B@k8@$9$k$3$H$K$h$jH!?t7A<0$NITDj85$r@8@.$G$-$k(B. |
| |
@item $BHyJ,H!?t(B diff $B$O$3$NH!?t7A<0$NITDj85$NHyJ,$r$d$O$jH!?t7A<0$NITDj85$H$7$F@8@.$9$k(B. |
| |
$B$?$H$($P(B f@{1,2@}(x,y) $B$O(B f $B$r(B x $B$K$D$$$F0l3,JPHyJ,(B, y $B$K$D$$$F(B 2$B3,JPHyJ,$7$?$b$N(B. |
| |
@item diff $B$O9g@.4X?t$H$7$F$N=hM}$b9T$&(B. |
| |
@end table |
| |
|
| |
|
| |
@example |
| |
[1915] function f(x,y); |
| |
[1916] F=f(f(x,y),y)$ |
| |
[1917] diff(F,y); |
| |
f@{1,0@}(f(x,y),y)*f@{0,1@}(x,y)+f@{0,1@}(f(x,y),y) |
| |
[1918] vtype(f(p,q)); |
| |
2 |
| |
[1919] deg(diff(F,y),f@{0,1@}(x,y)); |
| |
1 |
| |
@end example |
| |
|
| |
@xref{vtype} |
| |
@xref{diff} |
| |
|
| |
@comment --- ChangeLog |
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item $B$$$D$N(B commit $B$GF3F~$5$l$?$+ITL@(B. |
| |
@end itemize |
| |
|
| |
@comment **************************************************************** |
| |
|
| @node $B?tO@!&Be?t(B,,, $B<B83E*;EMM$N4X?t(B |
@node $B?tO@!&Be?t(B,,, $B<B83E*;EMM$N4X?t(B |
| @section $B?tO@!&Be?t(B |
@section $B?tO@!&Be?t(B |
| |
|
|
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.restriction(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9!#(B |
:: D $B2C72(B M = D / @var{Id} ($B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id}) $B$KBP$7$F(B, |
| |
$B=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
|
|
| |
|
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B) |
($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B) |
| @item |
@item |
| $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B. |
| $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, |
| x,y $B$K$D$$$F@)8B$r9T$&!#(B |
x,y $B$K$D$$$F@)8B$r9T$&(B. |
| @end itemize |
@end itemize |
| |
|
| $B0J2<$O!"%$%G%"%k(B |
$B0J2<$O(B, $B%$%G%"%k(B |
| @iftex |
@iftex |
| @tex |
@tex |
| $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ |
$I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ |
| @end tex |
@end tex |
| $B$N(B |
$B$H$*$$$?;~(B, D $B2C72(B |
| @tex |
@tex $M = D / I$ @end tex |
| $x$ |
$B$N(B |
| @end tex |
@tex $x$ @end tex |
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| I = D . @{ x dx -1, y dy - 1 @} $B$N(B x |
I = D . @{ x dx -1, y dy - 1 @} $B$H$*$$$?;~(B, |
| |
D $B2C72(B M = D / I $B$N(B x |
| @end ifinfo |
@end ifinfo |
| $B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B |
$B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B. |
| @example |
@example |
| [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]); |
[1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]); |
| -- generic_bfct_and_gr :0.001sec(0.001629sec) |
-- generic_bfct_and_gr :0.001sec(0.001629sec) |
| Line 2653 B_@{S0@} length : 2 |
|
| Line 2817 B_@{S0@} length : 2 |
|
| -- fctr(BF) + base :0.000999sec(0.0005109sec) |
-- fctr(BF) + base :0.000999sec(0.0005109sec) |
| [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]] |
[[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]] |
| @end example |
@end example |
| |
$BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B, |
| |
$B@)8B2C72$N4pDl(B |
| |
@iftex |
| |
@tex $\partial_x^1, \partial_x^0$ @end tex |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B |
| |
@tex $(y \partial_y - 1, 0), (0, y\partial_y-1), (-1,0)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
dx^1, dx^0 |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B |
| |
(y dy - 1, 0), (0, ydy-1), (-1,0) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| |
|
| @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
@node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| @subsection @code{nk_restriction.restriction_ideal} |
@subsection @code{nk_restriction.restriction_ideal} |
| @comment --- $B:w0zMQ%-!<%o!<%I(B |
@comment --- $B:w0zMQ%-!<%o!<%I(B |
| Line 2663 B_@{S0@} length : 2 |
|
| Line 2841 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9!#(B |
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B%$%G%"%k$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2680 B_@{S0@} length : 2 |
|
| Line 2858 B_@{S0@} length : 2 |
|
| |
|
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B) |
($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B) |
| @item |
@item |
| $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B. |
| $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, |
| x,y $B$K$D$$$F@)8B$r9T$&!#(B |
x,y $B$K$D$$$F@)8B$r9T$&(B. |
| @end itemize |
@end itemize |
| |
|
| $B0J2<$O!"%$%G%"%k(B |
$B0J2<$O(B, $B%$%G%"%k(B |
| @iftex |
@iftex |
| @tex |
@tex $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ @end tex |
| $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ |
|
| @end tex |
|
| $B$N(B |
$B$N(B |
| @tex |
@tex $x$ @end tex |
| $x$ |
|
| @end tex |
|
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| I = D . @{ x dx -1, y dy - 1 @} $B$N(B x |
I = D . @{ x dx -1, y dy - 1 @} $B$N(B x |
| Line 2721 B_@{S0@} length : 2 |
|
| Line 2895 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9!#(B |
