===================================================================
RCS file: /home/cvs/OpenXM/doc/Papers/jsiamb-noro.tex,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -p -r1.3 -r1.4
--- OpenXM/doc/Papers/jsiamb-noro.tex	2001/10/04 08:30:17	1.3
+++ OpenXM/doc/Papers/jsiamb-noro.tex	2001/10/09 01:44:21	1.4
@@ -1,15 +1,15 @@
-% $OpenXM: OpenXM/doc/Papers/jsiamb-noro.tex,v 1.2 2001/10/04 08:22:20 noro Exp $
+% $OpenXM: OpenXM/doc/Papers/jsiamb-noro.tex,v 1.3 2001/10/04 08:30:17 noro Exp $
 \setlength{\parskip}{10pt}
 
 \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}
 
 \begin{itemize}
 \item $BB?9`<04D$K$*$1$kBg5,LO9bB.7W;;$rL\;X$7$F3+H/(B
 
 \begin{itemize}
 \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}
 
 \item C $B8@8l$K;w$?%f!<%68@8l%$%s%?%U%'!<%9$r$b$D(B.
@@ -22,10 +22,12 @@
 \item $B%*!<%W%s%=!<%9(B
 
 \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 
+
+$\Rightarrow$ 2001 $BG/$h$j(B Kobe branch [Risa/Asir]
 $B$,%9%?!<%H(B
 
-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}
 
 \item OpenXM ((Open message eXchange protocol for Mathematics) $B%$%s%?%U%'!<%9(B
@@ -33,14 +35,13 @@ CVS $B$G:G?7HG$,F~<j2DG=(B ($BF~<jJ}K!$O8e=R(B)
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B<g$J5!G=(B}
+\fbox{\bf $B<g$J5!G=(B}
 
 \begin{itemize}
 \item $BB?9`<0$N4pK\1i;;(B
 
 \begin{itemize}
 \item $B2C8:>h=|(B, GCD, $B=*7k<0(B etc.
-representation
 \end{itemize}
 
 \item $BB?9`<00x?tJ,2r(B
@@ -60,11 +61,13 @@ representation
 
 \item 0 $B<!85%$%G%"%k$N(B change of ordering/RUR [Rouillier]
 
-\item $B=`AG%$%G%"%kJ,2r(B
+$BBe?tJ}Dx<0$N2r$r(B, $B0lJQ?tB?9`<0$N:,$GI=$9(B
 
+\item $B=`AG%$%G%"%kJ,2r(B [SY]
+
 $BB?JQ?tBe?tJ}Dx<07O$N2r$NJ,2r$rM?$($k(B
 
-\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]
 
 $b$-$B4X?t(B : $BB?9`<0$NNmE@$G$"$kD66JLL$NITJQNL(B
 
@@ -74,7 +77,7 @@ $D$-$B2C72$K$*$1$k7W;;$N(B, $BM-8B<!85$N@~7ABe?t$X$
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B<g$J5!G=(B ($B$D$E$-(B)}
+\fbox{\bf $B<g$J5!G=(B ($B$D$E$-(B)}
 
 \begin{itemize}
 
@@ -99,7 +102,7 @@ OpenXM server $B$H$7$F<B8=(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B3+H/$NNr;K(B : ---1994}
+\fbox{\bf $B3+H/$NNr;K(B : ---1994}
 
 \begin{itemize}
 \item --1989
@@ -132,7 +135,7 @@ $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B3+H/$NNr;K(B : 1994-1996}
+\fbox{\bf $B3+H/$NNr;K(B : 1994-1996}
 
 \begin{itemize}
 \item $B%P%$%J%jHG$rIY;NDL$h$j8x3+(B
@@ -159,7 +162,7 @@ $\Rightarrow$ trace lifting [Traverso] $B$N<BAu(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B3+H/$NNr;K(B : 1996-1998}
+\fbox{\bf $B3+H/$NNr;K(B : 1996-1998}
 
 \begin{itemize}
 \item $BJ,;67W;;5!G=$N<BAu(B
@@ -197,7 +200,7 @@ Faug\`ere $B$N(B FGb : $B$3$N7W;;$r(B 53 $BIC$G<B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B3+H/$NNr;K(B : 1998-2000}
+\fbox{\bf $B3+H/$NNr;K(B : 1998-2000}
 \begin{itemize}
 \item OpenXM
 
