===================================================================
RCS file: /home/cvs/OpenXM/doc/Papers/rims2002-noro.tex,v
retrieving revision 1.1
retrieving revision 1.3
diff -u -p -r1.1 -r1.3
--- OpenXM/doc/Papers/rims2002-noro.tex	2002/12/09 02:09:23	1.1
+++ OpenXM/doc/Papers/rims2002-noro.tex	2003/12/13 12:52:12	1.3
@@ -1,4 +1,4 @@
-% $OpenXM$
+% $OpenXM: OpenXM/doc/Papers/rims2002-noro.tex,v 1.2 2002/12/09 04:23:05 noro Exp $
 \documentclass{slides}
 \usepackage{color}
 \usepackage{rgb}
@@ -42,7 +42,7 @@
 \fbox{\fbc \large $BL5J?J}J,2r(B ($BI|=,(B)}
 \end{center}
 
-modification of Bernardin's algorithm [Ber97]
+modification of Bernardin's algorithm [1]
 
 $f \in F[x_1,\ldots,x_n]$, $F$ : $BM-8BBN(B $Char(F) = p$
 
@@ -53,7 +53,7 @@ $H=\prod h_k^{c_k}$ 
 $f_i, g_j, h_k$ : $BL5J?J}(B, $B8_$$$KAG(B.
 
 $'$ $B$r(B $d/dx_1$ $B$H$7$F(B
-$f_i' \neq 0$, $p \not{|}a_j$, $p | b_j$, $h_k' = 0$
+$f_i' \neq 0$, $p {\not|}a_j$, $p | b_j$, $h_k' = 0$
 $B$H=q$/$H(B
 
 $f' = F'GH$ $B$9$k$H(B $GCD(f,f') = GCD(F,F')GH$
@@ -190,9 +190,9 @@ $g_0$, $h_0$ $B$N(B $x$ $B$K4X$9$k<g78?t$N7h$aJ}(B
 $BF1MM$K(B $h_0$ $B$KBP$7$F$b(B $\lc_h$ $B$r5a$a$k(B. 
 
 $B$b$7(B, 
-$\lc_x(g_0) \not{|}\, \lc_g(a)$ $B$^$?$O(B $\lc_x(h_0) \not{|}\, \lc_h(a)$
+$\lc_x(g_0) {\not|}\, \lc_g(a)$ $B$^$?$O(B $\lc_x(h_0) {\not|}\, \lc_h(a)$
 $B$^$?$O(B, 
-$\lc_x(f) \not{|}\, \lc_g \cdot \lc_h$
+$\lc_x(f) {\not|}\, \lc_g \cdot \lc_h$
 $B$J$i$P(B, $B$=$l$O(B, $f_a$ $B$N0x;R$NAH9g$;$,@5$7$/$J$$$3$H$r0UL#$9$k$N$G(B, 
 $g_0$, $h_0$ $B$r$H$jD>$9(B. 
 
@@ -238,10 +238,10 @@ Hensel $B9=@.$O(B $\bmod\,  y^d$ $B$G9T$&(B. 
 \fbox{\fbc \large Hensel $B9=@.(B}
 \end{center}
 $f = g_kh_k \bmod (I^{k+1},y^d)$ $B$@$,(B, 
-$B==J,Bg$-$$(B $k$ $B$KBP$7(B $f = g_kh_k$
+$k$ $B==J,Bg(B $\Rightarrow$ $f = g_kh_k$
 
-$u$, $v$ $B$N7W;;(B : Hensel $B9=@.(B
-($g_0(a)|_{y=0}$, $h_0(a)_{y=0}$ $B$,8_$$$KAG(B)
+$u$, $v$ : Hensel $B9=@.(B
+($g_0(a)|_{y=0}$, $h_0(a)|_{y=0}$ $B$,8_$$$KAG(B)
 
 $K[y]$ $B>e$N(B Hensel $B9=@.$O<!$N$h$&$K9T$&(B. 
 
