| version 1.1, 2001/10/04 08:16:27 |
version 1.4, 2001/10/09 01:44:21 |
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| % $OpenXM$ |
% $OpenXM: OpenXM/doc/Papers/jsiamb-noro.tex,v 1.3 2001/10/04 08:30:17 noro Exp $ |
| \setlength{\parskip}{10pt} |
\setlength{\parskip}{10pt} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B7W;;5!Be?t%7%9%F%`(B Risa/Asir} |
\fbox{\bf $B7W;;5!Be?t%7%9%F%`(B Risa/Asir} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B |
\item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B |
| |
|
| \begin{itemize} |
\begin{itemize} |
| \item C $B$G5-=R(B |
\item C $B$G5-=R(B |
| \item $B%a%b%j4IM}$O(B Boehm's conservative GC $B$K$h$k(B |
\item $B%a%b%j4IM}$O(B Boehm's conservative GC [Boehm] $B$K$h$k(B |
| \end{itemize} |
\end{itemize} |
| |
|
| \item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B. |
\item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B. |
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|
| \item $B%*!<%W%s%=!<%9(B |
\item $B%*!<%W%s%=!<%9(B |
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|
| \begin{itemize} |
\begin{itemize} |
| \item 2000 $BG/$^$GIY;NDL8&$G3+H/(B $\Rightarrow$ $B?@8M(B branch [Risa/Asir] |
\item 2000 $BG/$^$GIY;NDL8&$G3+H/(B |
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$\Rightarrow$ 2001 $BG/$h$j(B Kobe branch [Risa/Asir] |
| $B$,%9%?!<%H(B |
$B$,%9%?!<%H(B |
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|
| CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B) |
\item CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B) |
| \end{itemize} |
\end{itemize} |
| |
|
| \item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B |
\item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B |
| Line 33 CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B) |
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| Line 35 CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B) |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B<g$J5!G=(B} |
\fbox{\bf $B<g$J5!G=(B} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $BB?9`<0$N4pK\1i;;(B |
\item $BB?9`<0$N4pK\1i;;(B |
| |
|
| \begin{itemize} |
\begin{itemize} |
| \item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc. |
\item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc. |
| representation |
|
| \end{itemize} |
\end{itemize} |
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|
| \item $BB?9`<00x?tJ,2r(B |
\item $BB?9`<00x?tJ,2r(B |
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| \item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier] |
\item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier] |
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|
| \item $B=`AG%$%G%"%kJ,2r(B |
$BBe?tJ}Dx<0$N2r$r(B, $B0lJQ?tB?9`<0$N:,$GI=$9(B |
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\item $B=`AG%$%G%"%kJ,2r(B [SY] |
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| $BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B |
$BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B |
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| \item $BB?9`<0$N(B $b$-$B4X?t$N7W;;(B [Oaku] |
\item $BB?9`<0$N(B $b$-$B4X?t(B (Bernstein-Sato polynomial) $B$N7W;;(B [Oaku] |
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| $b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B |
$b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B |
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| Line 74 $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$ |
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| Line 77 $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$ |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B<g$J5!G=(B ($B$D$E$-(B)} |
\fbox{\bf $B<g$J5!G=(B ($B$D$E$-(B)} |
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| \begin{itemize} |
\begin{itemize} |
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| Line 99 OpenXM server $B$H$7$F<B8=(B |
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| Line 102 OpenXM server $B$H$7$F<B8=(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B3+H/$NNr;K(B : ---1994} |
\fbox{\bf $B3+H/$NNr;K(B : ---1994} |
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| \begin{itemize} |
\begin{itemize} |
| \item --1989 |
\item --1989 |
| Line 132 $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B |
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| Line 135 $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B3+H/$NNr;K(B : 1994-1996} |
\fbox{\bf $B3+H/$NNr;K(B : 1994-1996} |
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| \begin{itemize} |
\begin{itemize} |
| \item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B |
\item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B |
| Line 159 $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B |
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| Line 162 $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B3+H/$NNr;K(B : 1996-1998} |
\fbox{\bf $B3+H/$NNr;K(B : 1996-1998} |
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| \begin{itemize} |
\begin{itemize} |
| \item $BJ,;67W;;5!G=$N<BAu(B |
\item $BJ,;67W;;5!G=$N<BAu(B |
| Line 190 Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B |
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| Line 193 Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B |
