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Revision 1.1, Wed Jan 23 02:36:14 2008 UTC (16 years, 7 months ago) by takayama
Branch: MAIN

Added online document for taji_alc.

\input texinfo
@iftex
@catcode`@#=6
@def@fref#1{@xrefX[#1,,@code{#1},,,]}
@def@b#1{{@bf@gt #1}}
@catcode`@#=@other
@end iftex
@overfullrule=0pt
@c -*-texinfo-*-
@comment $OpenXM: OpenXM/src/asir-contrib/packages/doc/taji_alc/taji_alc-ja.texi,v 1.1 2008/01/23 02:36:14 takayama Exp $
@comment %**start of header
@comment --- $B$*$^$8$J$$=*$j(B ---

@comment --- GNU info $B%U%!%$%k$NL>A0(B ---
@setfilename asir-contrib-taji_alc_ja

@comment --- $B%?%$%H%k(B ---
@settitle 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc

@comment %**end of header
@comment %@setchapternewpage odd

@comment --- $B$*$^$8$J$$(B ---
@ifinfo
@macro fref{name}
@ref{\name\,,@code{\name\}}
@end macro
@end ifinfo

@iftex
@comment @finalout
@end iftex

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

@comment --- $B%?%$%H%k(B, $B%P!<%8%g%s(B, $BCx<TL>(B, $BCx:n8"I=<((B ---
@title 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc
@subtitle 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ%Q%C%1!<%8(B taji_alc
@subtitle 1.0 $BHG(B
@subtitle 2007 $BG/(B 11 $B7n(B

@author  $B>1;JBnL4(B, $BEDEg?50l(B
@page
@vskip 0pt plus 1filll
Copyright @copyright{} Takumu Shoji, Shinichi Tajima.
2007. All rights reserved.  Licensed by GPL.
@end titlepage

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

@comment --- @node $B$O(B GNU info, HTML $BMQ(B ---
@comment --- @node  $B$N0z?t$O(B node-name,  next,  previous,  up --- 
@node Top,, (dir), (dir)

@comment --- @menu $B$O(B GNU info, HTML $BMQ(B ---
@comment --- chapter $BL>$r@53N$KJB$Y$k(B ---
@comment --- $B$3$NJ8=q$G$O(B chapter XYZ, Chapter Index $B$,$"$k(B.
@comment ---  Chapter XYZ $B$K$O(B section XYZ$B$K$D$$$F(B, section XYZ$B$K4X$9$k4X?t$,$"$k(B.
@menu
* 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B::
* Index::
@end menu

@comment --- chapter $B$N3+;O(B ---
@comment --- $B?F(B chapter $BL>$r@53N$K(B. $B?F$,$J$$>l9g$O(B Top ---
@node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B,,, Top
@chapter 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B

@comment --- section $BL>$r@53N$KJB$Y$k(B.  ---
@menu
* 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B::
* 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B::
@end menu

@comment --- section ``XYZ$B$K$D$$$F(B'' $B$N3+;O(B ---  section XYZ$B$K$D$$$F$N?F$O(B chapter XYZ
@node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B
@section 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F(B

@comment --- $B=qBN;XDj$K$D$$$F(B ---
@comment --- @code{} $B$O%?%$%W%i%$%?BNI=<((B ---
@comment --- @var{} $B$O<P;zBNI=<((B ---
@comment --- @b{} $B$O%\!<%k%II=<((B ---
@comment --- @samp{} $B$O%U%!%$%kL>$J$I$NI=<((B ---

$B$3$N@bL@=q$G$O(B
1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N%Q%C%1!<%8(B taji_alc $B$K$D$$$F@bL@$9$k(B.
$B?t3XE*2r@b$dGX7J$K$D$$$F$O(B, $B2r@b5-;v(B
``1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$KBP$9$k(B Risa/Asir $BMQ%Q%C%1!<%8(B taji_alc''
(Risa/Asir Journal (2007))
$B$*$h$S$=$N;29MJ88%$r;2>H(B.


@comment --- section ``$B<B83E*4X?t(B'' $B$N3+;O(B --- 
@node 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`(B
@section 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B

@comment --- section ``$B<B83E*4X?t(B'' $B$N(B subsection xyz_abc 
@comment --- subsection xyz_pqr xyz_stu $B$,$"$k(B.
@menu
* taji_alc.cpfd::
* taji_alc.snoether::
* taji_alc.laurent_expansion::
* taji_alc.residue::
* taji_alc.invpow::
* taji_alc.rem_formula::
* taji_alc.solve_ode_cp::
* taji_alc.solve_ode_cp_ps::
* taji_alc.fbt::
* taji_alc.inv::
@end menu

$BK\%;%/%7%g%s$N4X?t$r8F$S=P$9$K$O(B, 
@example
import("taji_alc.rr")$
@end example
$B$r<B9T$7$F%W%m%0%i%`$r%m!<%I$9$k(B.


@comment ****************************************************************
@node taji_alc.cpfd,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.cpfd}
@findex taji_alc.cpfd

@table @t
@item taji_alc.cpfd(@var{num},@var{den})
:: $BM-M}4X?t(B@var{num}/@var{den}$B$NItJ,J,?tJ,2r$r5a$a$k(B.
@end table

@table @var
@item return
@var{switch}$B$,(B0$B$+(B1$B$J$i$P(B, [[[$BJ,;R(B,[$BJ,Jl$N0x;R(B,$B=EJ#EY(B]],...],...] $B$J$k%j%9%H(B.

