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Diff for /OpenXM/src/asir-doc/exp/exp-ja.texi between version 1.41 and 1.46

version 1.41, 2010/09/29 00:33:23 version 1.46, 2012/09/18 11:41:18
Line 1 
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 %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.40 2010/09/28 07:24:34 takayama Exp $  %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.45 2012/02/26 01:25:30 takayama Exp $
 \input texinfo  \input texinfo
 @iftex  @iftex
 @catcode`@#=6  @catcode`@#=6
Line 38 
Line 38 
 @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 2010 $BG/(B 9 $B7n(B  @subtitle 2012 $BG/(B 9 $B7n(B
   
 @author  by Risa/Asir committers  @author  by Risa/Asir committers
 @page  @page
Line 138  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
Line 138  ChangeLog $B$N9`L\$O(B www.openxm.org $B$N(B cvswe
 * tk_pfn.graph::  * tk_pfn.graph::
 * 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::
 @end menu  @end menu
   
 @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B  @node $B%/%*!<%H(B,,, $B<B83E*;EMM$N4X?t(B
Line 1838  builtin/dp.c 1.49
Line 1839  builtin/dp.c 1.49
 @table @var  @table @var
 @item gentrace  @item gentrace
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B%0%l%V%J!<4pDl$N7W;;7P2a>pJs$r=PNO$9$k(B.
 @item gentsyz  @item gensyz
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B7W;;$5$l$?%0%l%V%J!<4pDl$KBP$9$k(B syzygy $B$N@8@.7O$r=PNO$9$k(B.
 @item nora  @item nora
 @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.  @var{value} $B$,(B 0 $B$G$J$$$H$-(B, $B:G=*%9%F%C%W$GAj8_4JLs$r9T$o$J$$(B.
Line 2844  B_@{S0@} length : 2
Line 2845  B_@{S0@} length : 2
 [1432]  [1432]
 @end example  @end example
   
 @node nk_restriction,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option)  @node nk_restriction.ann_mul,,, D $B2C72$N@)8B$K4X$9$k4X?t(B
   @subsection @code{nk_restriction.ann_mul}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ann_mul
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.ann_mul(@var{I}, @var{J}, @var{VL}, @var{DVL})
   :: @var{f} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k(B @var{I},
   @var{g} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$r(B @var{J} $B$H$7$?$H$-(B,
   @var{fg} $B$rNm2=$9$k%[%m%N%_%C%/(B D $B%$%G%"%k$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item I
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item J
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item test_ann_mul(), test_ann_mul2(), test_ann_mul3() $B$r;2>H(B.
   @end itemize
   
   
   @node nk_restriction (option) ,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option)
 @subsection @code{nk_restriction (option)}  @subsection @code{nk_restriction (option)}
 @comment --- $B:w0zMQ%-!<%o!<%I(B  @comment --- $B:w0zMQ%-!<%o!<%I(B
 @findex nk_restriction (option)  @findex nk_restriction (option)
Line 2989  $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
Line 3023  $\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \}
 $B$G$"$k$3$H$r0UL#$9$k(B.  $B$G$"$k$3$H$r0UL#$9$k(B.
 @end ifinfo  @end ifinfo
   
 @node nk_restriction,,, D $B2C72$N@QJ,%$%G%"%k$NHs@F<!ItJ,$K4X$9$k4X?t(B  @node nk_restriction.trans_inhomo,,, D $B2C72$N@QJ,%$%G%"%k$NHs@F<!ItJ,$K4X$9$k4X?t(B
 @subsection @code{nk_restriction.trans_inhomo}  @subsection @code{nk_restriction.trans_inhomo}
 @comment --- $B:w0zMQ%-!<%o!<%I(B  @comment --- $B:w0zMQ%-!<%o!<%I(B
 @findex trans_inhomo  @findex nk_restriction.trans_inhomo
   
