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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.50 and 1.58

version 1.50, 2015/08/08 06:28:38

version 1.58, 2020/09/06 03:26:47

Line 1

%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.49 2014/12/14 01:06:44 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

@catcode`@#=6

@def@fref#1{@xrefX[#1,,@code{#1},,,]}

@def@b#1{{@bf@gt #1}}

@def@b#1{{@bf #1}}

@catcode`@#=@other

@end iftex

@overfullrule=0pt

Line 12

@comment --- $B$*$^$8$J$$=*$j(B ---

@comment --- GNU info $B%U%!%$%k$NL>A0(B ---

@setfilename xyzman

@setfilename exp

@documentlanguage ja

@comment --- $B%?%$%H%k(B ---

@settitle $B<B83E*;EMM$N4X?t(B

Line 38

Line 39

@title $B<B83E*;EMM$N4X?t(B

@subtitle Risa/Asir $B<B83E*;EMM4X?t@bL@=q(B

@subtitle 1.0 $BHG(B

@subtitle 2014 $BG/(B 12 $B7n(B

@subtitle 2018 $BG/(B 3 $B7n(B

@author by Risa/Asir committers

@page

@vskip 0pt plus 1filll

@end titlepage

@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 --- subsection xyz_pqr xyz_stu $B$,$"$k(B.

@menu

* quotetotex::

* asir-port.sh asir-install.sh::

* quotetotex_env::

* asirgui.hnd::

* objtoquote::

* chdir pwd::

* copyright::

* string_to_tb::

* dcurrenttime::

* tb_to_string::

* write_to_tb::

* 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_order::

* dp_weyl_gr_main::

* list::

* eval_quote::

* mapat::

* f_res::

* set_print_function::

* fj_simplify.simplify::

* small_jacobi::

* 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::

* 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_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_rewrite::

* qt_set_coef::

* qt_set_ord::

* 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.rkn::

* tk_rk.runge_kutta_4::

* tk_rk.runge_kutta_4_linear::

* tk_rk.zonal::

* getpid::

@end menu

@node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B

Line 401 ChangeLog

Line 397 ChangeLog

@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 funargs_to_quote

@findex remove_paren

@findex get_function_name

@table @t

@item quote_to_funargs(@var{q})

Line 523 ChangeLog

Line 520 ChangeLog

@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

$B$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.

@end itemize

Line 1014 ChangeLog

Line 1011 ChangeLog

@end itemize

@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}

@findex qt_is_var

@findex qt_is_coef

Line 1328 ChangeLog

Line 1325 ChangeLog

@end itemize

@node sprintf,,, $BJ8;zNs=hM}(B

@node printf fprintf sprintf,,, $BJ8;zNs=hM}(B

@subsection @code{printf}, @code{fprintf}, @code{sprintf}

@findex printf

@findex fprintf

@findex sprintf

@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 --- $BJ#?t$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}

@findex asir-port.sh

@findex asir-install.sh

Line 2002 ChangeLog

Line 2001 ChangeLog

@comment ****************************************************************

@node chdir,,, $B%7%9%F%`(B

@node chdir pwd,,, $B%7%9%F%`(B

@subsection @code{chdir}, @code{pwd}

@findex chdir

@findex pwd

Line 2216 ChangeLog

Line 2215 ChangeLog

@node $B8@8l(B,,, $B<B83E*;EMM$N4X?t(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}

@findex get_struct_name

@findex get_element_names

Line 2439 ChangeLog

Line 2438 ChangeLog

@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}

@findex set_secure_flag

@findex set_secure_mode

Line 2595 ChangeLog

Line 2594 ChangeLog

@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));

[1919] deg(diff(F,y),f@{0,1@}(x,y));

@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

@section $B?tO@!&Be?t(B

Line 2729 ChangeLog

Line 2768 ChangeLog

@comment --- $B4X?t$N4JC1$J@bL@(B ---

@table @t

@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

@comment --- $B0z?t$N4JC1$J@bL@(B ---

Line 2746 ChangeLog

Line 2786 ChangeLog

@itemize @bullet

@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

$B@5$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

$B0J2<$O!"%$%G%"%k(B

$B0J2<$O(B, $B%$%G%"%k(B

@iftex

@tex

$I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $

@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

@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

$B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k!#(B

$B$K$D$$$F$N@)8B2C72$r7W;;$7$?Nc$G$"$k(B.