@var{switch}$B$,(B10$B$+(B11$B$J$i$P(B, [[$BJ,;R(B,[$BJ,Jl$N0x;R(B,$B=EJ#EY(B]],...] $B$J$k%j%9%H(B.

@item num
($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
@item den
($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B

$B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B)  [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
@item switch
$B%*%W%7%g%s;XDj(B

case 0 : complete$B$JItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$OM-M}?t78?tB?9`<0(B)

case 1 : complete$B$JItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$O@0?t78?t2=%j%9%H(B)

case 10 : $BJ,Jl$rQQE83+$7$J$$ItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$OM-M}?t78?tB?9`<0(B)

case 11 : $BJ,Jl$rQQE83+$7$J$$ItJ,J,?tJ,2r$rJV$9(B. ($BJ,;R$O@0?t78?t2=%j%9%H(B)

default : case 0
@end table

@itemize @bullet
@item taji_alc.cpfd()$B$O(B, proper$B$JM-M}4X?t$rBP>]$H$9$k(B.
$BF~NOCM$,(Bproper$B$G$J$$>l9g$G$b@5>o$KF0:n$9$k$,(B, $BB?9`<0$H$7$F=P$F$/$kItJ,$OI=<($7$J$$(B.
@item $BItJ,J,?tJ,2r$O(B, $BQQE83+$r$9$k(Bcomplete$B$J%?%$%W$H(B, $BQQE83+$r$7$J$$%?%$%W$N(B2$B$D$N%?%$%W$,$"$k(B.
taji_alc.cpfd()$B$G:NMQ$7$F$$$k%"%k%4%j%:%`$G$O(B, $BA0<T$,@h$K5a$^$k(B.
$B8e<T$O(B, $BA0<T$N%G!<%?$r%[!<%J!<K!$GB-$7>e$2$F5a$a$k(B.
@item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
$B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
$BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
@end itemize

@example
[235] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1);
[[[1/2*x-1,[x^2+1,1]]],[[-1/2,[x+1,2]],[1/2,[x+1,1]]]]
[236] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=1);
[[[[x-2,2],[x^2+1,1]]],[[[-1,2],[x+1,2]],[[1,2],[x+1,1]]]]
[237] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=10);
[[1/2*x-1,[x^2+1,1]],[1/2*x,[x+1,2]]]
[238] taji_alc.cpfd(x^3-x-1,x^4+2*x^3+2*x^2+2*x+1|switch=11);
[[[x-2,2],[x^2+1,1]],[[x,2],[x+1,2]]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.snoether,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.snoether}
@findex taji_alc.snoether

@table @t
@item taji_alc.snoether(@var{num},@var{den})
:: $BM-M}4X?t(B@var{num}/@var{den}$B$,Dj$a$kBe?tE*6I=j%3%[%b%m%8!<N`$N%M!<%?!<:nMQAG$r5a$a$k(B.
@end table

@table @var
@item return
[[$B0x;R(B,$B%M!<%?!<:nMQAG(B],...] $B$J$k%j%9%H(B.

$B%M!<%?!<:nMQAG$O(B, $B78?t$r9b3,$NItJ,$+$i9_=g$KJB$Y$?%j%9%H(B

@item num
($BM-M}4X?t$NJ,;R$N(B)$BB?9`<0(B
@item den
($BM-M}4X?t$NJ,Jl$N(B)$BB?9`<0(B

$B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B)  [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B.
@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B%M!<%?!<:nMQAG$r(B [$BM-M}?t78?tB?9`<0(B,...] $B$J$k%j%9%H$GJV$9(B.

case 1 : $B%M!<%?!<:nMQAG$r(B [$B@0?t78?t2=%j%9%H(B,...] $B$J$k%j%9%H$GJV$9(B.

case 10 : $B%M!<%?!<:nMQAG$r(B [[$B@0?t78?tB?9`<0(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.

case 20 : $B%M!<%?!<:nMQAG$r(B [[$B@0?t78?t2=%j%9%H(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item taji_alc.snoether()$B$O(B, @var{den}$B$r(BQ$B>e$G4{LsJ,2r$7(B,
$B3F0x;R$KBP1~$9$k%M!<%?!<:nMQAG$rJV$9(B.
@item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
$B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
$BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
@item $BLa$jCM$N7?$O(B@var{switch}$B$GA*Br$G$-$k(B.

case 10$B$O(B, $B%M!<%?!<:nMQAG$N3F78?tA4BN$rDLJ,$7(B, $B$=$NJ,JlItJ,$H3,>h$N@Q$r%j%9%H$GJ,$1$?I=8=$G$"$k(B.
$B$o$+$j$d$9$$$,(B, $BDLJ,CM$H78?tItJ,$H$GLsJ,$G$-$kItJ,$,$"$k(B($BFC$K9b3,$NItJ,$KB?$$(B)$B$N$G(B, $B>iD9@-$r$b$C$F$$$k(B.

case 20$B$O(B, $B3,>h$NItJ,$GA4BN$r$/$/$j(B($B%j%9%H$GJ,$1(B), $B%M!<%?!<:nMQAG$N3F78?t$r8DJL$KDLJ,$7%j%9%H2=$9$k(B.
$B3,>h$NItJ,$H78?tItJ,$H$GLsJ,$G$-$kItJ,$,$"$k(B($BFC$KDc3,$NItJ,$KB?$$(B)$B$N$G(B,
$B>iD9$H8@$($J$/$b$J$$(B(case 10$B$h$j$O$^$7(B)$B$,(B, $B?t3XE*$J9=B$$,e:No$K8+$($kI=8=$G$"$k(B.
@end itemize