:: D $B2C72(B M = D / @var{Id} ($B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id}) $B$KBP$7$F(B, $B=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2741 B_@{S0@} length : 2 |
|
| Line 2915 B_@{S0@} length : 2 |
|
| @comment --- @bullet $B$O9uE@IU$-(B --- |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B) |
($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B) |
| @item |
@item |
| $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B. |
| $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, |
| x,y $B$K$D$$$F@QJ,$r9T$&!#(B |
x,y $B$K$D$$$F@QJ,$r9T$&(B. |
| @end itemize |
@end itemize |
| |
|
| $B0J2<$O!"%$%G%"%k(B |
$B0J2<$O(B, $B%$%G%"%k(B |
| @iftex |
@iftex |
| @tex |
@tex $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\}$ @end tex |
| $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $ |
$B$H$*$$$?;~(B, D $B2C72(B |
| @end tex |
@tex $M = D / I$ @end tex |
| $B$N(B |
$B$N(B |
| @tex |
@tex $t$ @end tex |
| $t$ |
|
| @end tex |
|
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t |
I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} |
| |
$B$H$*$$$?;~(B, D $B2C72(B M = D / I $B$N(B t |
| @end ifinfo |
@end ifinfo |
| $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6]) |
$B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6]) |
| @example |
@example |
| [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x], |
[1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x], |
| [dt,dx],[1,0]); |
[dt,dx],[1,0]); |
| Line 2773 B_@{S0@} length : 2 |
|
| Line 2946 B_@{S0@} length : 2 |
|
| -- fctr(BF) + base :0.001sec(0.0006731sec) |
-- fctr(BF) + base :0.001sec(0.0006731sec) |
| [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]] |
[[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]] |
| @end example |
@end example |
| |
$BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B, |
| |
$B@QJ,2C72$N4pDl(B |
| |
@iftex |
| |
@tex $t^1, t^0$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
t^1, t^0 |
| |
@end ifinfo |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@QJ,2C72$O(B |
| |
@iftex |
| |
@tex $(4 x \partial_x^2 + 6 \partial_x, 0), (0, -4 x \partial_x^2 - 6 \partial_x), |
| |
(0, -2 x \partial_x), (0, 2 \partial_x)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
(4 x dx^2 + 6 dx, 0), (0, -4 x dx^2 - 6 dx), |
| |
(0, -2 x dx), (0, 2 dx) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
@node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| @subsection @code{nk_restriction.integration_ideal} |
@subsection @code{nk_restriction.integration_ideal} |
| Line 2782 B_@{S0@} length : 2 |
|
| Line 2974 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9!#(B |
:: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,%$%G%"%k$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2802 B_@{S0@} length : 2 |
|
| Line 2994 B_@{S0@} length : 2 |
|
| @comment --- @bullet $B$O9uE@IU$-(B --- |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(B |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| ($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B) |
($B$9$J$o$A(B, @code{[1,1,0,0,0]} $B$O(B OK $B$@$,(B, @code{[1,0,1,0,0]} $B$O%@%a(B) |
| @item |
@item |
| $B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B. |
| $BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, |
| x,y $B$K$D$$$F@QJ,$r9T$&!#(B |
x,y $B$K$D$$$F@QJ,$r9T$&(B. |
| @end itemize |
@end itemize |
| |
|
| $B0J2<$O!"%$%G%"%k(B |
$B0J2<$O(B, $B%$%G%"%k(B |
| @iftex |
@iftex |
| @tex |
@tex |
| $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $ |
$I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $ |
| @end tex |
@end tex |
| $B$N(B |
$B$N(B |
| @tex |
@tex $t$ @end tex |
| $t$ |
|
| @end tex |
|
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t |
I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t |
| @end ifinfo |
@end ifinfo |
| $B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k!#(B([SST, Ex5.5.2, Ex5.5.6]) |
$B$K$D$$$F$N@QJ,%$%G%"%k$r7W;;$7$?Nc$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6]) |
| @example |
@example |
| [1431] nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x], |
[1431] nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x], |
| [dt,dx],[1,0]); |
[dt,dx],[1,0]); |
| Line 2834 B_@{S0@} length : 2 |
|
| Line 3024 B_@{S0@} length : 2 |
|
| -- fctr(BF) + base :0.001sec(0.001091sec) |
-- fctr(BF) + base :0.001sec(0.001091sec) |
| -- integration_ideal_internal :0.002sec(0.001879sec) |
-- integration_ideal_internal :0.002sec(0.001879sec) |
| [2*x*dx+1] |
[2*x*dx+1] |
| [1432] |
|
| @end example |
@end example |
| |
|
| |
@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$$@bL@(B --- |
| |
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B --- |
| |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| |
@itemize @bullet |
| |
@item test_ann_mul(), test_ann_mul2(), test_ann_mul3() $B$r;2>H(B. |
| |
@end itemize |
| |
|
| |
|
| |
@node nk_restriction (option) ,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option) |
| |
@subsection @code{nk_restriction (option)} |
| |
@comment --- $B:w0zMQ%-!<%o!<%I(B |