@@ -293,9 +293,9 @@ Asir : $B>.0L?tM-8BBN(B $K$ $B$NBe?t3HBg$rI=8=$9$k7
 
 $K[y]/(m(y))$ $B$H$7$FI=8=(B $\Rightarrow$ $m(y)=y^d$ $B$H$7$FN.MQ(B
 
-$B5U857W;;$K$D$$$F$O(B, 0 $B$G$J$$Dj?t9`$r;}$DB?9`<0$O2D5U(B ($B8_=|K!(B)
+$B5U857W;;(B : $BDj?t9`$,(B 0 $B$G$J$$B?9`<0$O2D5U(B ($B8_=|K!(B)
 
-$\lc_x \neq 0$ $B$h$j(B $K[y]/(y^d)$ $B$,$3$NJ}K!$G$G$-$k(B. 
+$\lc_x(g)$ $B$NDj?t9`(B $\neq 0$ $B$h$j$3$NJ}K!$G7W;;2DG=(B
 
 $BB?JQ?tB?9`<0(B : Hensel $B9=@.$N:G=i$G(B, $B$3$N7?$N78?t$r;}$DB?9`<0$KJQ49(B
 
@@ -307,6 +307,104 @@ $\Rightarrow$ $BDL>o$NB?9`<01i;;$K$h$j(B $K[y]/(y^d)
 