@example
[296] taji_alc.snoether(1,[[x^3-x-1,3]]);
[[x^3-x-1,[9/529*x^2-27/1058*x+11/1058,-81/529*x^2-9/529*x+135/529,-49
05/12167*x^2+4563/12167*x+3270/12167]]]
[299] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=1);
[[x^3-x-1,[[18*x^2-27*x+11,1058],[-81*x^2-9*x+135,529],[-4905*x^2+4563
*x+3270,12167]]]]
[297] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=10);
[[x^3-x-1,[[414*x^2-621*x+253,-3726*x^2-414*x+6210,-9810*x^2+9126*x+65
40],24334]]]
[298] taji_alc.snoether(1,[[x^3-x-1,3]]|switch=20);
[[x^3-x-1,[[[18*x^2-27*x+11,529],[-162*x^2-18*x+270,529],[-9810*x^2+91
26*x+6540,12167]],2]]]

[241] taji_alc.snoether(x^3+1,x^18-2*x^14+x^10-x^8+2*x^4-1|switch=10);
[[x^4+x^3+x^2+x+1,[[-2*x^2-x-2],50]],[x^4-x^3+x^2-x+1,[[-2*x^3+4*x^2-x
-2],50]],[x^2+1,[[-x+1,8*x+5],32]],[x+1,[[-6,-39],320]],[x-1,[[2,-24,6
7],320]]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.laurent_expansion,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.laurent_expansion}
@findex taji_alc.laurent_expansion

@table @t
@item taji_alc.laurent_expansion(@var{num},@var{den})
:: $BM-M}4X?t(B@var{num}/@var{den}$B$N6K$K$*$1$k%m!<%i%sE83+$N<gMWIt$N78?t$r5a$a$k(B.
@end table

@table @var
@item return
[[$B0x;R(B,$B%m!<%i%sE83+$N78?t(B],...] $B$J$k%j%9%H(B.

$B%m!<%i%sE83+$N78?t$O(B, $B9b0L$N78?t$+$i=g$KJB$Y$?%j%9%H(B.

@item num
($BM-M}4X?t$NJ,;R$N(B)$BB?9`<0(B
@item den
($BM-M}4X?t$NJ,Jl$N(B)$BB?9`<0(B

$B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B)  [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B

@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B%m!<%i%sE83+$N78?t$r(B [$BM-M}?t78?tB?9`<0(B,...] $B$J$k%j%9%H$GJV$9(B.

case 1 : $B%m!<%i%sE83+$N78?t$r(B [$B@0?t78?t2=%j%9%H(B,...] $B$J$k%j%9%H$GJV$9(B.

case 10 : $B%m!<%i%sE83+$N78?t$r(B [[$B@0?t78?tB?9`<0(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.

case 20 : $B%m!<%i%sE83+$N78?t$r(B [[$B@0?t78?t2=%j%9%H(B,...],$B@0?t(B] $B$J$k%j%9%H$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item taji_alc.laurent_expansion()$B$O(B, taji_alc.snoether()$B$r;H$C$F(B, $B%m!<%i%sE83+$N78?t$r5a$a$k(B.
@item taji_alc.laurent_expansion()$B$G$O(B,
C$B>e$N(B1$BE@$KCmL\$9$k$N$G$O$J$/(B, Q$B>e$G$N4{Ls0x;R<+BN$KCmL\$7$F%m!<%i%sE83+$N78?t$r5a$a$k(B.
$BLa$jCM$N78?t%j%9%H$N3F@.J,$O(B, $B$=$N0x;R$NA4$F$NNmE@$,6&DL$KK~$?$9%m!<%i%sE83+$N78?tB?9`<0$G$"$k(B.
$B=>$C$F(B, 1$BE@$4$H$N%m!<%i%sE83+$N78?t$r$5$i$K5a$a$?$$>l9g$K$O(B,
$B5a$a$?%m!<%i%sE83+$N78?tB?9`<0$K0x;R$NNmE@(B($BB($AFC0[E@(B)$B$NCM$rBeF~$9$kI,MW$,$"$k(B.
@end itemize

@example
[354] taji_alc.laurent_expansion(x,(x-1)^3);
[[x-1,[1,1,0]]]
[356] taji_alc.laurent_expansion(x^5+x^4+x^3+x^2+x+1,(x^4+1)^3);
[[x^4+1,[1/64*x^2+1/64*x,1/16*x^3+1/16*x^2-3/128*x-5/128,-5/128*x^3-1/
8*x^2-3/16*x]]]
@end example

@table @t
@item $B;2>H(B
@ref{taji_alc.snoether}
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.residue,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.residue}
@findex taji_alc.residue

@table @t
@item taji_alc.residue(@var{num},@var{den})
:: $BM-M}4X?t(B@var{num}/@var{den}$B$N6K$K$*$1$kN1?t$r5a$a$k(B.
@end table

@table @var
@item return
[[$B0x;R(B,$BN1?t(B],...] $B$J$k%j%9%H(B

@item num
($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
@item den
($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B

$B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B)  [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $BN1?t$rM-M}?t78?tB?9`<0$GJV$9(B.

case 1 : $BN1?t$r@0?t78?t2=%j%9%H$GJV$9(B.