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| $BM-8BBN>e$NBJ1_6J@~$NM-M}E@8D?t7W;;MQ(B |
$BM-8BBN>e$NBJ1_6J@~$NM-M}E@8D?t7W;;MQ(B |
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|
| --- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t(B |
--- $B$3$N%W%m%0%i%`$O%U%j!<$G$O$J$$$,(B, $B4X78$9$k4X?t$O%U%j!<(B |
| $B$O%U%j!<(B |
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| \end{itemize} |
\end{itemize} |
| \end{itemize} |
\end{itemize} |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B3+H/$NNr;K(B : 1998-2000} |
\fbox{\bf $B3+H/$NNr;K(B : 1998-2000} |
| \begin{itemize} |
\begin{itemize} |
| \item OpenXM |
\item OpenXM |
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| Line 221 Visual C++ $B$G5-=R(B |
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| Line 223 Visual C++ $B$G5-=R(B |
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| \item $F_4$ $B$N;n83<BAu(B |
\item $F_4$ $B$N;n83<BAu(B |
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|
| \begin{itemize} |
\begin{itemize} |
| \item [Faug\`ere]$B$K=`5r$7$F5-=R(B |
\item $BO@J8(B [Faug\`ere] $B$K=`5r$7$F5-=R(B |
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| \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B |
\item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B |
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| Line 231 Visual C++ $B$G5-=R(B |
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| Line 233 Visual C++ $B$G5-=R(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B3+H/$NNr;K(B : 2000-current} |
\fbox{\bf $B3+H/$NNr;K(B : 2000-current} |
| \begin{itemize} |
\begin{itemize} |
| \item $B%*!<%W%s%=!<%92=(B |
\item $B%*!<%W%s%=!<%92=(B |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B |
\item $BLnO$$,IY;NDL8&$h$j?@8MBg$K0\@R(B |
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|
| Started Kobe branch $B$N%9%?!<%H(B |
Kobe branch $B$N%9%?!<%H(B |
| \end{itemize} |
\end{itemize} |
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|
| \item OpenXM |
\item OpenXM |
| Line 263 $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B |
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| Line 265 $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B |
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| \end{slide} |
\end{slide} |
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|
| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B@-G=(B --- $B0x?tJ,2r(B} |
\fbox{\bf $B@-G=(B --- $B0x?tJ,2r(B} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item 10 $BG/A0(B |
\item 10 $BG/A0(B |
| Line 285 REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B |
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| Line 287 REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B} |
\fbox{\bf $B@-G=(B --- $B%0%l%V%J4pDl4XO"5!G=(B} |
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| \begin{itemize} |
\begin{itemize} |
| \item 8 $BG/A0(B |
\item 8 $BG/A0(B |
| Line 294 REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B |
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| Line 296 REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B |
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| \item 7 $BG/A0(B |
\item 7 $BG/A0(B |
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| Rather trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere' $B$N(B Gb $B$K$O(B |
Trace lifting $B$K$h$j9b@-G=$@$C$?$,(B, Faug\`ere $B$N(B Gb $B$K$O(B |
| $BIi$1$F$$$?(B |
$BIi$1$F$$$?(B |
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| $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B |
$B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B |
| Line 315 Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B |
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| Line 317 Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B |
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| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$BBg5,LO7W;;$X$NBP1~(B} |
\fbox{\bf $BBg5,LO7W;;$X$NBP1~(B} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B |
\item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B |
| Line 329 Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B |
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| Line 331 Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B |
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| \item OpenXM $B$K$h$kJ,;67W;;(B |
\item OpenXM $B$K$h$kJ,;67W;;(B |
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|
| \begin{itemize} |
\begin{itemize} |
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\item $B$5$^$6$^$J%?%$%W$NJBNs7W;;$KBP1~(B |
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OX-RFC100, 101 : client-server $B7?(B (OX-RFC100, 101) |
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OX-RFC102 : server-server $BDL?.(B, collective operation |
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| \item $BJBNs2=$K$h$kBf?t8z2L(B |
\item $BJBNs2=$K$h$kBf?t8z2L(B |
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| \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B |
\item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B |
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$B7W;;NL$K$h$k8zN($NDjNLE*Hf3S$,$G$-$J$$>l9g(B |
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$B3d$j9~$_$K$h$kCfCG(B, $BI|5"$,MF0W(B |