| |
@findex nk_restriction (option) |
| |
|
| |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| |
@table @t |
| |
@item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
| |
@item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord}) |
| |
@item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
| |
@item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}, ht=@var{b}, ord=@var{ord}) |
| |
:: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B |
| |
@end table |
| |
|
| |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| |
@table @var |
| |
@item @var{n} |
| |
0 $B$^$?$O(B 1 |
| |
@item @var{p} |
| |
$B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B) |
| |
@item @var{m} |
| |
$B@0?t(B |
| |
@item @var{b} |
| |
0, 1, 2, 3 $B$N$$$:$l$+(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$$@bL@(B --- |
| |
@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B --- |
| |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| |
@itemize @bullet |
| |
@item @var{n} $B$,(B 0 $B$G$J$$$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. |
| |
|
| |
@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, |
| |
@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 |
| |
|
| |
@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 |
| |
|
| |
@node nk_restriction.module_restriction,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| |
@subsection @code{nk_restriction.module_restriction} |
| |
@comment --- $B:w0zMQ%-!<%o!<%I(B |
| |
@findex nk_restriction.module_restriction |
| |
|
| |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| |
@table @t |
| |
@item nk_restriction.module_restriction(@var{M}, @var{VL}, @var{DVL}, @var{W}) |
| |
:: D $B2C72(B D^r/@var{M} (@var{M} $B$O(B D^r $B$NItJ,2C72(B) $B$N=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@)8B2C72$rJV$9(B. |
| |
@end table |
| |
|
| |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| |
@table @var |
| |
@item M |
| |
D $B<+M32C72(B D^r $B$NItJ,2C72(B |
| |
@item VL |
| |
$BJQ?t$N%j%9%H(B |
| |
@item DVL |
| |
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B) |
| |
@item W |
| |
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item |
| |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| |
@comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)} |
| |
$B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@)8B$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B, |
| |
@var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B. |
| |
@item |
| |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B. |
| |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B |
| |
x $B$K$D$$$F@)8B$r9T$&(B. |
| |
@end itemize |
| |
|
| |
$B0J2<$O(B, D $B<+M32C72(B |
| |
@iftex |
| |
@tex $D^2$ @end tex |
| |
$B$NItJ,2C72(B |
| |
@tex |
| |
$M = D \cdot \{(\partial_x, \partial_y), (\partial_y, \partial_x), (x,y) \}$ |
| |
@end tex |
| |
$B$r$H$j(B, D $B2C72(B |
| |
@tex $D^2 / M$ @end tex |
| |
$B$N(B |
| |
@tex $x$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
D^2 $B$NItJ,2C72(B M = D . @{ (dx, dy), (dy, dx), (x, y) @} |
| |
$B$r$H$j(B, D $B2C72(B D^2 / M $B$N(B x |
| |
@end ifinfo |
| |
$B$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B. |
| |
@example |
| |
[2691] nk_restriction.module_restriction([[dx,dy],[dy,dx],[x,y]], [x,y], [dx,dy], [1,0]); |
| |
.... |
| |
bfunction : |
| |
s |
| |
[[1,1],[s,1]] |
| |
integer roots : |
| |
[0,0] |
| |
Generators: |
| |
[e1,e2] |
| |
Relations: |
| |
[-8*e2*dy,4*e2*dy^2,-4*e2*dy^3,4*e1*y*dy-4*e1,-4*e1*dy^2,-4*e2,-e2*y*dy^2+2*e2*dy,-e1*y*dy+e1,e1*y*dy-e1] |
| |
[[0,-1],[-dy^2,0],[y*dy-1,0]] |
| |
@end example |
| |
$B@)8B2C72$O(B |
| |
@iftex |
| |
@tex $(0, -1), (-\partial_y^2, 0), (y \partial_y -1 , 0)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
(0, -1), (-dy^2, 0), (y, dy-1, 0) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| |
@node nk_restriction.module_integration,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| |
@subsection @code{nk_restriction.module_integration} |
| |
@comment --- $B:w0zMQ%-!<%o!<%I(B |
| |
@findex nk_restriction.module_integration |
| |
|
| |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| |
@table @t |
| |
@item nk_restriction.module_integration(@var{M}, @var{VL}, @var{DVL}, @var{W}) |
| |
:: D $B2C72(B D^r/M (@var{M} $B$O(B D^r $B$NItJ,2C72(B) $B$N=E$_%Y%/%H%k(B @var{W} $B$K$D$$$F$N@QJ,2C72$rJV$9(B. |
| |
@end table |
| |
|
| |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| |
@table @var |
| |
@item M |
| |
D $B<+M32C72(B D^r $B$NItJ,2C72(B |
| |
@item VL |
| |
$BJQ?t$N%j%9%H(B |
| |
@item DVL |
| |
$BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B) |
| |
@item W |
| |
$B=E$_%Y%/%H%k$rI=$9%j%9%H(B |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item |
| |
@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(B. |
| |
@comment{($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)} |
| |
$B8=:_$N$H$3$m(B, 1 $BJQ?t$K$D$$$F$@$1@QJ,$r$H$k$h$&$K$7$+<BAu$7$F$$$J$$$?$a(B, |
| |
@var{W} $B$O(B 0 $BHVL\$NMWAG$@$1@5$N@0?t$,F~$k(B. |