default : case 0

@item pole
$B%*%W%7%g%s;XDj(B

[$B0x;R(B,...] $B$J$k%*%W%7%g%s%j%9%H(B
@end table

@itemize @bullet
@item taji_alc.residue()$B$O(B, @var{den}$B$r(BQ$B>e$G4{LsJ,2r$7(B, $B3F0x;R$NNmE@(B($BB($AM-M}4X?t$N6K(B)$B$K$*$1$kN1?t$rJV$9(B.
@item $B%*%W%7%g%s$G(B@var{pole}$B$r;XDj$9$l$P$=$N0x;R$N$_$NN1?t$rJV$9(B. $B;XDj$,ITE,Ev$@$H(B0$B$rJV$9(B.
@item taji_alc.residue()$B$G:NMQ$7$F$$$k%"%k%4%j%:%`$G$O(B,
C$B>e$N(B1$BE@$KCmL\$9$k$N$G$O$J$/(B, Q$B>e$G$N4{Ls0x;R<+BN$KCmL\$7$FN1?t$r5a$a$k(B.
$BLa$jCM$NN1?t$O(B, $B$=$N0x;R$NA4$F$NNmE@$,6&DL$KK~$?$9N1?tB?9`<0$G$"$k(B.
$B=>$C$F(B, 1$BE@$4$H$NN1?tCM$r$5$i$K5a$a$?$$>l9g$K$O(B,
$B5a$a$?N1?tB?9`<0$K0x;R$NNmE@(B($BB($AFC0[E@(B)$B$NCM$rBeF~$9$kI,MW$,$"$k(B.

@example
[219] taji_alc.residue(1,x^4+1);
[[x^4+1,-1/4*x]]
@end example

$B$3$NNc$G8@$&$H(B, $B5a$a$?N1?tB?9`<0(B-1/4*x$B$K(B, x^4+1$B$N(B(4$B$D$"$k(B)$BNmE@$r$=$l$>$lBeF~$7$?$b$N$,8DJL$NN1?tCM$G$"$k(B.
@item @var{den}$B$O(B, $B%j%9%H$G$NF~NO$,K>$^$7$$(B.
($BB?9`<0$GF~NO$9$k$H(B, $B4JLs2=$N=hM}$,@8$8$k$?$a=E$/$J$k(B.)
$B$?$@$7$=$N>l9g$K$O(B, $B4{Ls%A%'%C%/(B, $BM-M}<0$NLsJ,(B, $B@0?t78?t2=$O9T$o$J$$$N$GCm0U$9$k(B.
$BF~NOCM$O%f!<%6B&$,@UG$$r$b$D(B.
@end itemize

@example
[221] taji_alc.residue(x^8,[[x^3-x-1,3]]);
[[x^3-x-1,-2243/12167*x^2+2801/12167*x+5551/12167]]
[222] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]);
[[x^2+3*x-1,-284/4563*x-311/1521],[x-1,89/432],[x+1,7/432]]
[223] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]|switch=1)
;
[[x^2+3*x-1,[-284*x-933,4563]],[x-1,[89,432]],[x+1,[7,432]]]
[234] taji_alc.residue(x^2+x,[[x+1,3],[x-1,3],[x^2+3*x-1,2]]|switch=1,
pole=[x+1]);
[[x+1,[7,432]]]
[225] taji_alc.residue(x^3+1,x^18-2*x^14+x^10-x^8+2*x^4-1);
[[x^4+x^3+x^2+x+1,-1/25*x^2-1/50*x-1/25],[x^4-x^3+x^2-x+1,-1/25*x^3+2/
25*x^2-1/50*x-1/25],[x^2+1,1/4*x+5/32],[x+1,-39/320],[x-1,67/320]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.invpow,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.invpow}
@findex taji_alc.invpow

@table @t
@item taji_alc.invpow(@var{poly},@var{f},@var{m})
:: $B>jM>BN(BQ[x]/<@var{f}>$B>e$G$N(B@var{poly}$B$N5U85$N(B@var{m}$B>h$r5a$a$k(B.
@end table

@table @var
@item return
$B5UQQ(B

@item poly
$BB?9`<0(B
@item f
Q$B>e$G4{Ls$JB?9`<0(B
@item m
$B<+A3?t(B
@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B5UQQ$rM-M}?t78?tB?9`<0$GJV$9(B.

case 1 : $B5UQQ$r@0?t78?t2=%j%9%H$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item @var{poly}$B$H(B@var{f}$B$O8_$$$KAG$G$J$1$l$P$J$i$J$$(B.
@item $B%"%k%4%j%:%`$N9|3J$O7+$jJV$7(B2$B>hK!$G$"$k(B. $B$=$3$K:G>.B?9`<0$NM}O@$r1~MQ$7$F9bB.2=$7$F$$$k(B.
@end itemize

@example
[236] taji_alc.invpow(3*x^2-1,x^3-x-1,1);
-6/23*x^2+9/23*x+4/23
[237] taji_alc.invpow(3*x^2-1,x^3-x-1,1|switch=1);
[-6*x^2+9*x+4,23]
[238] taji_alc.invpow(3*x^2-1,x^3-x-1,30|switch=1);
[1857324483*x^2-2100154824*x-477264412,266635235464391245607]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.rem_formula,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.rem_formula}
@findex taji_alc.rem_formula

@table @t
@item taji_alc.rem_formula(@var{polylist})
:: $BB?9`<0(Bf(x)$B$rM?$($?$H$-$N>jM>8x<0$r5a$a$k(B.
@end table

