| version 1.48, 2014/05/29 13:18:18 |
version 1.58, 2020/09/06 03:26:47 |
|
|
| %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.47 2013/02/18 07:18:32 takayama Exp $ |
%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.57 2018/10/17 00:33:49 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},,,]} |
| @def@b#1{{@bf@gt #1}} |
@def@b#1{{@bf #1}} |
| @catcode`@#=@other |
@catcode`@#=@other |
| @end iftex |
@end iftex |
| @overfullrule=0pt |
@overfullrule=0pt |
|
|
| @comment --- $B$*$^$8$J$$=*$j(B --- |
@comment --- $B$*$^$8$J$$=*$j(B --- |
| |
|
| @comment --- GNU info $B%U%!%$%k$NL>A0(B --- |
@comment --- GNU info $B%U%!%$%k$NL>A0(B --- |
| @setfilename xyzman |
@setfilename exp |
| |
@documentlanguage ja |
| |
|
| @comment --- $B%?%$%H%k(B --- |
@comment --- $B%?%$%H%k(B --- |
| @settitle $B<B83E*;EMM$N4X?t(B |
@settitle $B<B83E*;EMM$N4X?t(B |
|
|
| @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 2013 $BG/(B 2 $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--2010. 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 84 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.rkn:: |
|
| * tk_pfn.graph:: |
* tk_pfn.graph:: |
| |
* tk_pfn.rkn:: |
| * tk_rk.runge_kutta_4:: |
* tk_rk.runge_kutta_4:: |
| * tk_rk.runge_kutta_4_linear:: |
* tk_rk.runge_kutta_4_linear:: |
| * tk_rk.zonal:: |
|
| * 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 |
|
|
| @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 1893 builtin/dp.c 1.49 |
|
| Line 1892 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 **************************************************************** |
| |
|
| @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 |
|
|
| @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$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B. |
| @example |
@example |
| [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]); |
[1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]); |
| -- generic_bfct_and_gr :0.001sec(0.001629sec) |
-- generic_bfct_and_gr :0.001sec(0.001629sec) |
| Line 2777 B_@{S0@} length : 2 |
|
| Line 2818 B_@{S0@} length : 2 |
|
| -- fctr(BF) + base :0.000999sec(0.0005109sec) |
-- fctr(BF) + base :0.000999sec(0.0005109sec) |
| [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]] |
[[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]] |
| @end example |
@end example |
| |
$BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B, |
| |
$B@)8B2C72$N4pDl(B |
| |
@iftex |
| |
@tex $\partial_x^1, \partial_x^0$ @end tex |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B |
| |
@tex $(y \partial_y - 1, 0), (0, y\partial_y-1), (-1,0)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
dx^1, dx^0 |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@)8B2C72$O(B |
| |
(y dy - 1, 0), (0, ydy-1), (-1,0) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| |
|
| @node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
@node nk_restriction.restriction_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| @subsection @code{nk_restriction.restriction_ideal} |
@subsection @code{nk_restriction.restriction_ideal} |
| @comment --- $B:w0zMQ%-!<%o!<%I(B |
@comment --- $B:w0zMQ%-!<%o!<%I(B |
| Line 2787 B_@{S0@} length : 2 |
|
| Line 2842 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.restriction_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$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$$$F$N@)8B%$%G%"%k$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2804 B_@{S0@} length : 2 |
|
| Line 2859 B_@{S0@} length : 2 |
|
| |
|
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(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$$$F@)8B$r9T$&(B. |