 @comment --- $B4X?t$N4JC1$J@bL@(B ---  @comment --- $B4X?t$N4JC1$J@bL@(B ---
 @table @t  @table @t
Line 3024  nk_restriction.restriction_ideal( ... |inhomo=1); $B$
Line 3058  nk_restriction.restriction_ideal( ... |inhomo=1); $B$
 @item $B$b$7(B, @var{P} $B$,(B @var{INT[0]} $B$G@8@.$5$l$k@QJ,(B, $B@)8B%$%G%"%k$N85$G$J$$>l9g$O%(%i!<%a%C%;!<%8$,I=<($5$l$k(B.  @item $B$b$7(B, @var{P} $B$,(B @var{INT[0]} $B$G@8@.$5$l$k@QJ,(B, $B@)8B%$%G%"%k$N85$G$J$$>l9g$O%(%i!<%a%C%;!<%8$,I=<($5$l$k(B.
 @end itemize  @end itemize
   
   @node nk_restriction.ost_integration_ideal,,, D $B2C72$N@QJ,%$%G%"%k(B
   @subsection @code{nk_restriction.ost_integration_ideal}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ost_integration_ideal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   $B@QJ,NN0h$,6h4V$ND>@Q$G$"$k$h$&$J@QJ,$NK~$?$9(B
   $B%[%m%N%_%C%/@F<!HyJ,J}Dx<07O$rJV$9(B (Oaku-Shiraki-Takayama, 2003).
   @table @t
   @item nk_restriction.ost_integration_ideal(@var{Id}, @var{VL}, @var{DVL}, @var{W}, @var{LB}, @var{UB})
   :: Heaviside $B4X?t$H$N@Q$NK~$?$9HyJ,J}Dx<07O$N7W;;$K%7%g!<%H%+%C%HK!$rMQ$$$k(B.
   @item nk_restriction.ost_integration_ideal2(@var{Id}, @var{VL}, @var{DVL}, @var{W}, @var{LB}, @var{UB})
   :: Heaviside $B4X?t$H$N@Q$NK~$?$9HyJ,J}Dx<07O$N7W;;$K@)8B%$%G%"%k$rMQ$$$k(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$kHyJ,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @item LB
   $B@QJ,6h4V$N2<C<$rI=$9%j%9%H(B
   @item UB
   $B@QJ,6h4V$N>eC<$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item $B2<C<(B, $B>eC<$KL58BBg$r;XDj$9$k$H$-$O(B, $BJ8;zNs(B  "inf", "+inf", "-inf" $B$rMQ$$$k(B.
   @end itemize
   
   $B0J2<$O(B, Oaku-Shiraki-Takayama (2003) $B$NNc(B5.1$B$r7W;;$7$?$b$N$G$"$k(B.
   @iftex
   @tex
   $ \int_0^\infty \exp((-t^3+t)x) dt $
   @end tex
   $B$NHo@QJ,4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   @tex
   $ I = \langle \partial_t +(3t^2-1)x, \partial_x+t^3-t \rangle $
   @end tex
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end iftex
   @ifinfo
   \int_0^$B!g(B exp((-t^3+t)x) dt
   $B$NHs@QJ,4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   I = < dt +(3t^2-1)x, dx+t^3-t >
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end ifinfo
   @example
   [1871] Id=[dt+(3*t^2-1)*x, dx+t^3-t]$
   [1872] VL=[t,x]$
   [1873] DVL=[dt,dx]$
   [1874] W=[1,0]$
   [1875] nk_restriction.ost_integration_ideal(Id,VL,DVL,W,[0],["inf"]);
   -- nd_weyl_gr :0.008sec(0.006768sec)
   -- weyl_minipoly :0.004001sec(0.003029sec)
   -- generic_bfct_and_gr :0.012sec(0.0129sec)
   generic bfct : [[1,1],[s,1],[s-2,1]]
   S0 : 2
   B_{S0} length : 3
   -- fctr(BF) + base :0.008sec(0.007395sec)
   -- integration_ideal_internal :0.012sec + gc : 0.016sec(0.04311sec)
   [-27*x^3*dx^3-54*x^2*dx^2+(4*x^3+3*x)*dx+4*x^2-3,27*x^2*dx^4+135*x*dx^3+(-4*x^2+105)*dx^2-16*x*dx-8]
   