@table @var
@item return
@var{switch} $B$*$h$S(B $B@bL@J8$r;2>H(B

@item polylist
f(x)$B$r(BQ$B>e$G4{LsJ,2r$7$?(B [[$B0x;R(B,$B=EJ#EY(B,$BNmE@$N5-9f(B],...] $B$J$k%j%9%H(B

@item switch
$B%*%W%7%g%s;XDj(B

case 0 : x$B$NQQ$G@0M}$7(B, $B%j%9%H$GJV$9(B.

case 10 : f(x)$B$NQQ$G@0M}$7(B, $B%j%9%H$GJV$9(B. ($B0l0x;R$N>l9g$N$_BP1~(B)

case 20 : x$B$NQQ$G@0M}$7(B, symbolic$B$JI=8=$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item $B%"%k%4%j%:%`$O(B, $B%(%k%_!<%H$NJd4V>jM>$rMQ$$$F$$$k(B.
@item $B>jM>8x<0$NI=8=J}K!$O$$$/$D$+9M$($i$l$k$?$a(B, @var{switch}$B$GA*Br<0$H$7$?(B.
@item @var{switch}=0 $B$NLa$jCM$N8+J}$r=R$Y$k(B. $BNc$H$7$F(B, f(x)=f1(x)^m1*f2(x)^m2$B$r9M$($k(B.
$BF~NO$O(B [[f1(x),m1,z1],[f2(x),m2,z2]] $B$H$J$k(B. $B$=$N$H$-La$jCM$O(B,

[r_{f1}(x,z1),r_{f2}(x,z2)]

$B$J$k%j%9%H$GJV$5$l$k(B. $B$3$l$O(B, $B>jM>8x<0$,(B

@tex
$r(x)=r_{f1}(x,z1)+r_{f2}(x,z2)$
@end tex

$B$J$k7A$GM?$($i$l$k$3$H$r0UL#$7$F$$$k(B.
$B3F@.J,$N(Br_{fi}(x,zi)$B$O(B,

[p^(mi-1)(zi)$B$N78?t$H$J$k(Bx$B$H(Bzi$B$NB?9`<0(B,...,p^(0)(zi)$B$N78?t$H$J$k(Bx$B$H(Bzi$B$NB?9`<0(B]

$B$J$k%j%9%H$G$"$k(B.
@item @var{switch}=10 $B$NLa$jCM$N8+J}$r=R$Y$k(B. $BNc$H$7$F(B, f(x)=f1(x)^m$B$r9M$($k(B.
$BF~NO$O(B [[f1(x),m,z]] $B$H$J$k(B. $B$=$N$H$-La$jCM$O(B,

[r_(m-1)(x,z),...,r_0(x,z)]

$B$J$k%j%9%H$GJV$5$l$k(B. $B3F@.J,$O(B, $B>jM>8x<0$r(B

@tex
$r(x)=r_{m-1}(x,z)f_1(x)^{m-1}+\cdots+r_0(x,z)$
@end tex

$B$N$h$&$K(Bf1(x)$B$NQQ$GE83+$7$?$H$-$N3F78?t$r0UL#$7$F$$$k(B. 
$B3F@.J,$N(Br_{i}(x,z)$B$O(B,

[p^(m-1)(z)$B$N78?t$H$J$k(Bx$B$H(Bz$B$NB?9`<0(B,...,p^(0)(z)$B$N78?t$H$J$k(Bx$B$H(Bz$B$NB?9`<0(B]

$B$J$k%j%9%H$G$"$k(B.
@item @var{switch}=20 $B$NLa$jCM$N8+J}$r=R$Y$k(B.
symbolic$B$J=PNO$N(Bp^(m)(z)$B$O(B, p(x)$B$N(Bm$B3,$NF34X?t$K(Bz$B$rBeF~$7$?CM$H$$$&0UL#$G$"$k(B.
@item $BLa$jCM$O(B, $BM?$($?0x;R$NA4$F$NNmE@$rBeF~$7$?$b$N$NOB$H$7$F8+$k(B.
$B$3$l$O0x;R$,(B2$B<!0J>e$NB?9`<0$N>l9g$K4X78$7$F$/$k(B. $BNc$($P(B,

@example
[228] taji_alc.rem_formula([[x^2+1,1,z]]);
[[-1/2*z*x+1/2]]
@end example

$B$N@5$7$$8+J}$O(B, x^2+1$B$NNmE@$r(Ba1,a2$B$H$*$$$?$H$-$K(B, z$B$K(Ba1$B$H(Ba2$B$rBeF~$7$?(B,

r(x)=(-1/2*a1*x+1/2)+(-1/2*a2*x+1/2)
$B$G$"$k(B. $B$7$+$7=PNO$G$O(B, $BNmE@$NOB$NItJ,$rJX59>e>JN,$7$FJV$9(B.
@end itemize

@example
[583] taji_alc.rem_formula([[x-1,1,z1],[x-2,1,z2]]);
[[-x+2],[x-1]]
[584] taji_alc.rem_formula([[x-1,1,z1],[x-2,1,z2]]|switch=20);
(-p^(0)(z1)+p^(0)(z2))*x+2*p^(0)(z1)-p^(0)(z2)

[587] taji_alc.rem_formula([[x-1,2,z1]]);
[[x-1,1]]
[588] taji_alc.rem_formula([[x-1,2,z1]]|switch=20);
p^(1)(z1)*x-p^(1)(z1)+p^(0)(z1)