| @end itemize |
@end itemize |
| |
|
| $B0J2<$O!"%$%G%"%k(B |
$B0J2<$O(B, $B%$%G%"%k(B |
| @iftex |
@iftex |
| @tex |
@tex $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ @end tex |
| $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ |
|
| @end tex |
|
| $B$N(B |
$B$N(B |
| @tex |
@tex $x$ @end tex |
| $x$ |
|
| @end tex |
|
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| I = D . @{ x dx -1, y dy - 1 @} $B$N(B x |
I = D . @{ x dx -1, y dy - 1 @} $B$N(B x |
| Line 2845 B_@{S0@} length : 2 |
|
| Line 2896 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.integration(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$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$$$F$N@QJ,2C72$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2865 B_@{S0@} length : 2 |
|
| Line 2916 B_@{S0@} length : 2 |
|
| @comment --- @bullet $B$O9uE@IU$-(B --- |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(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$$$F$N@QJ,2C72$r7W;;$7$?Nc$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6]) |
| @example |
@example |
| [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x], |
[1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x], |
| [dt,dx],[1,0]); |
[dt,dx],[1,0]); |
| Line 2897 B_@{S0@} length : 2 |
|
| Line 2947 B_@{S0@} length : 2 |
|
| -- fctr(BF) + base :0.001sec(0.0006731sec) |
-- fctr(BF) + base :0.001sec(0.0006731sec) |
| [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]] |
[[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]] |
| @end example |
@end example |
| |
$BJV$jCM$NBh(B 1 $BHVL\$NMWAG(B @code{[[1],[0]]]} $B$O(B, |
| |
$B@QJ,2C72$N4pDl(B |
| |
@iftex |
| |
@tex $t^1, t^0$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
t^1, t^0 |
| |
@end ifinfo |
| |
$B$r0UL#$7(B, |
| |
$BJV$jCM$NBh(B 0 $BHVL\$NMWAG$+$i(B, $B@QJ,2C72$O(B |
| |
@iftex |
| |
@tex $(4 x \partial_x^2 + 6 \partial_x, 0), (0, -4 x \partial_x^2 - 6 \partial_x), |
| |
(0, -2 x \partial_x), (0, 2 \partial_x)$ @end tex |
| |
@end iftex |
| |
@ifinfo |
| |
(4 x dx^2 + 6 dx, 0), (0, -4 x dx^2 - 6 dx), |
| |
(0, -2 x dx), (0, 2 dx) |
| |
@end ifinfo |
| |
$B$G@8@.$5$l$k$3$H$,$o$+$k(B. |
| |
|
| @node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
@node nk_restriction.integration_ideal,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
| @subsection @code{nk_restriction.integration_ideal} |
@subsection @code{nk_restriction.integration_ideal} |
| Line 2906 B_@{S0@} length : 2 |
|
| Line 2975 B_@{S0@} length : 2 |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@comment --- $B4X?t$N4JC1$J@bL@(B --- |
| @table @t |
@table @t |
| @item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
@item nk_restriction.integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}) |
| :: $B%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{Id} $B$r=E$_%Y%/%H%k(B @var{W} $B$K$D$$$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$$$F$N@QJ,%$%G%"%k$rJV$9(B. |
| @end table |
@end table |
| |
|
| @comment --- $B0z?t$N4JC1$J@bL@(B --- |
@comment --- $B0z?t$N4JC1$J@bL@(B --- |
| Line 2926 B_@{S0@} length : 2 |
|
| Line 2995 B_@{S0@} length : 2 |
|
| @comment --- @bullet $B$O9uE@IU$-(B --- |
@comment --- @bullet $B$O9uE@IU$-(B --- |
| @itemize @bullet |
@itemize @bullet |
| @item |
@item |
| @var{W} $B$NMWAG$OHsIi@0?t$G!"(B0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$!#(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 2958 B_@{S0@} length : 2 |
|
| Line 3025 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 |
@node nk_restriction.ann_mul,,, D $B2C72$N@)8B$K4X$9$k4X?t(B |
|
|