@example

[1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);

-- 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)

[[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]

@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

@subsection @code{nk_restriction.restriction_ideal}

@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 ---

@table @t

@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

@comment --- $B0z?t$N4JC1$J@bL@(B ---

Line 2804 B_@{S0@} length : 2

Line 2859 B_@{S0@} length : 2

@itemize @bullet

@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

$B@5$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

$B0J2<$O!"%$%G%"%k(B

$B0J2<$O(B, $B%$%G%"%k(B

@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

@tex

@tex $x$ @end tex

$x$

@end tex

@end iftex

@ifinfo

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 ---

@table @t

@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

@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 ---

@itemize @bullet

@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

$B@5$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

$B0J2<$O!"%$%G%"%k(B

$B0J2<$O(B, $B%$%G%"%k(B

@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

@tex

@tex $t$ @end tex

$t$

@end tex

@end iftex

@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

$B$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

[1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],

[dt,dx],[1,0]);

Line 2897 B_@{S0@} length : 2

Line 2947 B_@{S0@} length : 2

-- 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]]]

@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

@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 ---

@table @t

@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

@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 ---

@itemize @bullet

@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

$B@5$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

$B0J2<$O!"%$%G%"%k(B

$B0J2<$O(B, $B%$%G%"%k(B

@iftex

@tex

$I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\} $

@end tex

$B$N(B

@tex

@tex $t$ @end tex

$t$

@end tex

@end iftex

@ifinfo

I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t

@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

[1431] nk_restriction.integration_ideal([2*t*dx+dt,t*dt+2*x*dx+2],[t,x],

[dt,dx],[1,0]);

Line 2958 B_@{S0@} length : 2

Line 3025 B_@{S0@} length : 2

-- fctr(BF) + base :0.001sec(0.001091sec)

-- integration_ideal_internal :0.002sec(0.001879sec)

[2*x*dx+1]

[1432]

@end example

@node nk_restriction.ann_mul,,, D $B2C72$N@)8B$K4X$9$k4X?t(B

Line 3103 $J$

Line 3169 $J$

$B$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}

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 @}

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 : [[-1,1],[s,1],[s-a+c-1,1]]

S0 : 0

B_{S0} length : 1

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]]]

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 : [[1,1],[s,1],[s-2,1]]

S0 : 2

B_{S0} length : 3

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]

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.

@end iftex

@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

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.

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 : [[1,1],[s,1]]

S0 : 0

B_{S0} length : 1

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 :

[[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 :

[[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

ChangeLog

@itemize @bullet

Line 3326 ChangeLog

Line 3539 ChangeLog

@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

@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();

$B$3$3$G(B testgraph1() $B$O0J2<$N$H$*$j(B.

def testgraph1() {

def testgraph1() @{

/* tk_bess2.bess2pf(1/2); */

Pf= [[[ 0, (1)/(x), 0 ],

[ -x, (2*x^2+1)/(x), -2*x ],

Line 3439 def testgraph1() {

Line 3653 def testgraph1() {

Dom=[[0.5,1.5],[1.5,9]];

Step = 0.5;

return tk_pfn.graph(Pf,Dom,Iv,Step | fit=1);

}

@end example

Line 3494 ChangeLog

Line 3708 ChangeLog

$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() {

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

Line 3564 ChangeLog

Line 3778 ChangeLog

@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 --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---

@table @t

@item fj_simp.simplify(@var{arg1})

@item fj_simplify.simplify(@var{arg1})

:: arg1 $B$r4JC12=$9$k(B.

@end table

Line 3583 ChangeLog

Line 3797 ChangeLog

@end table

@itemize @bullet

@item

$B8=:_$N%P!<%8%g%s$G$O(B fj_simp.simplify $B$G$J$/(B, $BC1$K(B simplify $B$H$h$V(B.

@item

$B$3$N4X?t$O(B

Joel S. Cohen, Computer Algebra and Symbolic Computation,

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

@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))

[1435] simplify((2^(1/2))^2);

[1435] fj_simplify.simplify((2^(1/2))^2);

[1436] simplify((2+2^(1/2))^3);

[1436] fj_simplify.simplify((2+2^(1/2))^3);

14*((2)^(1/2))+20

[1437] simplify(exp(x)*exp(-x+y));

[1437] fj_simplify.simplify(exp(x)*exp(-x+y));

((@@e)^(y))

@end example

Line 3618 load("fj_simplify.rr");

Line 3830 load("fj_simplify.rr");

ChangeLog

@itemize @bullet

@item

$B>-MhE*$K$O(B module $B2=$7$F(B fj_simp module $B$K4^$a$kM=Dj(B.

poly_simplify $B$+$i(B fj_simp.simplify $B$r8F$V(B.

@item

Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification $B$N5!G=(B.

@item

$B$3$N4X?t$O(B 2010.01 $B$K(B M.Fujimoto $B$K$h$j:G=i$NHG$,=q$+$l$?(B.

Line 4053 ChangeLog

Line 4262 ChangeLog

@end itemize

@node pari,,, $B<B83E*;EMM$N4X?t(B

@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

Line 4131 asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB?

Line 4340 asir2000/engine/bf.c, asir2000/builtin/parif.c $BEyB?

@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 --- $BJ#?t$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}

@findex xyz_pqr

@findex xyz_stu

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