[494] taji_alc.rem_formula([[x-1,3,z1]]|switch=20);
1/2*p^(2)(z1)*x^2+(-p^(2)(z1)+p^(1)(z1))*x+1/2*p^(2)(z1)-p^(1)(z1)+p^(
0)(z1)

[229] taji_alc.rem_formula([[x+1,2,z1],[x^3-x-1,1,z2]]);
[[-x^4-x^3+x^2+2*x+1,-2*x^4-3*x^3+2*x^2+5*x+3],[(-1/23*z2^2-10/23*z2+1
6/23)*x^4+(-12/23*z2^2-5/23*z2+31/23)*x^3+(-5/23*z2^2+19/23*z2-12/23)*
x^2+(22/23*z2^2+13/23*z2-53/23)*x+16/23*z2^2-1/23*z2-26/23]]
[230] taji_alc.rem_formula([[x+1,2,z1],[x^3-x-1,1,z2]]|switch=20);
(-1/23*p^(0)(z2)*z2^2-10/23*p^(0)(z2)*z2-2*p^(0)(z1)+16/23*p^(0)(z2)-p
^(1)(z1))*x^4+(-12/23*p^(0)(z2)*z2^2-5/23*p^(0)(z2)*z2-3*p^(0)(z1)+31/
23*p^(0)(z2)-p^(1)(z1))*x^3+(-5/23*p^(0)(z2)*z2^2+19/23*p^(0)(z2)*z2+2
*p^(0)(z1)-12/23*p^(0)(z2)+p^(1)(z1))*x^2+(22/23*p^(0)(z2)*z2^2+13/23*
p^(0)(z2)*z2+5*p^(0)(z1)-53/23*p^(0)(z2)+2*p^(1)(z1))*x+16/23*p^(0)(z2
)*z2^2-1/23*p^(0)(z2)*z2+3*p^(0)(z1)-26/23*p^(0)(z2)+p^(1)(z1)

[231] taji_alc.rem_formula([[x^3-x-1,2,z]]|switch=10);
[[[(3/23*z^2-4/23)*x^2+(-1/23*z+3/23)*x-4/23*z^2+3/23*z+4/23,(162/529*
z^2-174/529*z-108/529)*x^2+(-105/529*z^2+54/529*z+70/529)*x-108/529*z^
2+116/529*z+72/529],[(-6/23*z^2+9/23*z+4/23)*x^2+(9/23*z^2-2/23*z-6/23
)*x+4/23*z^2-6/23*z+5/23]]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.solve_ode_cp,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.solve_ode_cp}
@findex taji_alc.solve_ode_cp

@table @t
@item taji_alc.solve_ode_cp(@var{poly},@var{var},@var{exppoly})
:: $BM-M}?t78?t$N@~7A>oHyJ,J}Dx<0$N%3!<%7!<LdBj(B

@tex
$Pu(z)=f(z)$, $u^{(0)}(0)=c_0,\ldots,u^{(n-1)}(0)=c_{n-1}$
@end tex

$B$N2r$r5a$a$k(B.

$B$?$@$7(B, P$B$O(Bn$B3,$NM-M}?t78?t$N@~7A>oHyJ,:nMQAG(B, f(z)$B$O;X?tB?9`<0$H$9$k(B.
@end table

@table @var
@item return
2$BDL$j$NI=8=$,$"$k(B.

$B!&I=8=(B1 ($B%3!<%7!<%G!<%?$G@0M}$7$?7A(B)

$B%3!<%7!<LdBj$N0lHL2r(Bu(z)$B$O(B,

@tex$u(z)=c_0u_0(z)+\cdots+c_{n-1}u_{n-1}(z)+v(z)$@end tex

$B$J$k@~7A7k9g$N7A$GM?$($i$l$k(B.
@tex$u_0(z),\ldots,u_{n-1}(z)$@end tex
$B$r%3!<%7!<LdBj$N4pK\2r(B,
@tex$v(z)$@end tex
$B$r%3!<%7!<LdBj$NFC<l2r$H$$$$(B,

[u_0(z),...,u_(n-1)(z),v(z)]

$B$J$k%j%9%H$GJV$9(B.
$B4pK\2r$HFC<l2r$O(B, $B;X?tB?9`<0%j%9%H$G$"$k(B.

$B!&I=8=(B2 ($B;X?t4X?t$G@0M}$7$?7A(B)

@var{data}$B$K%3!<%7!<%G!<%?$rM?$($k$H(B,
$B%3!<%7!<LdBj$N0lHL2r(Bu(z)$B$N(B
@tex$c_0,\ldots,c_{n-1}$@end tex
$B$N$H$3$m$K%G!<%?$rBeF~$7(B,
$B$=$l$r;X?t4X?t$G@0M}$7D>$7$?;X?tB?9`<0%j%9%H$rJV$9(B.

@item poly
$BB?9`<0(B (P$B$NFC@-B?9`<0(B)

$B$^$?$O(B (P$B$NFC@-B?9`<0$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B

@item var
$BITDj85(B ($B4X?t$NFHN)JQ?t(B)

@item exppoly
$B@F<!7A$N$H$-(B0, $BHs@F<!7A$N$H$-(Bf(z)$B$N;X?tB?9`<0%j%9%H(B.

