===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/exp/exp-ja.texi,v
retrieving revision 1.50
retrieving revision 1.57
diff -u -p -r1.50 -r1.57
--- OpenXM/src/asir-doc/exp/exp-ja.texi	2015/08/08 06:28:38	1.50
+++ OpenXM/src/asir-doc/exp/exp-ja.texi	2018/10/17 00:33:49	1.57
@@ -1,5 +1,5 @@
-%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.49 2014/12/14 01:06:44 takayama Exp $
-\input texinfo
+%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.56 2018/03/28 07:44:06 takayama Exp $
+\input texinfo-ja
 @iftex
 @catcode`@#=6
 @def@fref#1{@xrefX[#1,,@code{#1},,,]}
@@ -38,13 +38,13 @@
 @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
 Copyright @copyright{} Risa/Asir committers
-2004--2010. All rights reserved.
+2004--2018. All rights reserved.
 @end titlepage
 
 @comment --- $B$*$^$8$J$$(B ---
@@ -83,63 +83,58 @@ 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::
-* quotetotex_env::
-* objtoquote::
+* asir-port.sh asir-install.sh::
+* asirgui.hnd::
+* chdir pwd::
 * copyright::
-* string_to_tb::
-* tb_to_string::
-* write_to_tb::
+* dcurrenttime::
 * 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::
-* mapat::
-* set_print_function::
-* small_jacobi::
+* eval_quote::
+* f_res::
+* fj_simplify.simplify::
 * flatten_quote::
-* printf::
-* fprintf::
-* sprintf::
-* quote_to_funargs::
-* funargs_to_quote::
-* get_function_name::
-* remove_paren::
-* set_secure_mode::
-* set_secure_flag::
+* function::
+* get_struct_name get_element_names get_element_at put_element_at::
+* getpid::
 * 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::
-* qt_is_var::
-* qt_is_ceof::
-* qt_rewrite::
-* asirgui.hnd::
-* noro_matrix.rr:
-* f_res::
-* chdir::
-* pwd::
-* dcurrenttime::
-* nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (module)::
-* nd_gr nd_gr_trace nd_weyl_gr nd_weyl_gr_trace (option)::
-* tk_pfn.rkn::
+* quote_to_funargs funargs_to_quote remove_paren get_function_name::
+* quotetotex quotetotex_env::
+* set_print_function::
+* set_secure_flag set_secure_mode::
+* small_jacobi::
+* string_to_tb tb_to_string write_to_tb::
+* tk_fd.abc2ahg::
+* tk_fd.ahvec_abc::
+* tk_hgpoly.hgpoly::
+* tk_hgpoly.optip::
+* tk_jack.zonal::
 * 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
@@ -401,11 +396,12 @@ ChangeLog
 @end itemize
 
 
-@node quote_to_funargs,,, $B%/%*!<%H(B
-@subsection @code{quote_to_funargs}, @code{funargs_to_quote}, @code{remove_paren}
+@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}, @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})
@@ -523,7 +519,7 @@ 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
 
@@ -1014,7 +1010,7 @@ 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
@@ -1328,8 +1324,10 @@ 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
@@ -1893,7 +1891,7 @@ 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
@@ -2002,7 +2000,7 @@ 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
@@ -2216,7 +2214,7 @@ 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
@@ -2439,7 +2437,7 @@ 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
@@ -2595,6 +2593,46 @@ 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));
+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
 @section $B?tO@!&Be?t(B
 