| $B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} |
t^@{b-1@} (1-t)^@{c-b-1@} (1-xt)^@{-a@} |
| $B$N(B annihilator |
$B$N(B annihilator |
| I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab, |
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 @} |
(1-t)x dx+t(1-t)dt+(2-c)t+b-1, (xt-1)dx+at @} |
| Line 3120 I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab, |
|
| Line 3186 I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab, |
|
| -- generic_bfct_and_gr :0.008001sec(0.006181sec) |
-- generic_bfct_and_gr :0.008001sec(0.006181sec) |
| generic bfct : [[-1,1],[s,1],[s-a+c-1,1]] |
generic bfct : [[-1,1],[s,1],[s-a+c-1,1]] |
| S0 : 0 |
S0 : 0 |
| B_{S0} length : 1 |
B_@{S0@} length : 1 |
| -- fctr(BF) + base :0sec(0.003848sec) |
-- fctr(BF) + base :0sec(0.003848sec) |
| -- integration_ideal_internal :0sec(0.07707sec) |
-- integration_ideal_internal :0sec(0.07707sec) |
| [[(x^2-x)*dx^2+((a+b+1)*x-c)*dx+b*a],[[[[dt,(-t+1)*dx]],1]]] |
[[(x^2-x)*dx^2+((a+b+1)*x-c)*dx+b*a],[[[[dt,(-t+1)*dx]],1]]] |
| Line 3240 I = < dt +(3t^2-1)x, dx+t^3-t > |
|
| Line 3306 I = < dt +(3t^2-1)x, dx+t^3-t > |
|
| -- generic_bfct_and_gr :0.012sec(0.0129sec) |
-- generic_bfct_and_gr :0.012sec(0.0129sec) |
| generic bfct : [[1,1],[s,1],[s-2,1]] |
generic bfct : [[1,1],[s,1],[s-2,1]] |
| S0 : 2 |
S0 : 2 |
| B_{S0} length : 3 |
B_@{S0@} length : 3 |
| -- fctr(BF) + base :0.008sec(0.007395sec) |
-- fctr(BF) + base :0.008sec(0.007395sec) |
| -- integration_ideal_internal :0.012sec + gc : 0.016sec(0.04311sec) |
-- 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] |
[-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] |
| Line 3295 $ I = \langle (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) \rangle |
|
| Line 3361 $ I = \langle (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) \rangle |
|
| $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B. |
$B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B. |
| @end iftex |
@end iftex |
| @ifinfo |
@ifinfo |
| \sum_{k=a}^b n_C_k |
\sum_@{k=a@}^b n_C_k |
| $B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B |
$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) > |
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. |
$B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B. |
| Line 3311 I = < (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) > |
|
| Line 3377 I = < (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) > |
|
| -- generic_bfct_and_gr :0.01sec(0.007085sec) |
-- generic_bfct_and_gr :0.01sec(0.007085sec) |
| generic bfct : [[1,1],[s,1]] |
generic bfct : [[1,1],[s,1]] |
| S0 : 0 |
S0 : 0 |
| B_{S0} length : 1 |
B_@{S0@} length : 1 |
| -- fctr(BF) + base :0.003333sec(0.001785sec) |
-- fctr(BF) + base :0.003333sec(0.001785sec) |
| -- restriction_ideal_internal :0sec(0.002336sec) |
-- restriction_ideal_internal :0sec(0.002336sec) |
| [[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]] |
[[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]] |
| @end example |
@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 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 |
@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. |
$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 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($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B |
@node $B$=$NB>(B($BL$J,N`(B),,, $B<B83E*;EMM$N4X?t(B |
| Line 3426 y $B$NCM$,30B&%k!<%W(B, x $B$NCM$,FbB&%k!<%W$N7A<0$ |
|
| Line 3640 y $B$NCM$,30B&%k!<%W(B, x $B$NCM$,FbB&%k!<%W$N7A<0$ |
|
| [1590] tk_pfn.testgraph1(); |
[1590] tk_pfn.testgraph1(); |
| |
|
| $B$3$3$G(B testgraph1() $B$O0J2<$N$H$*$j(B. |