   
   [1876] nk_restriction.ost_integration_ideal2(Id,VL,DVL,W,[0],["inf"]);
   ($BN,(B)
   [27*x^3*dx^3+54*x^2*dx^2+(-4*x^3-3*x)*dx-4*x^2+3,-27*x^2*dx^4-135*x*dx^3+(4*x^2-105)*dx^2+16*x*dx+8]
   @end example
   $B$3$N=PNO$O(B, $B@QJ,$rNm2=$9$k%[%m%N%_%C%/7O$G$"$k(B.
   
   @node nk_restriction.ost_sum,,, D $B2C72$N@QJ,%$%G%"%k(B
   @subsection @code{nk_restriction.ost_sum}
   @comment --- $B:w0zMQ%-!<%o!<%I(B
   @findex nk_restriction.ost_sum
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @table @t
   @item nk_restriction.ost_sum(@var{Id}, @var{VL}, @var{DVL}, @var{W})
   :: $BOB$NK~$?$9(B($B@F<!(B/$BHs@F<!(B)$B:9J,J}Dx<07O$rJV$9(B.
   @end table
   
   @comment --- $B0z?t$N4JC1$J@bL@(B ---
   @table @var
   @item Id
   $B%$%G%"%k$N@8@.85$N%j%9%H(B
   @item VL
   $BJQ?t$N%j%9%H(B
   @item DVL
   $BJQ?t$N%j%9%H(B(@var{VL} $B$KBP1~$9$k:9J,:nMQAG$NJ}$NJQ?t(B)
   @item W
   $B=E$_%Y%/%H%k$rI=$9%j%9%H(B
   @end table
   
   @comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B ---
   @comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B ---
   @comment --- @bullet $B$O9uE@IU$-(B ---
   @itemize @bullet
   @item Oaku-Shiraki-Takayama (2003) $B$NBh(B6$B@a$N%"%k%4%j%:%`$N<BAu(B.
   @item $B%*%W%7%g%s(B inhomo $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$rM?$($k>pJs$bJV$9(B.
   @end itemize
   
   $B0J2<$O(B, Oaku-Shiraki-Takayama (2003) $B$NNc(B6.5$B$NHs@F<!ItJ,$^$G7W;;$7$?$b$N$G$"$k(B.
   @iftex
   @tex
   $ \sum_{k=a}^b {n \choose k} $
   @end tex
   $B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   @tex
   $ I = \langle (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) \rangle $
   @end tex
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end iftex
   @ifinfo
   \sum_{k=a}^b n_C_k
   $B$NHsOB4X?t$NK~$?$9%[%m%N%_%C%/%$%G%"%k$O(B
   I = < (n-k+1)E_n-(n+1), (k+1)E_k-(n-k) >
   $B$G$"$k$+$i(B, $B$3$l$rF~NO$H$7$F<!$N$h$&$K7W;;$r9T$&(B.
   @end ifinfo
   @example
   [1871] Id=[(n-k+1)*en-(n+1), (k+1)*ek-(n-k)]$
   [1872] VL=[k,n]$
   [1873] DVL=[ek,en]$
   [1874] W=[1,0]$
   [1875] nk_restriction.ost_sum(Id,VL,DVL,W|inhomo=1);
   -- nd_weyl_gr :0.006667sec(0.004057sec)
   -- weyl_minipoly :0sec(0.001163sec)
   -- generic_bfct_and_gr :0.01sec(0.007085sec)
   generic bfct : [[1,1],[s,1]]
   S0 : 0
   B_{S0} length : 1
   -- fctr(BF) + base :0.003333sec(0.001785sec)
   -- restriction_ideal_internal :0sec(0.002336sec)
   [[(en-2)*n+en-2],[[[[ek-1,[(-en+1)*n-en+1,1]]],1]]]
   @end example
   