@@ -2729,7 +2767,8 @@ 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 ---
@@ -2746,28 +2785,29 @@ 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$$!#(B
-($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
+@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(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)
 @item
-$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
-$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
-x,y $B$K$D$$$F@)8B$r9T$&!#(B
+$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B. 
+$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, 
+x,y $B$K$D$$$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
-@tex
-$x$
-@end tex
+$B$H$*$$$?;~(B, D $B2C72(B 
+@tex $M = D / I$ @end tex
+$B$N(B 
+@tex $x$ @end tex
 @end iftex
 @ifinfo
-I = D . @{ x dx -1, y dy - 1 @} $B$N(B x
+I = D . @{ x dx -1, y dy - 1 @} $B$H$*$$$?;~(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$G$"$k(B.
 @example
 [1432] nk_restriction.restriction([x*dx-1,y*dy-1],[x,y],[dx,dy],[1,0]);
 -- generic_bfct_and_gr :0.001sec(0.001629sec)
@@ -2777,8 +2817,22 @@ B_@{S0@} length : 2
 -- fctr(BF) + base :0.000999sec(0.0005109sec)
 [[y*dy-1,(y*dy-1)*dx,-1],[[1],[0]]]
 @end example
+$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
@@ -2787,7 +2841,7 @@ 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 ---
@@ -2804,23 +2858,19 @@ 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$$!#(B
-($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
+@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(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)
 @item
-$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&!#(B
-$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
-x,y $B$K$D$$$F@)8B$r9T$&!#(B
+$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@)8B$r9T$&(B. 
+$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, 
+x,y $B$K$D$$$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
+@tex $I = D \cdot \{x \partial_x -1, y \partial_y - 1\} $ @end tex
 $B$N(B
-@tex
-$x$
-@end tex
+@tex $x$ @end tex
 @end iftex
 @ifinfo
 I = D . @{ x dx -1, y dy - 1 @} $B$N(B x
@@ -2845,7 +2895,7 @@ 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 ---
@@ -2865,28 +2915,27 @@ 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$$!#(B
-($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
+@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(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)
 @item
-$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
-$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
-x,y $B$K$D$$$F@QJ,$r9T$&!#(B
+$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B. 
+$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, 
+x,y $B$K$D$$$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
-$t$
-@end tex
+@tex $I = D \cdot \{2 t \partial_x + \partial_t, t \partial_t + 2 x \partial_x + 2\}$ @end tex
+$B$H$*$$$?;~(B, D $B2C72(B 
+@tex $M = D / I$ @end tex 
+$B$N(B 
+@tex $t$ @end tex
 @end iftex
 @ifinfo
-I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} $B$N(B t
+I = D . @{2 t dx + dt, t dt + 2 x dx + 2 @} 
+$B$H$*$$$?;~(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$G$"$k(B. ([SST, Ex5.5.2, Ex5.5.6])
 @example
 [1351] nk_restriction.integration([2*t*dx+dt,2*x*dx+t*dt+2],[t,x],
 [dt,dx],[1,0]);
@@ -2897,6 +2946,25 @@ B_@{S0@} length : 2
 -- fctr(BF) + base :0.001sec(0.0006731sec)
 [[4*x*dx^2+6*dx,-4*t*x*dx^2-6*t*dx,2*x*dx+1,-2*t*x*dx,2*t*dx],[[1],[0]]]
 @end example
+$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}
@@ -2906,7 +2974,7 @@ 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 ---
@@ -2926,28 +2994,26 @@ 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$$!#(B
-($B$9$J$o$A!"(B@code{[1,1,0,0,0]} $B$O(B OK $B$@$,!"(B @code{[1,0,1,0,0]} $B$O%@%a(B)
+@var{W} $B$NMWAG$OHsIi@0?t$G(B, 0 $BHVL\$NMWAG$+$iO"B3$7$F@5$N@0?t$,F~$i$J$1$l$P$J$i$J$$(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)
 @item
-$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&!#(B
-$BNc$($P!"(B@var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B
-x,y $B$K$D$$$F@QJ,$r9T$&!#(B
+$B@5$N=E$_$r;}$DJQ?t$K$D$$$F$N@QJ,$r9T$&(B. 
+$BNc$($P(B, @var{VL} @code{=[x,y,z]}, @var{W} @code{=[1,1,0]} $B$G$"$l$P(B, 
+x,y $B$K$D$$$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
-$t$
-@end tex
+@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]);
@@ -2958,7 +3024,6 @@ 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
@@ -3103,7 +3168,7 @@ $J$
 $B$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 @}
@@ -3120,7 +3185,7 @@ 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]]]
@@ -3240,7 +3305,7 @@ 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]
@@ -3295,7 +3360,7 @@ $ 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.
@@ -3311,13 +3376,160 @@ 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$G$"$k(B. 
+@example
+[2691] nk_restriction.module_restriction([[dx,dy],[dy,dx],[x,y]], [x,y], [dx,dy], [1,0]);
+....
+bfunction : 
+s
+[[1,1],[s,1]]
+integer roots :
+[0,0]
+Generators: 
+[e1,e2]
+Relations: 
+[-8*e2*dy,4*e2*dy^2,-4*e2*dy^3,4*e1*y*dy-4*e1,-4*e1*dy^2,-4*e2,-e2*y*dy^2+2*e2*dy,-e1*y*dy+e1,e1*y*dy-e1]
+[[0,-1],[-dy^2,0],[y*dy-1,0]]
+@end example
+$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
 ChangeLog
 @itemize @bullet
@@ -3326,6 +3538,7 @@ 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
@@ -3426,7 +3639,7 @@ 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 ],
@@ -3439,7 +3652,7 @@ 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
@@ -3494,11 +3707,11 @@ 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
 
@@ -3564,14 +3777,14 @@ ChangeLog
 
 
 
-@node fj_simp.simplify,,, $B<B83E*;EMM$N4X?t(B
-@subsection @code{fj_simp.simplify}
-@findex fj_simp.simplify
+@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_simp.simplify(@var{arg1})
+@item fj_simplify.simplify(@var{arg1})
 :: arg1 $B$r4JC12=$9$k(B.
 @end table
 
@@ -3583,8 +3796,6 @@ 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,
@@ -3598,14 +3809,14 @@ B.F.Caviness, R.J.Fateman, Simplification of Radical E
 @end itemize
 
 @example
-load("fj_simplify.rr");
-[1434] simplify((x^(1/2))^3);
+import("fj_simplify.rr");
+[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);
 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
 
@@ -3618,9 +3829,6 @@ 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. 
@@ -4053,7 +4261,7 @@ 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
@@ -4131,7 +4339,8 @@ 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