| version 1.35, 2009/12/09 04:58:29 |
version 1.36, 2010/02/05 07:45:48 |
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| %% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.34 2009/05/16 04:56:32 ohara Exp $ |
%% $OpenXM: OpenXM/src/asir-doc/exp/exp-ja.texi,v 1.35 2009/12/09 04:58:29 takayama Exp $ |
| \input texinfo |
\input texinfo |
| @iftex |
@iftex |
| @catcode`@#=6 |
@catcode`@#=6 |
| Line 2837 B_@{S0@} length : 2 |
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| Line 2837 B_@{S0@} length : 2 |
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| [1432] |
[1432] |
| @end example |
@end example |
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@node nk_restriction,,, D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N@bL@(B (option) |
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@subsection @code{nk_restriction (option)} |
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@comment --- $B:w0zMQ%-!<%o!<%I(B |
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@findex nk_restriction (option) |
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|
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@comment --- $B4X?t$N4JC1$J@bL@(B --- |
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@table @t |
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@item nk_restriction.restriction(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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@item nk_restriction.restriction_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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@item nk_restriction.integration(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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@item nk_restriction.integration_ideal(... | inhomo=@var{n}, param=@var{p}, s0=@var{m}) |
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:: D $B2C72$N@)8B(B, $B@QJ,$K4X$9$k4X?t$N%*%W%7%g%s$N@bL@(B |
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@end table |
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|
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@comment --- $B0z?t$N4JC1$J@bL@(B --- |
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@table @var |
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@item @var{n} |
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0 $B$^$?$O(B 1 |
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@item @var{p} |
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$B%j%9%H(B ($B78?tBN$KB0$9$kJQ?t$N%j%9%H(B) |
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@item @var{m} |
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$B@0?t(B |
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@end table |
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|
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@comment --- $B$3$3$G4X?t$N>\$7$$@bL@(B --- |
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@comment --- @itemize$B!A(B@end itemize $B$O2U>r=q$-(B --- |
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@comment --- @bullet $B$O9uE@IU$-(B --- |
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@itemize @bullet |
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@item @var{n} $B$,(B 0 $B$G$J$$$H$-(B, $BHs@F<!ItJ,$N7W;;$r9T$&(B. |
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|
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restriction_ideal (integration_ideal) $B$K4X$7$F$O(B, $B%$%G%"%k(B @code{I} $B$N(B |
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@code{M} $BJQ?t$K$D$$$F$N@)8B(B($B@QJ,(B)$B%$%G%"%k(B @code{J} $B$H(B |
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|
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@iftex |
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@tex |
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{\tt J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1])} $\in$ {\tt I} |
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@end tex |
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@end iftex |
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@ifinfo |
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J[K]-(1/IH[K][1])(IH[K][0][0][0]IH[K][0][0][1]+...+IH[K][0][M][0]IH[K][0][M][1]) \in I |
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@end ifinfo |
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|
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$B$rK~$?$9Hs@F<!ItJ,$r9=@.$9$k>pJs(B @code{IH} $B$H$N%Z%"(B @code{[J,IH]} $B$r=PNO$9$k(B. |
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$B>\$7$$=PNO$N8+J}$K$D$$$F$O(B, $B2<$NNc$d%=!<%9$N(B @code{inhomo_part} $B$N(B |
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$B%3%a%s%H$r;2>H(B. |
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|
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restriction, integration $B$KBP$9$k(B @code{inhomo} $B%*%W%7%g%s$O(B |
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restriction_ideal, integration_ideal $B$N%5%V%k!<%A%s$H$7$F$N<B9TMQ$J$N$G(B, |
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$B%f!<%6$,L@<(E*$K;HMQ$9$k$3$H$O$J$$(B. |
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|
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@item @var{param} $B$K;XDj$5$l$?JQ?t$O78?tBN$KB0$9$k$b$N$H$_$J$5$l$F7W;;$,9T$o$l$k(B. |
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$B$^$?(B, ``generic'' $B$G$"$k$3$H$,2>Dj$5$l$k(B. |
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$B$D$^$j(B, $B$3$l$i$NJQ?t$K0MB8$9$k$h$&$J(B generic b-$B4X?t$N:,$O(B, |
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$B:GBg@0?t:,$G$J$$$H$$$&$3$H$G$"$k(B. |
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|
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@item @var{param} $B$,;XDj$5$l$k$H(B, generic b-$B4X?t$N7W;;$O(B noro $B$K$h$k(B |
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$B9bB.%"%k%4%j%:%`$G$O$J$/(B, $B>C5nK!$,MQ$$$i$l$k(B. |
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@var{param} $B$K6u%j%9%H$r;XDj$9$k$3$H$G(B, b-$B4X?t$N7W;;J}K!$N%U%i%0$H$7$F$b(B |