   
 @noindent  @noindent
 ChangeLog  ChangeLog
 @itemize @bullet  @itemize @bullet
Line 3031  ChangeLog
Line 3209  ChangeLog
 @item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B. 1.7--1.9 $B$r8+$h(B.  @item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B. 1.7--1.9 $B$r8+$h(B.
 @item 2010-05 $B$+$i(B 2010-07 $B$K$+$1$F(B 2 $B$D$N(B option (@code{ht}, @code{ord}) $B$H(B  @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.
 @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 3330  Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification
Line 3509  Todo: exp $B0J30$NFC<l4X?t$K$D$$$F$N(Bsimplification
 @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.
 OpenXM/src/asir-contrib/packages/src/fj_simplify.rr  OpenXM/src/asir-contrib/packages/src/fj_simplify.rr
   @end itemize
   
   @node tk_jack.zonal,,, $B<B83E*;EMM$N4X?t(B
   @subsection @code{tk_jack.zonal}
   @findex tk_jack.zonal
   
   @comment --- $B4X?t$N4JC1$J@bL@(B ---
   @comment --- @itemx $B$OJ#?t$KBP$7$F@bL@$r0l$D$D$1$k>l9g$K;H$&(B ---
   @table @t
   @item tk_jack.zonel(@var{p},@var{n})
   :: $BJ,3d(B p $B$KBP$9$k(B n $BJQ?t$N(B zonal $BB?9`<0$r=PNO$9$k(B.
   @end table
   
   @table @var
   @item return
   $BB?9`<0(B. x_1, x_2, ... $B$,JQ?t(B.
   @item p
   $B?t$N%j%9%H(B. p=[p0,p1,...] $B$N;~(B p0>=p1>=...>0.
   @item n
   $B<+A3?t(B
   @end table
   
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B
   Koev-Edelman $B$K$h$k(B Pieri $B7?8x<0$rMQ$$$?(B Jack symmetric function $B$N7W;;(B
   $B%"%k%4%j%:%`$N<BAu$G$"$k(B.
   $B>\$7$/$O(B Wikipedia $B1Q8lHG(B Jack symmetric function $B$N9`$r;2>H(B.
   @item zonal(P,N) = jack(P,N,2) $B$G$"$k(B.
   @end itemize
   
   @example
   load("tk_jack.rr");
   [1434] tk_jack.zonal([3,2,1],3);
   (112*x_3*x_2^2+112*x_3^2*x_2)*x_1^3+(112*x_3*x_2^3+168*x_3^2*x_2^2+112*x_3^3*x_2)*x_1^2+(112*x_3^2*x_2^3+112*x_3^3*x_2^2)*x_1
   [1435] tk_jack.zonal([1,1],3);
   (2*x_2+2*x_3)*x_1+2*x_3*x_2
   [1436]  tk_jack.jack([1,1],3,2);
   (2*x_2+2*x_3)*x_1+2*x_3*x_2
   @end example
   
   @table @t
   @item $B;2>H(B
   @end table
   
   @noindent
   ChangeLog
   @itemize @bullet
   @item
   $B$3$N4X?t$O(B wishart $BJ,I[$K=>$&BP>N9TNs$NBh0l8GM-CM$,(B x $B0J2<$G$"$k3NN($N7W;;$r(B
   holonomic gradient method $B$G$d$k$?$a$K$=$N=i4|CM$r7W;;$9$k(B C $B$N%W%m%0%i%`$,(B
   $BI,MW$G$"$C$?(B. $B$=$l$r(B debug $B$9$k$?$a$K$H$j$"$($:=q$$$?$b$N(B.
   @item $B:GE,2=$r$^$@$^$@$5$\$C$F$k(B.
 @end itemize  @end itemize
   
 @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.  @comment -----------  $B0J2<$O8+K\(B. $B>C$9$J(B.
Legend:
Removed from v.1.41  
changed lines
  Added in v.1.46
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