@@ -220,7 +223,7 @@ Visual C++ $B$G5-=R(B
 \item $F_4$ $B$N;n83<BAu(B
 
 \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
 
 \item $GF(p)$ $B>e(B : $B$J$+$J$+$h$$(B
 
@@ -230,7 +233,7 @@ Visual C++ $B$G5-=R(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B3+H/$NNr;K(B : 2000-current}
+\fbox{\bf $B3+H/$NNr;K(B : 2000-current}
 \begin{itemize}
 \item $B%*!<%W%s%=!<%92=(B
 
@@ -262,7 +265,7 @@ $b$-$B4X?t$r:G>.B?9`<0$H$7$F%b%8%e%i7W;;(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B@-G=(B --- $B0x?tJ,2r(B}
+\fbox{\bf $B@-G=(B --- $B0x?tJ,2r(B}
 
 \begin{itemize}
 \item 10 $BG/A0(B
@@ -284,7 +287,7 @@ REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
 \end{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}
 
 \begin{itemize}
 \item 8 $BG/A0(B
@@ -293,7 +296,7 @@ REDUCE, Mathematica $B$KHf$Y$F9b@-G=$@$C$?(B
 
 \item 7 $BG/A0(B
 
-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
 
 $B$7$+$7(B, $B@F<!2=$H$NAH9g$;$K$h$j(B, $B$h$j9-$$HO0O$NF~NO$KBP$7$F%0%l%V%J(B
@@ -314,7 +317,7 @@ Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$BBg5,LO7W;;$X$NBP1~(B}
+\fbox{\bf $BBg5,LO7W;;$X$NBP1~(B}
 
 \begin{itemize}
 \item $B%0%l%V%J4pDl7W;;Cf$K@8@.$5$l$?4pDl$r%G%#%9%/$KJ]B8(B
@@ -328,16 +331,28 @@ Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
 \item OpenXM $B$K$h$kJ,;67W;;(B
 
 \begin{itemize}
+\item $B$5$^$6$^$J%?%$%W$NJBNs7W;;$KBP1~(B
+
+OX-RFC100, 101 : client-server $B7?(B (OX-RFC100, 101)
+
+OX-RFC102 : server-server $BDL?.(B, collective operation
+
 \item $BJBNs2=$K$h$kBf?t8z2L(B
 
 \item $BJ#?t$N%"%k%4%j%:%`$N6%AhE*<B9T$,MF0W(B
+
+$B7W;;NL$K$h$k8zN($NDjNLE*Hf3S$,$G$-$J$$>l9g(B
+
+$B3d$j9~$_$K$h$kCfCG(B, $BI|5"$,MF0W(B
+
+$\Rightarrow$ $B%G!<%?$rJ];}$7$?$^$^7W;;$,B39T$G$-$k(B
 \end{itemize}
 
 \end{itemize}
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B1~MQ;vNc(B}
+\fbox{\bf $B1~MQ;vNc(B}
 
 \begin{itemize}
 \item $BBJ1_6J@~0E9f%Q%i%a%?@8@.(B [IKNY]
@@ -346,7 +361,7 @@ Singular [Singular] $B$OB?9`<0$N8zN($h$$I=8=$K$h$j(B
 
 \item $D$-$B2C72$K$*$1$k<o!9$N7W;;(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
+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)
 
 \item $BBe?tJ}Dx<07O$N5a2r(B
@@ -355,7 +370,7 @@ de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
 
 $BL$Dj78?tK!$K$h$k2D@QJ,7O$N7hDj(B
 
-$BBPOCE*%7%9%F%`$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)
 
 \item $B%"%k%4%j%:%`<BAu<B83%D!<%k(B
 
@@ -364,9 +379,10 @@ de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
 $B2~JQ$b2DG=(B
 
 \end{itemize}
+\end{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}
 
 \begin{itemize}
 \item $BM-8BBN>e$NB?JQ?tB?9`<0$N0x?tJ,2r(B, $BM-8BBN>e$N=`AGJ,2r(B
@@ -384,17 +400,46 @@ de Rham $B%3%[%b%m%8(B, $BBe?tE*6I=j%3%[%b%m%8(B, 
 \begin{itemize}
 \item $B8=>u$G$O(B, $B2D49B?9`<04D0J30$N%G!<%?$N<+A3$J<h$j07$$$,:$Fq(B
 