$B$3$3$G(B testgraph1() $B$O0J2<$N$H$*$j(B. |
| def testgraph1() { |
def testgraph1() @{ |
| /* tk_bess2.bess2pf(1/2); */ |
/* tk_bess2.bess2pf(1/2); */ |
| Pf= [[[ 0, (1)/(x), 0 ], |
Pf= [[[ 0, (1)/(x), 0 ], |
| [ -x, (2*x^2+1)/(x), -2*x ], |
[ -x, (2*x^2+1)/(x), -2*x ], |
| Line 3439 def testgraph1() { |
|
| Line 3653 def testgraph1() { |
|
| Dom=[[0.5,1.5],[1.5,9]]; |
Dom=[[0.5,1.5],[1.5,9]]; |
| Step = 0.5; |
Step = 0.5; |
| return tk_pfn.graph(Pf,Dom,Iv,Step | fit=1); |
return tk_pfn.graph(Pf,Dom,Iv,Step | fit=1); |
| } |
@} |
| |
|
| |
|
| @end example |
@end example |
|
|
| $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) |
$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. |
taka_plot_auto $B$O2<J}8~$G(B y $B$,@5(B. |
| |
|
| def test4() { |
def test4() @{ |
| A=runge_kutta_4([y1,-y0],x,[y0,y1],0,[1,0],3.14*2,0.1); |
A=runge_kutta_4([y1,-y0],x,[y0,y1],0,[1,0],3.14*2,0.1); |
| taka_plot_auto(A); |
taka_plot_auto(A); |
| return(A); |
return(A); |
| } |
@} |
| |
|
| @end example |
@end example |
| |
|
|
|
| |
|
| |
|
| |
|
| @node fj_simp.simplify,,, $B<B83E*;EMM$N4X?t(B |
@node fj_simplify.simplify,,, $B<B83E*;EMM$N4X?t(B |
| @subsection @code{fj_simp.simplify} |
@subsection @code{fj_simplify.simplify} |
| @findex fj_simp.simplify |
@findex fj_simplify.simplify |
| |
|
| @comment --- $B4X?t$N4JC1$J@bL@(B --- |
@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 --- |
@comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B --- |
| @table @t |
@table @t |
| @item fj_simp.simplify(@var{arg1}) |
@item fj_simplify.simplify(@var{arg1}) |
| :: arg1 $B$r4JC12=$9$k(B. |
:: arg1 $B$r4JC12=$9$k(B. |
| @end table |
@end table |
| |
|
|
|
| @end table |
@end table |
| |
|
| @itemize @bullet |
@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 |
@item |
| $B$3$N4X?t$O(B |
$B$3$N4X?t$O(B |
| Joel S. Cohen, Computer Algebra and Symbolic Computation, |
Joel S. Cohen, Computer Algebra and Symbolic Computation, |
| Line 3598 B.F.Caviness, R.J.Fateman, Simplification of Radical E |
|
| Line 3810 B.F.Caviness, R.J.Fateman, Simplification of Radical E |
|
| @end itemize |
@end itemize |
| |
|
| @example |
@example |
| load("fj_simplify.rr"); |
import("fj_simplify.rr"); |
| [1434] simplify((x^(1/2))^3); |
[1434] fj_simplify.simplify((x^(1/2))^3); |
| ((x)^(3/2)) |
((x)^(3/2)) |
| [1435] simplify((2^(1/2))^2); |
[1435] fj_simplify.simplify((2^(1/2))^2); |
| 2 |
2 |
| [1436] simplify((2+2^(1/2))^3); |
[1436] fj_simplify.simplify((2+2^(1/2))^3); |
| 14*((2)^(1/2))+20 |
14*((2)^(1/2))+20 |
| [1437] simplify(exp(x)*exp(-x+y)); |
[1437] fj_simplify.simplify(exp(x)*exp(-x+y)); |
| ((@@e)^(y)) |
((@@e)^(y)) |
| @end example |
@end example |
| |
|
| Line 3618 load("fj_simplify.rr"); |
|
| Line 3830 load("fj_simplify.rr"); |
|
| ChangeLog |
ChangeLog |
| @itemize @bullet |
@itemize @bullet |
| @item |
@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. |
Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification $B$N5!G=(B. |
| @item |
@item |
| $B$3$N4X?t$O(B 2010.01 $B$K(B M.Fujimoto $B$K$h$j:G=i$NHG$,=q$+$l$?(B. |
$B$3$N4X?t$O(B 2010.01 $B$K(B M.Fujimoto $B$K$h$j:G=i$NHG$,=q$+$l$?(B. |
| Line 3680 holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7 |
|
| Line 3889 holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7 |
|
| @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B. |
@item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B. |
| @end itemize |
@end itemize |
| |
|
| @comment ----------- $B0J2<$O8+K\(B. $B>C$9$J(B. template |
@node ot_hgm_ahg.cbase,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{ot_hgm_ahg.cbase} |
| |
@findex ot_hgm_ahg.cbase |
| |
|
| |
@table @t |