| |
@item |
| |
$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B. |
| |
$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,0,0]} $B$G$"$l$P(B |
| |
x $B$K$D$$$F@QJ,$r9T$&(B. |
| |
@end itemize |
| |
|
| |
$B0J2<$O(B, D $B<+M32C72(B |
| |
@iftex |
| |
@tex $D^2$ @end tex |
| |
$B$NItJ,2C72(B |
| |
@tex $M = D \cdot \{(x, y), (y, x), (\partial_x, \partial_y) \}$ @end tex |
| |
$B$r$H$j(B, D $B2C72(B |
| |
@tex $D^2/M$ @end tex |
| |
$B$N(B |
| |
@tex $x$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
D^2 $B$NItJ,2C72(B M = D . @{ (x, y), (y, x), (dx, dy) @} $B$r$H$j(B, |
| |
D $B2C72(B D^2 / M $B$N(B x |
| |
@end ifinfo |
| |
$B$K$D$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k(B. |
| |
@example |
| |
[2702] nk_restriction.module_integration([[x,y],[y,x],[dx,dy]], [x,y], [dx,dy], [1,0]); |
| |
... |
| |
bfunction : |
| |
s |
| |
[[1,1],[s,1]] |
| |
integer roots : |
| |
[0,0] |
| |
Generators: |
| |
[e1,e2] |
| |
Relations: |
| |
[-8*e2*y,-4*e2*y^2,-4*e2*y^3,-4*e1*y*dy-8*e1,-4*e1*y^2,-4*e2,-e2*y^2*dy-4*e2*y,e1*y*dy+2*e1,e1*y*dy+2*e1] |
| |
[[0,-1],[y*dy+2,0],[-y^2,0]] |
| |
@end example |
| |
$B@QJ,2C72$O(B |
| |
@iftex |
| |
@tex $(0, -1), (y \partial_y + 2, 0), (-y^2, 0)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
(0, -1), (y dy + 2, 0), (-y^2, 0) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| @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. |
| |
@item 2016-05 $B$K(B module_integration(), module_restriction() $B$,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) |
| |
|
| @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_simplify.simplify,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{fj_simplify.simplify} |
| |
@findex fj_simplify.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_simplify.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 |
| |
$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$$$N$G(B, $B7k2L$rJ#AG4X?t$K;H$&$H$-$O(B |
| |
$BCm0U$,I,MW$G$"$k(B. (x^a = exp(a*log(x)) $B$J$N$G(B) |
| |
@end itemize |
| |
|
| |
@example |
| |
import("fj_simplify.rr"); |
| |
[1434] fj_simplify.simplify((x^(1/2))^3); |
| |
((x)^(3/2)) |
| |
[1435] fj_simplify.simplify((2^(1/2))^2); |
| |
2 |
| |
[1436] fj_simplify.simplify((2+2^(1/2))^3); |
| |
14*((2)^(1/2))+20 |
| |
[1437] fj_simplify.simplify(exp(x)*exp(-x+y)); |
| |
((@@e)^(y)) |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{quote} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
Todo: exp $B0J30$NFC<l4X?t$K$D$$$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 |
| |
|
| |
@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); |
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|
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[[[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]] |
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@end example |
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|
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@table @t |
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@item $B;2>H(B |
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@ref{abc2marginal} |
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@ref{marginal2abc} |
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@end table |
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|
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@noindent |
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ChangeLog |
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@itemize @bullet |
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@item |
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$B$3$N4X?t$O(B 2014-12-13 $B$K(B tk_fd.rr $B$KDI2C$5$l$?(B. |
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@end itemize |
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|
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@comment ------------------- |
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@comment tk_fd.ahvec_abc |
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@comment ------------------- |
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@node tk_fd.ahvec_abc,,, $B<B83E*;EMM$N4X?t(B |
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@subsection @code{tk_fd.ahvec_abc} |
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@findex tk_fd.ahvec_abc |
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@table @t |
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@item tk_fd.ahvec_abc(@var{A},@var{B},@var{C},@var{Y} | all=1) |
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:: 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] |
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(2$BHVL\$N9T(B)$B$K$D$$$F$NJPHyJ,$r7W;;$9$k(B. |
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@end table |
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|
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@table @var |
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@item return |