-\item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k%G!<%?=hM}$,2DG=$J$h$&$K(B
-$BFbItI=8=$r3HD%Cf(B
+\item $B0[<o%7%9%F%`$H$N%G!<%?8r49(B, $B%f!<%6$K$h$k(B flexible $B$J(B
+$B%G!<%?=hM}$,2DG=$J$h$&$KFbItI=8=$r3HD%Cf(B
 \end{itemize}
 
+\item $B2C72BP1~(B
+
+\begin{itemize}
+\item $BEvA3$"$C$F$7$+$k$Y$-$J$N$K$J$+$C$?(B
+
+Buchberger $B%"%k%4%j%:%`$OMF0W(B, $B<+M3J,2r$OBgJQ(B
 \end{itemize}
+
+\item $B@~7ABe?t(B
+\begin{itemize}
+\item $B8=>u$O$"$^$j$KIO<e(B. $B$7$+$7(B, $B9-HO0O$NF~NO$KBP1~$9$k$N$OFq$7$$(B.
+\end{itemize}
+\end{itemize}
 \end{slide}
 
+\begin{slide}{}
+\fbox{\bf RUR $B7W;;$*$h$SAH$_9~$_%G%P%C%,;HMQK!$NNc(B }
+
+$BJ}Dx<0(B : $\{f_1(x_1,\ldots,x_n)=0, \ldots, f_m(x_1,\ldots,x_n)=0\}$
+
+lex $B=g=x%0%l%V%J4pDl(B : $\{g_1(x_1)=0, x_2 = h_2(x_1),\ldots,
+x_n=h_n(x_1)\}$
+
+RUR : $\{g_1(x_1)=0, x_2 = {g_2(x_1) \over g'_1(x_1)},\ldots,
+x_n={g_n(x_1) \over g'_1(x_1)}\}$
+
+$\Rightarrow$ $g_i$ $B$N78?t(B $<<$ $h_i$ $B$N78?t(B
+
+$B4JC1$JLdBj(B (Katsura-N) $B$G<B:]$KHf3S(B
+
++ $B7W;;ESCf$N3d$j9~$_$+$i%G%P%C%0%b!<%I$X$N0\9T(B, $BJQ?t$NFbMF(B
+$B$NI=<($N%G%b(B
 \end{slide}
 
 \begin{slide}{}
-\fbox{$BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }
+\fbox{\bf $BJ,;67W;;$NNc(B --- $F_4$ vs. $Buchberger$ }
 
 \begin{verbatim}
 /* competitive Gbase computation over GF(M) */
@@ -419,8 +464,32 @@ def grvsf4(G,V,M,O)
 \end{slide}
 
 \begin{slide}{}
-\fbox{$B;29MJ88%(B}
+\fbox{\bf $BF~<jJ}K!(B : $BF?L>(B CVS}
 
+$B>r7o(B : CVS $B$,%$%s%9%H!<%k:Q(B ({\tt http://www.cvshome.org/} $B$+$iF~<j2DG=(B)
+
+$B:G=i$O%Q%9%o!<%IEPO?$,I,MW(B
+
+\begin{verbatim}
+% setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
+% cvs login
+\end{verbatim}
+
+$B%Q%9%o!<%I(B : anoncvs $\Rightarrow$ {\tt \$HOME/.cvspass} 
+
+\begin{verbatim}
+% setenv CVSROOT :pserver:anoncvs@kerberos.math.kobe-u.ac.jp:/home/cvs
+% cvs checkout OpenXM OpenXM_contrib OpenXM_contrib2
+\end{verbatim}
+
+$B$3$l$G(B, {\tt OpenXM}, {\tt OpenXM\_contrib}, {\tt OpenXM\_contrib2}
+$B$,$G$-$k(B
+
+\end{slide}
+
+\begin{slide}{}
+\fbox{\bf $B;29MJ88%(B}
+
 [Bernardin] L. Bernardin, On square-free factorization of 
 multivariate polynomials over a finite field, Theoretical
 Computer Science 187 (1997), 105-116.
@@ -431,7 +500,7 @@ Computer Science 187 (1997), 105-116.
 A new efficient algorithm for computing Groebner bases  ($F_4$),
 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).
 
 [IKNY] Izu et al. Efficient implementation of Schoof's algorithm, LNCS 1514