| |
@item cbase(@var{A}) |
| |
:: @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(B Pfaffian $B$N4pDl$r5a$a$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
Pfaffian$B$N4pDl(B($BHyJ,:nMQAG$N%b%N%_%"%k(B)$B$N%j%9%H(B |
| |
@item A |
| |
$B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item A-$BD64v2?%$%G%"%k$N(B Q(x)[dx] $B$K$*$1$kI8=`4pDl$O(B Pfaffian $B$N4pDl$H$J$k$,(B, $B5U$O$+$J$i$:$7$b??$G$O$J$$(B. $B8D?t$O$b$A$m$sF1$8$G$"$k(B. |
| |
@item |
| |
$B%"%k%4%j%:%`$O(B |
| |
T.Hibi, K.Nishiyama, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103 |
| |
$B$K$h$k(B. |
| |
$B$5$i$K%Q%i%a!<%?(B b $B$r?t$KFC<l2=$9$k3NN(;;K!$rMQ$$$F$$$k(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[2190] import("ot_hgm_ahg.rr"); |
| |
1 |
| |
[2191] ot_hgm_ahg.cbase([[1,1,1,1],[0,1,2,3]]); |
| |
We use a probabilistic algorithm to determine the base.[dx2^2,dx3*dx2,dx3^2] |
| |
|
| |
[dx3,dx4,1] |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{get_mat2} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2012 $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B. |
| |
@item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B. |
| |
@end itemize |
| |
|
| |
@node ot_hgm_ahg.get_mat2,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{ot_hgm_ahg.get_mat2} |
| |
@findex ot_hgm_ahg.get_mat2 |
| |
@comment get_mat2 |
| |
@table @t |
| |
@item get_mat2(@var{A},@var{W},@var{Std},@var{Mset}) |
| |
:: @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O(B H_A $B$N(B Pfaffian $B$N4pDl$r5a$a$k$?$a$N(B Sylvester $BK!(B $B$rE,MQ$9$k$?$a$N9TNs$r@8@.$9$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B%j%9%H(B |
| |
@item A |
| |
$B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B |
| |
@item W |
| |
$B%j%9%H(B. toric ideal $B$N%0%l%V%J!<4pDl$r7W;;$9$k$?$a$N(B weight vector. |
| |
$BB?J,$J$s$G$b$$$$$O$:(B. |
| |
@item Std |
| |
$B%j%9%H(B. Pfaffian $B$N4pDl(B. cbase(A) $B$N=PNO$rMQ$$$k(B. |
| |
@item Mset |
| |
Sylvester $B7?9TNs$r:n$k$?$a$NHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B. |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item $B=PNO$r(B @var{P} $B$KBeF~$9$k$H(B, |
| |
@var{P}[0]*@var{P}[2] - @var{P}[1]*@var{Std} $B$,(B modulo H_A $B$G(B 0 $B$H$J$k(B. |
| |
@var{P}[0] $B$H(B @var{P}[2] $B$r7k9g$7$?9TNs$,(B, sylvester $B9TNs(B ($BO@J8$N5-9f$G$N(B F'). |
| |
@var{P}[2], @var{Std} $B$,(B index $B%b%N%_%"%k$G$"$k(B. |
| |
$BO@J8$G$N5-9f$G$O(B @var{P}[2] $B$O(B M_t, @var{Std} $B$O(B S. |
| |
@item |
| |
$B%"%k%4%j%:%`$O(B |
| |
K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method |
| |
$B$K$h$k(B. $BO@J8$N9TNs(B F'. |
| |
@end itemize |
| |
|
| |
@example |
| |
[2190] import("ot_hgm_ahg.rr"); |
| |
1 |
| |
[2191] A=[[1,1,1,1],[0,1,2,3]]$ |
| |
Std=ot_hgm_ahg.cbase(A)$ |
| |
W=[[dx1,1,dx2,1,dx3,1,dx4,1]]$ |
| |
Mset=[1,dx1,dx2,dx3,dx4]$ |
| |
[2192] ot_hgm_ahg.get_mat2(A,W,Std,Mset); |
| |
|
| |
$B>JN,(B |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{cbase} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2012 $B$+$i(B 2014-$B=U5Y$_$K$+$1$F$+$+$l$?(B. |
| |
@item version 1.1 $B0JA0$NHG$O(B h-mle/A-hg/Prog ($B8&5f%0%k!<%W$N6&M-%U%)%k%@(B) $B$K$"$j(B. |
| |
@item |
| |
$B%=!<%9(B ot_hgm_ahg.rr $B$N(B test3(), test3b(), test4(), test5(), test6(), test6c() $BEy$KMxMQNc$,$"$k(B. |
| |
@item |
| |
test3b() $B$G(B @var{Mset} $B$r0l<!<0A4It$K$7$?$b$N$,(B, $BO@J8$NNc(B. |
| |
@end itemize |
| |
|
| |
@comment ------------------- |
| |
@comment hgm_ahg_contiguity |
| |
@comment ------------------- |
| |
@node ot_hgm_ahg.hgm_ahg_contiguity,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{ot_hgm_ahg.hgm_ahg_contiguity} |
| |