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$\Rightarrow$ $B%G!<%?$rJ];}$7$?$^$^7W;;$,B39T$G$-$k(B |
| \end{itemize} |
\end{itemize} |
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| \end{itemize} |
\end{itemize} |
| \end{slide} |
\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B1~MQ;vNc(B} |
\fbox{\bf $B1~MQ;vNc(B} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B |
\item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B [IKNY] |
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| $BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B |
$BM-8BBN>e$NB?9`<00x?tJ,2r$N1~MQ(B |
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| \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B |
\item $D$-$B2C72$K$*$1$k<o!9$N7W;;(B |
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|
| de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, $D$-$B2C72$N@)8B(B, $B%F%s%=%k@Q(B |
de Rham $B%3%[%b%m%8!<(B, $BBe?tE*6I=j%3%[%b%m%8!<(B, $D$-$B2C72$N@)8B(B, $B%F%s%=%k@Q(B |
| $B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B) |
$B7W;;$K$*$$$F(B, $BB?9`<00x?tJ,2r(B, $B=`AGJ,2r(B, $b$-$B4X?t7W;;$rC4Ev(B (OpenXM $B7PM3(B) |
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| \item $BBe?tJ}Dx<07O$N5a2r(B |
\item $BBe?tJ}Dx<07O$N5a2r(B |
| Line 356 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
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| Line 370 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
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| $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B |
$BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B |
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| $BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B |
$BBPOCE*%7%9%F%`$N%P%C%/%(%s%I$GBe?tJ}Dx<05a2r(B($B%0%l%V%J4pDl7W;;(B) |
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| \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B |
\item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B |
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| Line 365 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
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| Line 379 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
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| $B2~JQ$b2DG=(B |
$B2~JQ$b2DG=(B |
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|
| \end{itemize} |
\end{itemize} |
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\end{slide} |
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| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B8=:_3+H/Cf$N5!G=(B} |
\fbox{\bf $B8=:_3+H/Cf(B($BM=Dj(B)$B$N5!G=(B} |
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|
| \begin{itemize} |
\begin{itemize} |
| \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B |
\item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B |
| Line 385 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
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| Line 400 de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, |
|
| \begin{itemize} |
\begin{itemize} |
| \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B |
\item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B |
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| \item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k%G!<%?=hM}$,2DG=$J$h$&$K(B |
\item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k(B flexible $B$J(B |
| $BFbItI=8=$r3HD%Cf(B |
$B%G!<%?=hM}$,2DG=$J$h$&$KFbItI=8=$r3HD%Cf(B |
| \end{itemize} |
\end{itemize} |
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\item $B2C72BP1~(B |
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\begin{itemize} |
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\item $BEvA3$"$C$F$7$+$k$Y$-$J$N$K$J$+$C$?(B |
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Buchberger $B%"%k%4%j%:%`$OMF0W(B, $B<+M3J,2r$OBgJQ(B |
| \end{itemize} |
\end{itemize} |
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\item $B@~7ABe?t(B |
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\begin{itemize} |
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\item $B8=>u$O$"$^$j$KIO<e(B. $B$7$+$7(B, $B9-HO0O$NF~NO$KBP1~$9$k$N$OFq$7$$(B. |
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\end{itemize} |
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\end{itemize} |
| \end{slide} |
\end{slide} |
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\begin{slide}{} |
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\fbox{\bf RUR $B7W;;$*$h$SAH$_9~$_%G%P%C%,;HMQK!$NNc(B } |
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$BJ}Dx<0(B : $\{f_1(x_1,\ldots,x_n)=0, \ldots, f_m(x_1,\ldots,x_n)=0\}$ |
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lex $B=g=x%0%l%V%J4pDl(B : $\{g_1(x_1)=0, x_2 = h_2(x_1),\ldots, |
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x_n=h_n(x_1)\}$ |
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RUR : $\{g_1(x_1)=0, x_2 = {g_2(x_1) \over g'_1(x_1)},\ldots, |
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x_n={g_n(x_1) \over g'_1(x_1)}\}$ |
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$\Rightarrow$ $g_i$ $B$N78?t(B $<<$ $h_i$ $B$N78?t(B |
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$B4JC1$JLdBj(B (Katsura-N) $B$G<B:]$KHf3S(B |