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$BMxMQ$G$-$k(B. |
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|
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@item @var{m} $B$,Ii$G$J$$$H$-(B, $B7W;;$r9T$o$:$K(B s-m $B$r(B generic b-$B4X?t$H$7$F(B |
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$B@)8B(B, $B@QJ,Ey$N7W;;$r9T$&(B. |
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@end itemize |
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|
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$B0J2<$O(B, |
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@iftex |
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@tex |
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$ t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} $ |
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@end tex |
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$B$N(B annihilator |
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@tex |
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$I = D \cdot \{ x(1-x) \partial_x^2+((1-t) \partial_t-(a+b+1)x+c-1) |
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\partial_x-ab, (1-t)x \partial_x+t(1-t) \partial_t+(2-c)t+b-1, |
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(xt-1) \partial_x+at \}$ |
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@end tex |
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$B$N(B |
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@tex |
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$t$ |
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@end tex |
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$B$K$D$$$F$N@QJ,%$%G%"%k(B |
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@tex |
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$J$ |
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@end tex |
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$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
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@end iftex |
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@ifinfo |
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t^{b-1} (1-t)^{c-b-1} (1-xt)^{-a} |
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$B$N(B annihilator |
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I = D . @{ x(1-x)dx^2+((1-t)dt-(a+b+1)x+c-1)dx-ab, |
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(1-t)x dx+t(1-t)dt+(2-c)t+b-1, (xt-1)dx+at @} |
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$B$N(B t $B$K$D$$$F$N@QJ,%$%G%"%k(B J |
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$B$r7W;;$7(B, Gauss $B$ND64v2?HyJ,J}Dx<0$rF3=P$7$?Nc$G$"$k(B. ([SST, Chap 1.3]) |
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@end ifinfo |
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@example |
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[1555] A=ndbf.ann_n([t,1-t,1-x*t])$ |
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[1556] I=map(subst,A,s0,b-1,s1,c-b-1,s2,-a); |
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[(x^2-x)*dx^2+((t-1)*dt+(a+b+1)*x-c+1)*dx+b*a,(-t+1)*x*dx+(t^2-t)*dt+(-c+2)*t+b-1,(t*x-1)*dx+a*t] |
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[1557] J=nk_restriction.integration_ideal(I,[t,x],[dt,dx],[1,0]|inhomo=1, param=[a,b,c]); |
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-- nd_weyl_gr :0sec(0.001875sec) |
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-- weyl_minipoly_by_elim :0.008001sec(0.006133sec) |
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-- generic_bfct_and_gr :0.008001sec(0.006181sec) |
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generic bfct : [[-1,1],[s,1],[s-a+c-1,1]] |
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S0 : 0 |
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B_{S0} length : 1 |
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-- fctr(BF) + base :0sec(0.003848sec) |
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-- integration_ideal_internal :0sec(0.07707sec) |
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[[(x^2-x)*dx^2+((a+b+1)*x-c)*dx+b*a],[[[[dt,(-t+1)*dx]],1]]] |
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@end example |
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@iftex |
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$B$3$N=PNO$O(B |
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@tex |
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$\{(x^2-x) \partial_x^2+((a+b+1)x-c) \partial_x+ab \} |
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- 1/1 \{ \partial_t (-t+1) \partial_x \} \in I$ |
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@end tex |
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$B$G$"$k$3$H$r0UL#$9$k(B. |
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@end iftex |
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@ifinfo |
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$B$3$N=PNO$O(B |
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@{(x^2-x)dx^2+((a+b+1)x-c)dx+ab @} - 1/1 @{ dt (-t+1)dx @} \in I |
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$B$G$"$k$3$H$r0UL#$9$k(B. |
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@end ifinfo |
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|
| @noindent |
@noindent |
| ChangeLog |
ChangeLog |
| @itemize @bullet |
@itemize @bullet |
| @item $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B. |
@item $B$3$l$i$N4X?t$O(B OpenXM/src/asir-contrib/packages/src/nk_restriction.rr $B$GDj5A$5$l$F$$$k(B. nk_restriction.rr, 1.1--1.6 $B$r8+$h(B. |
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@item 2010-02-05 $B$K(B 3 $B$D$N(B option (@code{inhomo}, @code{param}, @code{s0}) $B$,DI2C$5$l$?(B. |
| @end itemize |
@end itemize |
| |
|
| @node $B$=$NB>(B,,, $B<B83E*;EMM$N4X?t(B |
@node $B$=$NB>(B,,, $B<B83E*;EMM$N4X?t(B |
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