@findex ot_hgm_ahg.hgm_ahg_contiguity |
| |
|
| |
@table @t |
| |
@item hgm_ahg_contiguity(@var{A},@var{StdMon},@var{Line},@var{X0},@var{InitVal},@var{Start},@var{End}) |
| |
:: @var{A} $B$GDj5A$5$l$k(B A-$BD64v2?J}Dx<07O$N(Bcontiguity relation |
| |
$B$r(B Sylvester matrix $B$rMQ$$$F7W;;$7(B, $B$=$l$rMQ$$$FD64v2?4X?t$NCM$r5a$a$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$NCM(B F(End;X0) ?? |
| |
@item A |
| |
$B@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B. |
| |
@item StdMon |
| |
$B%j%9%H(B. Pfaffian $B$N4pDl$rM?$($kHyJ,:nMQAG$N%b%N%_%"%k$N%j%9%H(B. |
| |
@item Line |
| |
$B%j%9%H(B [ContiDir,Beta,Z]. |
| |
@item X0 |
| |
$B%j%9%H(B. x $BJQ?t$NCM(B. |
| |
@item InitVal |
| |
$B%j%9%H(B. $B4pDl$rD64v2?4X?t$K:nMQ$5$;$?%Y%/%H%k$N=i4|CM(B F(Start;X0) |
| |
@item Start |
| |
$B%j%9%H(B. Z $B%Q%i%a!<%?$N=i4|CM(B?? |
| |
@item End |
| |
$B%j%9%H(B. Z $B%Q%i%a!<%?$N=*C<CM(B?? |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item Todo, $B$3$N4X?t$N%$%s%?%U%'!<%9$OJQ99$5$l$kM=Dj(B. |
| |
@item X0 $B$OM-M}?t$N%j%9%H(B. |
| |
@item ContiDir $B$O(B End-Start $B$HF1$8J}8~(B. |
| |
@item Beta. A$BD64v2?4X?t$N(B B $B%Q%i%a!<%?$N=i4|CM(B ?? |
| |
@item Z. ContiDir $B$G$N0l<!85(B contiguity $B$rI=8=$9$k$?$a$NITDj85$NL>A0(B. |
| |
@item $B%=!<%9Cf$NMxMQNc(B. test_fd_conti(), test_c111_conti() |
| |
@item |
| |
$B%"%k%4%j%:%`$*$h$SMxE@$O(B |
| |
K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations II, Holonomic Gradient Method |
| |
$B;2>H(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[2190] import("ot_hgm_ahg.rr"); |
| |
1 |
| |
[2191] ot_hgm_ahg.test_fd_conti(); |
| |
(Todo, $B0z?t$,$I$&$J$k$+$NNc$r2C$($k(B.) |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{get_mat2} |
| |
@ref{hgm_ahg_expected_value_contiguity} |
| |
@ref{hgm_ahg} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2014-07-11 $B$K:G=i$NHG$,(B 1.10$BHG(B ot_hgm_ahg.rr $B$K(B commit $B$5$l$?(B. |
| |
@item $B%$%s%?%U%'!<%9$,99?7$5$l$?HG$O(B, 1.??$BHG(B. |
| |
@end itemize |
| |
|
| |
@comment ------------------- |
| |
@comment tk_hgpoly.optip |
| |
@comment ------------------- |
| |
@node tk_hgpoly.optip,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{tk_hgpoly.optip} |
| |
@findex tk_hgpoly.optip |
| |
|
| |
@table @t |
| |
@item hgpoly.optip(@var{A},@var{B},@var{W}) |
| |
:: $B@0?t7W2hLdBj$r%0%l%V%J!<4pDl$rMQ$$$F2r$/(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B%j%9%H(B. |
| |
@item A |
| |
$BHsIi@0?t$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B |
| |
@item B |
| |
$BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B |
| |
@item W |
| |
$BHsIi@0?t$r@.J,$H$9$k%Y%/%H%k$rI=$9%j%9%H(B |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item @var{A} U = @var{B} $B$rK~$?$9HsIi$N@0?t%Y%/%H%k(B U $B$NCf$G(B, |
| |
$BFb@Q(B @var{W} U $B$r:G>.2=$9$k(B U $B$rLa$9(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[0] import("tk_hgpoly.rr"); |
| |
[2191] tk_hgpoly.optip([[1,1,1,1],[0,1,2,3]],[20,40],[1,1,1,0]); |
| |
[6,1,0,13] |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{feasible} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2014-12-12 $B$K(B commit $B$5$l$?(B. |
| |
$B85HG$O(B h-mle/A-hg/Prog |
| |
@end itemize |
| |
|
| |
@comment ------------------- |
| |
@comment tk_hgpoly.hgpoly |
| |
@comment ------------------- |
| |
@node tk_hgpoly.hgpoly,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{tk_hgpoly.hgpoly} |
| |
@findex tk_hgpoly.hgpoly |
| |
@table @t |
| |
@item hgpoly.hgpoly(@var{A},@var{B}) |
| |
:: @var{A}, @var{B} $B$GDj5A$5$l$kD64v2?B?9`<0$r7W;;$9$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B%j%9%H(B. |
| |
@item A |
| |