@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.

case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.

default : case 0
@item data
$B%*%W%7%g%s;XDj(B

$B%3!<%7!<%G!<%?$r(B [c_0,...,c_(n-1)] $B$N=g$KJB$Y$?%j%9%H(B.
@end table

@itemize @bullet
@item $B2rK!$O%(%k%_!<%H$NJ}K!(B($BN1?t7W;;$K5"Ce$5$;$kJ}K!(B)$B$r:NMQ$7$F$$$k(B.
@item $BJQ?t$O(B2$B<oN`I,MW(B($BFC@-B?9`<0$NJQ?t$H4X?t$NFHN)JQ?t(B).
@var{poly}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
@item $BLa$jCM$NFC<l2r(B
@tex
$v(z)$
@end tex
$B$O(B, $B%3!<%7!<>r7o(B
@tex
$v(0)=0,\ldots,v^{(n-1)}(0)=0$
@end tex
$B$rK~$?$9%3!<%7!<LdBj$NFC<l2r$G$"$k(B.
@end itemize

@example
[287] taji_alc.solve_ode_cp(x*(x-3)^2,z,0);
[[[x-3,0],[x,1]],[[x-3,-z+2/3],[x,-2/3]],[[x-3,1/3*z-1/9],[x,1/9]]]

[289] taji_alc.solve_ode_cp((x^3-x-1)^2,z,0|switch=1);
[[[x^3-x-1,[(92*z+200)*x^2+(-69*z-254)*x-92*z+43,529]]],[[x^3-x-1,[(92
*z+420)*x^2+(-46*z-216)*x-161*z-280,529]]],[[x^3-x-1,[(-69*z-195)*x^2+
(23*z+327)*x+23*z+130,529]]],[[x^3-x-1,[(-161*z-270)*x^2+(69*z+290)*x+
184*z+180,529]]],[[x^3-x-1,[-105*x^2+(-23*z+54)*x+69*z+70,529]]],[[x^3
-x-1,[(69*z+162)*x^2-174*x-92*z-108,529]]]]

[277] taji_alc.solve_ode_cp(x^2-4,z,0);
[[[x+2,1/2],[x-2,1/2]],[[x+2,-1/4],[x-2,1/4]]]
[278] taji_alc.solve_ode_cp(x^2-4,z,0|data=[1,-1]);
[[x+2,3/4],[x-2,1/4]]
[279] taji_alc.solve_ode_cp(x^2-4,z,0|data=[c0,c1]);
[[x+2,1/2*c0-1/4*c1],[x-2,1/2*c0+1/4*c1]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.solve_ode_cp_ps,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.solve_ode_cp_ps}
@findex taji_alc.solve_ode_cp_ps

@table @t
@item taji_alc.solve_ode_cp_ps(@var{poly},@var{var},@var{exppoly})
:: $BM-M}?t78?t$N@~7A>oHyJ,J}Dx<0$N%3!<%7!<LdBj(B

@tex
$Pu(z)=f(z)$, $u^{(0)}(0)=c_0,\ldots,u^{(n-1)}(0)=c_{n-1}$
@end tex

$B$NFC<l2r$r5a$a$k(B.

$B$?$@$7(B, $BHs@F<!7A$N$_$rBP>]$H$7$F$$$k$N$G(B,
@tex
$f(z)\neq0$
@end tex
$B$H$9$k(B.

@end table

@table @var
@item return
$B;X?tB?9`<0%j%9%H(B

@item poly
$BB?9`<0(B (P$B$NFC@-B?9`<0(B)

$B$^$?$O(B (P$B$NFC@-B?9`<0$r(BQ$B>e$G4{LsJ,2r$7$?(B) [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B

@item var
$BITDj85(B ($B4X?t$NFHN)JQ?t(B)

@item exppoly
f(z)$B$N;X?tB?9`<0%j%9%H(B

@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.

case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.

default : case 0

@item switch2
$B%*%W%7%g%s;XDj(B

case 0 : $B%3!<%7!<LdBj$NFC<l2r$rJV$9(B.

case 1 : $B4JC1$J7A$NFC<l2r$rJV$9(B.

default : case 0
@end table

@itemize @bullet
@item $BJQ?t$O(B2$B<oN`I,MW(B($BFC@-B?9`<0$NJQ?t$H4X?t$NFHN)JQ?t(B).
@var{poly}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
@end itemize

@example
[345] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-1,1]]);
[[x+3,1/20],[x-1,-1/4],[x-2,1/5]]
[346] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-1,1]]|switch2=1);
[[x-1,-1/4]]
[347] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-2,1]]);
[[x+3,1/25],[x-2,1/5*z-1/25]]
[348] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x-2,1]]|switch2=1);
[[x-2,1/5*z-1/25]]
[349] taji_alc.solve_ode_cp_ps((x-2)*(x+3),z,[[x+1,1],[x-2,1]]|switch2
=1);
[[x+1,-1/6],[x-2,1/5*z+2/75]]

[350] taji_alc.solve_ode_cp_ps((x^3-x-1)*(x-3)^2,z,[[x-3,2],[x-1,3*z^2
+1]]);
[[x-1,[-6*z^2-36*z-119,8]],[x^3-x-1,[42291*x^2+55504*x+32313,12167]],[
x-3,[4232*z^2-4278*z-4295,97336]]]
@end example

@table @t
@item $B;2>H(B
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.fbt,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.fbt}
@findex taji_alc.fbt

@table @t
@item taji_alc.fbt(@var{num},@var{den},@var{var})
:: $BM-M}4X?t(B@var{num}/@var{den}$B$,Dj$a$kBe?tE*6I=j%3%[%b%m%8!<N`$N%U!<%j%(!&%\%l%kJQ49$r9T$&(B.
@end table