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+ $B7W;;ESCf$N3d$j9~$_$+$i%G%P%C%0%b!<%I$X$N0\9T(B, $BJQ?t$NFbMF(B |
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$B$NI=<($N%G%b(B |
| \end{slide} |
\end{slide} |
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|
| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ } |
\fbox{\bf $BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ } |
| |
|
| \begin{verbatim} |
\begin{verbatim} |
| /* competitive Gbase computation over GF(M) */ |
/* competitive Gbase computation over GF(M) */ |
| Line 420 def grvsf4(G,V,M,O) |
|
| Line 464 def grvsf4(G,V,M,O) |
|
| \end{slide} |
\end{slide} |
| |
|
| \begin{slide}{} |
\begin{slide}{} |
| \fbox{$B;29MJ88%(B} |
\fbox{\bf $BF~<jJ}K!(B : $BF?L>(B CVS} |
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|
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$B>r7o(B : CVS $B$,%$%s%9%H!<%k:Q(B ({\tt http://www.cvshome.org/} $B$+$iF~<j2DG=(B) |
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$B:G=i$O%Q%9%o!<%IEPO?$,I,MW(B |
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|
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\begin{verbatim} |
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% setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs |
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% cvs login |
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\end{verbatim} |
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$B%Q%9%o!<%I(B : anoncvs $\Rightarrow$ {\tt \$HOME/.cvspass} |
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\begin{verbatim} |
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% setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs |
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% cvs checkout OpenXM OpenXM_contrib OpenXM_contrib2 |
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\end{verbatim} |
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|
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$B$3$l$G(B, {\tt OpenXM}, {\tt OpenXM\_contrib}, {\tt OpenXM\_contrib2} |
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$B$,$G$-$k(B |
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\end{slide} |
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|
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\begin{slide}{} |
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\fbox{\bf $B;29MJ88%(B} |
| |
|
| [Bernardin] L. Bernardin, On square-free factorization of |
[Bernardin] L. Bernardin, On square-free factorization of |
| multivariate polynomials over a finite field, Theoretical |
multivariate polynomials over a finite field, Theoretical |
| Computer Science 187 (1997), 105-116. |
Computer Science 187 (1997), 105-116. |
| Line 432 Computer Science 187 (1997), 105-116. |
|
| Line 500 Computer Science 187 (1997), 105-116. |
|
| A new efficient algorithm for computing Groebner bases ($F_4$), |
A new efficient algorithm for computing Groebner bases ($F_4$), |
| Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88. |
Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88. |
| |
|
| [Hoeij] M. van Heoij, Factoring polynomials and the knapsack problem, |
[Hoeij] M. van Hoeij, Factoring polynomials and the knapsack problem, |
| to appear in Journal of Number Theory (2000). |
to appear in Journal of Number Theory (2000). |
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|
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[IKNY] Izu et al. Efficient implementation of Schoof's algorithm, LNCS 1514 |
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(Proc. of ASIACRYPT'98) (1998), 66-79. |
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[Noro] M. Noro, J. McKay, |
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Computation of replicable functions on Risa/Asir. |
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Proc. of PASCO'97, ACM Press (1997), 130-138. |
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|
| [NY] M. Noro, K. Yokoyama, |
[NY] M. Noro, K. Yokoyama, |
| A Modular Method to Compute the Rational Univariate |
A Modular Method to Compute the Rational Univariate |
| Representation of Zero-Dimensional Ideals. |
Representation of Zero-Dimensional Ideals. |
| J. Symb. Comp. {\bf 28}/1 (1999), 243-263. |
J. Symb. Comp. {\bf 28}/1 (1999), 243-263. |
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\end{slide} |
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|
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\begin{slide}{} |
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|
| [Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic |
[Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic |
| local cohomology groups of $D$-modules. |
local cohomology groups of $D$-modules. |
| Advancees in Applied Mathematics, 19 (1997), 61-105. |
Advancees in Applied Mathematics, 19 (1997), 61-105. |
| |
|
| \end{slide} |
|
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|
| \begin{slide}{} |
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| [OpenMath] {\tt http://www.openmath.org} |
[OpenMath] {\tt http://www.openmath.org} |
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|
| [OpenXM] {\tt http://www.openxm.org} |
[OpenXM] {\tt http://www.openxm.org} |
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