$BHsIi@0?t(B(todo, $B:FEY3NG'(B)$B$r@.J,$H$9$k9TNs(B (maximal rank $B$N$b$N(B)$B$rI=$9%j%9%H(B |
| |
@item B |
| |
$BHsIi@0?t$r@.J,$H$9$k%j%9%H(B. |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item $BLa$jCM$r(B F $B$H$9$k$H$-(B, F[0] $B$,D64v2?B?9`<0(B. $BJQ?t$O(B x_1, x_2, ... |
| |
F[1] $B$O(B F[0] $B$NJ,;6I=8=B?9`<0(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[0] import("tk_hgpoly.rr"); |
| |
[2191] tk_hgpoly.hgpoly([[1,1,1,1],[0,1,2,3]],[2,2]); |
| |
[x_3*x_1+1/2*x_2^2,(1/2)*<<0,2,0,0>>+(1)*<<1,0,1,0>>] |
| |
@end example |
| |
|
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2014-12-12 $B$K(B commit $B$5$l$?(B. |
| |
@end itemize |
| |
|
| |
@comment ------------------- |
| |
@comment tk_fd.abc2ahg |
| |
@comment ------------------- |
| |
@node tk_fd.abc2ahg,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{tk_fd.abc2ahg} |
| |
@findex tk_fd.abc2ahg |
| |
@table @t |
| |
@item tk_fd.abc2ahg(@var{A},@var{B},@var{C}) |
| |
:: F_D(@var{A}, @var{B},@var{C}) $B$r2r$K$b$D(B A-$BD64v2?J}Dx<07O$r5a$a$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B%j%9%H(B. |
| |
@item A |
| |
$B?t(B |
| |
@item B |
| |
$B?t$N%j%9%H(B |
| |
@item C |
| |
$B?t(B |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item $BLa$jCM%j%9%H$NBh#0@.J,$O(B A-$BD64v2?J}Dx<07O$rDj5A$9$k9TNs(B. |
| |
$BBh#1@.J,$O(BA-$BD64v2?J}Dx<07O$N%Q%i%a!<%?&B(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[2191] tk_fd.abc2ahg(-3,[-4,-5],3); |
| |
|
| |
[[[0,0,0,1,1,1],[1,0,0,1,0,0],[0,1,0,0,1,0],[0,0,1,0,0,1]],[11,5,4,5]] |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{abc2marginal} |
| |
@ref{marginal2abc} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2014-12-13 $B$K(B tk_fd.rr $B$KDI2C$5$l$?(B. |
| |
@end itemize |
| |
|
| |
@comment ------------------- |
| |
@comment tk_fd.ahvec_abc |
| |
@comment ------------------- |
| |
@node tk_fd.ahvec_abc,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{tk_fd.ahvec_abc} |
| |
@findex tk_fd.ahvec_abc |
| |
@table @t |
| |
@item tk_fd.ahvec_abc(@var{A},@var{B},@var{C},@var{Y} | all=1) |
| |
:: abc2marginal(@var{A}, @var{B},@var{C}) $B$r<~JUOB$K$b$D(B (2,m+1) $BJ,3dI=A4BN$K$D$$$F$N@55,2=Dj?t(B Z, $B$*$h$S(B Z $B$NJQ?t(B Y[1][0], ..., Y[1][m] |
| |
(2$BHVL\$N9T(B)$B$K$D$$$F$NJPHyJ,$r7W;;$9$k(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B%j%9%H(B @var{Ans} |
| |
@item A |
| |
$B?t(B |
| |
@item B |
| |
$B?t$N%j%9%H(B. $BD9$5$O(B m. |
| |
@item C |
| |
$B?t(B |
| |
@item Y |
| |
(2,m+1) $BJQ?tCM$r$"$i$o$9%j%9%H$N%j%9%H(B. |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item |
| |
@var{A}, @var{B}, @var{C}, $B$K8=$l$k?t$O@0?t$rM?$($k(B. |
| |
@var{Y} $B$N@.J,$OM-M}?t$rM?$($k(B. |
| |
@item |
| |
@var{Ans}[2]*@var{Ans}[1] $B$,(B Z. |
| |
@var{Ans}[2]*@var{Ans}[0][I] $B$,(B Z $B$N(B Y[1][I] $B$K$D$$$F$NJPHyJ,(B. |
| |
@item |
| |
$BO@J8(B |
| |
1.Y.Goto, Contiguity relations of Lauricella's F_D revisited, arxiv:1412.3256 |
| |
$B$GF3=P$5$l$F$$$k(B |
| |
contiguity relation $B$rMQ$$$F7W;;$9$k(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[2449] marginal2abc([3,12],[6,3,3,3]); |
| |
[-3,[-3,-3,-3],4] |
| |
|
| |
[2450] tk_fd.ahvec_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]); |
| |
[[ 24041/1152 143551/11520 16973/1280 78827/5760 ],1/7776] |
| |
|
| |
[2451] expectation_abc(-3,[-3,-3,-3],4,[[1,1/2,1/3,1/4],[1,1,1,1]]); |
| |
[721230/173593,430653/173593,458271/173593,67566/24799] |
| |
@end example |
| |
|
| |
@table @t |
| |
@item $B;2>H(B |
| |
@ref{expectation_abc} |
| |
@end table |
| |
|
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item |
| |
$B$3$N4X?t$O(B 2014-$B2F$K3+H/$5$l$?(B. |
| |
@end itemize |
| |
|
| |
|