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$B%j%9%H(B @var{Ans} |
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@item A |
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$B?t(B |
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@item B |
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$B?t$N%j%9%H(B. $BD9$5$O(B m. |
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@item C |
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$B?t(B |
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@item Y |
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(2,m+1) $BJQ?tCM$r$"$i$o$9%j%9%H$N%j%9%H(B. |
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@end table |
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|
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@itemize @bullet |
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@item |
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@var{A}, @var{B}, @var{C}, $B$K8=$l$k?t$O@0?t$rM?$($k(B. |
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@var{Y} $B$N@.J,$OM-M}?t$rM?$($k(B. |
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@item |
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@var{Ans}[2]*@var{Ans}[1] $B$,(B Z. |
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@var{Ans}[2]*@var{Ans}[0][I] $B$,(B Z $B$N(B Y[1][I] $B$K$D$$$F$NJPHyJ,(B. |
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@item |
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$BO@J8(B |
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1.Y.Goto, Contiguity relations of Lauricella's F_D revisited, arxiv:1412.3256 |
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$B$GF3=P$5$l$F$$$k(B |
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contiguity relation $B$rMQ$$$F7W;;$9$k(B. |
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@end itemize |
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|
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@example |
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[2449] marginal2abc([3,12],[6,3,3,3]); |
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[-3,[-3,-3,-3],4] |
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|
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[2450] tk_fd.ahvec_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]); |
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[[ 24041/1152 143551/11520 16973/1280 78827/5760 ],1/7776] |
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|
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[2451] expectation_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]); |
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[721230/173593,430653/173593,458271/173593,67566/24799] |
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@end example |
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|
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@table @t |
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@item $B;2>H(B |
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@ref{expectation_abc} |
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@end table |
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|
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@noindent |
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ChangeLog |
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@itemize @bullet |
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@item |
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$B$3$N4X?t$O(B 2014-$B2F$K3+H/$5$l$?(B. |
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@end itemize |
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|
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|
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@node pari setbprec setround todouble mpfr_gamma mpfr_floor mpfr_round,,, $B<B83E*;EMM$N4X?t(B |
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@subsection @code{pari}, @code{setbprec},@code{setround},@code{todouble},@code{mpfr_gamma},@code{mpfr_floor},@code{mpfr_round}, |
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@findex pari |
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@findex setbprec |
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@findex setround |
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@findex todouble |
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@findex mpfr_gamma |
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@findex mpfr_floor |
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@findex mpfr_round |
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|
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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 pari(@var{arg1},@var{arg2},...) |
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:: MPFR $B$G(B pari $B$N4X?t$r(B emulate $B$9$k$+(B ox_pari $B%5!<%P!<$r8F$S=P$9(B. |
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@itemx setbprec(@var{arg1}) |
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@itemx setround(@var{arg1}) |