@table @var
@item return
[$B;X?tB?9`<0%j%9%H(B,...] $B$J$k%j%9%H(B

@item num
($BM-M}4X?t$NJ,;R$N(B) $BB?9`<0(B
@item den
($BM-M}4X?t$NJ,Jl$N(B) $BB?9`<0(B

$B$^$?$O(B ($BM-M}4X?t$NJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?(B)  [[$B0x;R(B,$B=EJ#EY(B],...] $B$J$k%j%9%H(B
@item var
$BITDj85(B ($BA|$NFHN)JQ?t(B)
@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$rM-M}?t78?tB?9`<0$GJV$9(B.

case 1 : $B;X?tB?9`<0%j%9%H$N(B2$BHVL\$N@.J,$r@0?t78?t2=%j%9%H$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item $BJQ?t$O(B2$B<oN`I,MW(B($BBe?tE*6I=j%3%[%b%m%8!<N`$NJQ?t$HA|$NFHN)JQ?t(B).
@var{num/den}$B$NITDj85$H(B@var{var}$B$NITDj85$,>WFM$7$J$$$h$&Cm0U(B.
@item taji_alc.fbt()$B$O(B, Res(Rat*exp(z*x))$B$J$k7A$NM-M}7A4X?t$NN1?t$r5a$a$k(B.
$B$3$NM-M}7A4X?t$NN1?t$O;X?tB?9`<0$H$J$k$?$a(B, $B;X?tB?9`<0%j%9%H$GJV$9(B.
@item $BFbIt$N%"%k%4%j%:%`$O(Btaji_alc.residue()$B$H$[$\F1$8$G$"$j(B, $B<B:]$K(Btaji_alc.residue()$B$r8F$S=P$7$F7W;;$r9T$C$F$$$k(B.
@end itemize

@example
[235] taji_alc.fbt(1,(x^3-x-1)^3,z);
[[x^3-x-1,(9/529*z^2-81/529*z-4905/12167)*x^2+(-27/1058*z^2-9/529*z+45
63/12167)*x+11/1058*z^2+135/529*z+3270/12167]]
@end example

@table @t
@item $B;2>H(B
@ref{taji_alc.residue, taji_alc.invfbt}
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************


@page
@comment ****************************************************************
@node taji_alc.inv,,, 1$BJQ?tBe?tE*6I=j%3%[%b%m%8!<N`MQ$N4X?t(B
@subsection @code{taji_alc.invfbt}
@findex taji_alc.invfbt

@table @t
@item taji_alc.invfbt(@var{exppoly},@var{var})
:: $B;X?tB?9`<0$N5U%U!<%j%(!&%\%l%kJQ49$r9T$&(B.
@end table

@table @var
@item return
$BM-M}4X?t(B

@item exppoly
$B;X?tB?9`<0%j%9%H(B
@item var
$BITDj85(B ($B;X?tB?9`<0$NFHN)JQ?t(B)

@item switch
$B%*%W%7%g%s;XDj(B

case 0 : $BM-M}4X?t$GJV$9(B.

case 1 : $BM-M}4X?t$r(B[$BJ,;R(B,$BJ,Jl$r(BQ$B>e$G4{LsJ,2r$7$?%j%9%H(B]$B$J$k%j%9%H$GJV$9(B.

default : case 0
@end table

@itemize @bullet
@item $BJQ?t$O(B2$B<oN`I,MW(B($BBe?tE*?t$N:G>.B?9`<0$NJQ?t$H;X?tB?9`<0$NFHN)JQ?t(B).
$B>WFM$7$J$$$h$&Cm0U(B.
@item taji_alc.invfbt()$B$O(B, exppoly$B$r(B, Res(Rat*exp(z*x))$B$J$k7A$NN1?tI=<($KJQ49$7(B, Rat$BItJ,$rJV$9(B.
@item taji_alc.fbt()$B$N5U1i;;$G$"$k(B.
@end itemize

@example
[8] taji_alc.invfbt([[x^3-x-1,2*x^2*z^2+x*z+1],[x^2+1,z*x+z^2]],z|swit
ch=1);
[3*x^14+14*x^12+39*x^11+33*x^10+179*x^9+206*x^8+350*x^7+223*x^6+126*x^
5+176*x^4+107*x^3+101*x^2+15*x-4,[[x^2+1,3],[x^3-x-1,3]]]

[9] taji_alc.fbt(3*x^14+14*x^12+39*x^11+33*x^10+179*x^9+206*x^8+350*x^
7+223*x^6+126*x^5+176*x^4+107*x^3+101*x^2+15*x-4,[[x^2+1,3],[x^3-x-1,3
]],z);
[[x^3-x-1,2*z^2*x^2+z*x+1],[x^2+1,z*x+z^2]]
@end example

@table @t
@item $B;2>H(B
@ref{taji_alc.fbt}
@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
@comment --- openxm $B$N30It$+$i$N4sM?$b=R$Y$k(B. Credit.
@noindent
ChangeLog
@itemize @bullet
@end itemize
@comment ****************************************************************






@comment --- $B$*$^$8$J$$(B ---
@node Index,,, Top
@unnumbered Index
@printindex fn
@printindex cp
@iftex
@vfill @eject
@end iftex
@summarycontents
@contents
@bye
@comment --- $B$*$^$8$J$$=*$j(B ---