| |
@node pari setbprec setround todouble mpfr_gamma mpfr_floor mpfr_round,,, $B<B83E*;EMM$N4X?t(B |
| |
@subsection @code{pari}, @code{setbprec},@code{setround},@code{todouble},@code{mpfr_gamma},@code{mpfr_floor},@code{mpfr_round}, |
| |
@findex pari |
| |
@findex setbprec |
| |
@findex setround |
| |
@findex todouble |
| |
@findex mpfr_gamma |
| |
@findex mpfr_floor |
| |
@findex mpfr_round |
| |
|
| |
@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 pari(@var{arg1},@var{arg2},...) |
| |
:: 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. |
| |
@itemx setbprec(@var{arg1}) |
| |
@itemx setround(@var{arg1}) |
| |
$B4]$a$NJ}K!$N;XDj(B. mpfr $B=`5r(B. |
| |
@itemx todouble(@var{arg1}) |
| |
:: bigfloat $B7?$r(B double $B$KJQ49$9$k(B. |
| |
@itemx mpfr_gamma(@var{arg1}) |
| |
:: gamma $B4X?t$N7W;;(B. |
| |
@itemx mpfr_floor(@var{arg1}) |
| |
:: floor $B$N7W;;(B. |
| |
@itemx mpfr_round(@var{arg1}) |
| |
:: $B4]$a$N7W;;(B. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
$B8e=R(B. |
| |
@item arg1, arg2 |
| |
$B8e=R(B. |
| |
@end table |
| |
|
| |
@itemize @bullet |
| |
@item 20150807 $B0J9_$N(B asir $B$G$O(B, bigfloat $B$,(B pari $B$G$O$J$/(B mpfr $B$rMQ$$$F7W;;$5$l$k(B. |
| |
Todo, pari $B$O(B ox_pari $B$r8F$S=P$9$,(B, $B$^$@(B ox_pari $B$KL$<BAu$N5!G=$,B?$/$"$k(B. |
| |
$B6h4V1i;;$X$NBP1~$O9T$C$F$$$J$$(B. |
| |
@item |
| |
pari(floor,@var{arg1}), |
| |
pari(round,@var{arg1}), |
| |
pari(gamma,@var{arg1}) |
| |
$B$O(B mpfr $B$G(B pari $B$r(B emulate $B$7$F$$$k$N$G(B, $BF0:n$,0[$J$k(B. |
| |
$BFC$K(B gamma $B$OJ#AG?t$N0z?t$r<u$1<h$i$J$$(B. |
| |
pari $B$N(B floor $B$O7e?t$,B-$j$J$/$J$k$H%(%i!<$G=*N;$7$?$,(B, |
| |
$B$3$N(B floor $B$G$O(B setprec $B$G;XDj$7$?7e?t0JFb$J$i@5$7$/(B floor $B$rLa$9(B. |
| |
Todo, ox_pari $B$r;XDj$7$F8F$S=P$9J}K!(B. |
| |
@end itemize |
| |
|
| |
@example |
| |
[219] ctrl("bigfloat",1)$ |
| |
[220] setprec(100)$ |
| |
[221] pari(floor,1111111111111.1+1/10); |
| |
1111111111111 |
| |
@end example |
| |
|
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@table @t |
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@item $B;2>H(B |
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@ref{pari} |
| |
@end table |
| |
|
| |
@comment --- ChangeLog $B$r=q$/(B. $BF05!(B. $B%=!<%9%3!<%I$N0LCV(B. $BJQ99F|;~(B $B$J$I(B CVS$B%5!<%P$r8+$k$?$a(B |
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@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit. |
| |
@noindent |
| |
ChangeLog |
| |
@itemize @bullet |
| |
@item $B$3$l$i$NBgJQ99$O(B 2015-08-03 $B$h$j(B 08-07 $B$N(B asir $B9g=I$G$*$3$J$o$l$?(B. |
| |
$B$^$@:n6HCf(B. Todo, asirgui $B$X$NBP1~(B. debug, ... |
| |
@item $BJQ99$r$&$1$?%=!<%9%3!<%I$O(B asir2000/builtin/bfaux.c, |
| |
asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB??t(B. |
| |
@end itemize |
| |
|
| @comment **************************************************************** |
@comment **************************************************************** |
| @comment --- $B"~"~"~"~(B $B0J2<B>$N4X?t$K$D$$$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$$4X?t$N@bL@$r=q$/$?$a$N%F%s%W%l!<%H$G$"$k(B. $B>C$9$J(B. |
| @comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
@comment --- $B"~"~"~"~(B $B4X?t(B syz_pqr, xyz_stu $B$N@bL@(B $B"~"~"~"~(B |
| @comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
@comment --- $BJ#?t$N4X?t$r$^$H$a$F@bL@$9$kNc(B --- |
| @node xyz_pqr,,, $B<B83E*;EMM$N4X?t(B |
@node xyz_pqr syz_stu,,, $B<B83E*;EMM$N4X?t(B |
| |
@comment @menu $B$K$b(B * syz_pqr syz_stu:: $B$HB3$1$F=q$/;v(B. $BJ,$1$F$O$$$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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