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$B4]$a$NJ}K!$N;XDj(B. mpfr $B=`5r(B. |
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@itemx todouble(@var{arg1}) |
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:: bigfloat $B7?$r(B double $B$KJQ49$9$k(B. |
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@itemx mpfr_gamma(@var{arg1}) |
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:: gamma $B4X?t$N7W;;(B. |
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@itemx mpfr_floor(@var{arg1}) |
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:: floor $B$N7W;;(B. |
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@itemx mpfr_round(@var{arg1}) |
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:: $B4]$a$N7W;;(B. |
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@end table |
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|
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@table @var |
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@item return |
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$B8e=R(B. |
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@item arg1, arg2 |
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$B8e=R(B. |
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@end table |
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|
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@itemize @bullet |
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@item 20150807 $B0J9_$N(B asir $B$G$O(B, bigfloat $B$,(B pari $B$G$O$J$/(B mpfr $B$rMQ$$$F7W;;$5$l$k(B. |
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Todo, pari $B$O(B ox_pari $B$r8F$S=P$9$,(B, $B$^$@(B ox_pari $B$KL$<BAu$N5!G=$,B?$/$"$k(B. |
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$B6h4V1i;;$X$NBP1~$O9T$C$F$$$J$$(B. |
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@item |
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pari(floor,@var{arg1}), |
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pari(round,@var{arg1}), |
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pari(gamma,@var{arg1}) |
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$B$O(B mpfr $B$G(B pari $B$r(B emulate $B$7$F$$$k$N$G(B, $BF0:n$,0[$J$k(B. |
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$BFC$K(B gamma $B$OJ#AG?t$N0z?t$r<u$1<h$i$J$$(B. |
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pari $B$N(B floor $B$O7e?t$,B-$j$J$/$J$k$H%(%i!<$G=*N;$7$?$,(B, |
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$B$3$N(B floor $B$G$O(B setprec $B$G;XDj$7$?7e?t0JFb$J$i@5$7$/(B floor $B$rLa$9(B. |
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Todo, ox_pari $B$r;XDj$7$F8F$S=P$9J}K!(B. |
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@end itemize |
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|
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@example |
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[219] ctrl("bigfloat",1)$ |
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[220] setprec(100)$ |
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[221] pari(floor,1111111111111.1+1/10); |
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1111111111111 |
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@end example |
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|
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@table @t |
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@item $B;2>H(B |
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@ref{pari} |
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@end table |
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|
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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$l$i$NBgJQ99$O(B 2015-08-03 $B$h$j(B 08-07 $B$N(B asir $B9g=I$G$*$3$J$o$l$?(B. |
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$B$^$@:n6HCf(B. Todo, asirgui $B$X$NBP1~(B. debug, ... |
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@item $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B asir2000/builtin/bfaux.c, |
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asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB??t(B. |
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@end itemize |
| |
|
| @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$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B. |
| @comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
@comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
| @comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
| @node xyz_pqr,,, $B<B83E*;EMM$N4X?t(B |
@node xyz_pqr syz_stu,,, $B<B83E*;EMM$N4X?t(B |
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@comment @menu $B$K$b(B * syz_pqr syz_stu:: $B$HB3$1$F=q$/;v(B. $BJ,$1$F$O$$$1$J$$(B. |
| @subsection @code{xyz_pqr}, @code{syz_stu} |
@subsection @code{xyz_pqr}, @code{syz_stu} |
| @findex xyz_pqr |
@findex xyz_pqr |
| @findex xyz_stu |
@findex xyz_stu |
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