 \begin{slide}{}
 \begin{center}
+\fbox{\fbc \large Timing data (Wang $B$NNc(B)}
+\end{center}
+
+{\tt OpenXM\_contrib2/asir2000/lib/fctrdata} $B$N(B
+
+ {\tt Wang[1],\ldots,Wang[15]} $B$G%F%9%H(B. 
+
+$B%^%7%s(B : Athlon 1900+
+
+Maple7 $B$HHf3S(B --- Maple7 $B$b(B Kernel $B$G=t1i;;$r%5%]!<%H$7$F$$$k$N$G(B, $B%"%s%U%'%"$G$O$J$$$@$m$&(B
+
+$B7k2L(B : $B0lIt(B ({\tt Wang[8]}) $B$r=|$$$FNI9%(B
+\end{slide}
+
+\begin{slide}{}
+\begin{center}
+\fbox{\fbc \large Timing data (Maple7)}
+\end{center}
+
+\begin{center}
+% &  &  &  &  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
+{\small
+\begin{tabular}{c|ccccccccc} \hline
+$p$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
+2 & N & F & F & F & N & N & 0.01 & 1 & 0.01 \\ \hline
+3 & 0.07 & 0.1 & 0.07 & N & 0.4 & N & 0.01 & 0.02 & 0.06 \\ \hline
+5 & N & 0.05 & 0.08 & 3.5 & 0.2 & 0.4 & 0.01 & 0.6 & 0.1 \\ \hline
+7 & 0.08  & 0.1  & 0.1  & 0.25 & 0.6  & 0.5  & 0.02  & 1  & F \\ \hline
+\end{tabular}
+
+\begin{tabular}{c|cccccc} \hline
+$p$ & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline
+2 & F & N & 0.005 & 0.006 & 0.008 & F \\ \hline
+3 & 4 & N & 0.004 & 0.007 & 0.14  & 0.02 \\ \hline
+5 & 0.2  & F  & 0.005 & 0.006 & 0.03  &  0.4 \\ \hline
+7 & 0.6  & 14  & 0.005  & 0.16  & 0.04 & 0.6 \\ \hline
+\end{tabular}
+
+\begin{tabular}{c|ccccccccc} \hline
+$p$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
+547 & 0.2& 0.2& 0.1& 0.3& 1& 1.2& 0.02& 6& F\\ \hline
+32003&  0.2& 0.2&  0.2& 0.4 & 1 & 1 & 0.02 & 4.2 & F  \\ \hline
+99981793 & 0.5 & 0.6 & 0.5 & 3 & 3 & 4.5 & 0.02 & N &  F\\ \hline
+\end{tabular}
+
+\begin{tabular}{c|cccccc} \hline
+$p$ & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline
+547 & 0.9 &3.3  & 0.005 & 0.2 & 0.1 & 0.4  \\ \hline
+32003 & 1.8 & 4.9 &0.006  & 0.3 & 0.1  & 0.4 \\ \hline
+99981793 & 2.6  & 11  & 0.006 & 0.9 & 0.5  & 1.4  \\ \hline
+\end{tabular}
+}
+\end{center}
+\end{slide}
+
+\begin{slide}{}
+\begin{center}
+\fbox{\fbc \large Timing data (Asir)}
+\end{center}
+
+\begin{center}
+% &  &  &  &  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
+{\small
+\begin{tabular}{c|ccccccccc} \hline
+$p$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
+2(5) & 0.003 & 0.003 & 0.004 & 0.01 & 0.02 & 0.05 & 0.001 & 0.01 & 0.0003 \\ \hline
+3(5) & 0.003 & 0.002 & 0.005 & 0.003 & 0.003 & 0.1 & 0.002 & 0.001 & 0.003  \\ \hline
+5(2) & 0.004 & 0.003 & 0.004 & 0.02 & 0.06 & 0.4 & 0.002 & 0.4 & 0.005 \\ \hline
+7(2) & 0.004  & 0.004  & 0.005 & 0.03 & 0.1  & 0.1  & 0.004  & 1.8  & 0.2 \\ \hline
+\end{tabular}
+
+\begin{tabular}{c|cccccc} \hline
+$p$ & 10 & 11 & 12 & 13 & 14 &  15 \\ \hline
+2(5) & 0.03 & 0.07 & 0.0006 & 0.001 & 0.002 & 0.001  \\ \hline
+3(5) & 0.04 & 0.2 & 0.0001  & 0.0005 & 0.02  & 0.001 \\ \hline
+5(2) & 0.01  & 0.2  & 0.001 & 0.001 & 0.004  & 0.01  \\ \hline
+7(2) & 0.02  & 0.6  & 0.001  & 0.007  & 0.005 & 0.01 \\ \hline
+\end{tabular}
+
+\begin{tabular}{c|ccccccccc} \hline
+$p$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
+547 & 0.004 & 0.004 & 0.005 & 0.03 & 0.05 & 0.2 & 0.02& 2& 0.2\\ \hline
+32003 & 0.004  &  0.004 & 0.005  &0.04  &0.07  & 0.2 & 0.004 & 2 & 0.2 \\ \hline
+99981793& 0.004 & 0.004& 0.005 & 0.03 & 0.03 & 0.2 & 0.004 & 4 & 0.2  \\ \hline
+\end{tabular}
+
+\begin{tabular}{c|cccccc} \hline
+$p$ & 10 & 11 & 12 & 13 & 14 &  15 \\ \hline
+547 & 0.04 & 0.3 & 0.001 &0.006  & 0.006 & 0.01  \\ \hline
+32003 & 0.04 &0.2  &0.001  &0.007  & 0.006  & 0.03 \\ \hline
+99981793 & 0.04  & 0.3  &0.001  & 0.008 & 0.008  & 0.01  \\ \hline
+\end{tabular}
+}
+\end{center}
+\end{slide}
+
+\begin{slide}{}
+\begin{center}
 \fbox{\fbc \large $B:#8e$NM=Dj(B}
 \end{center}
 
@@ -318,24 +416,26 @@ $\Rightarrow$ $BDL>o$NB?9`<01i;;$K$h$j(B $K[y]/(y^d)
 \item $BBN$NI8?t$,==J,Bg$-$$>l9g$K(B, $BL5J?J}J,2r$rI8?t(B 0 $B$H(B
 $BF1MM$N(B Hensel $B9=@.$G9T$&$h$&$K$9$k(B. 
 
-\item 2 $BJQ?t$N0x?tJ,2r$K$*$$$F(B, \cite{funny01} $B$G=R$Y$?(B, $BB?9`<0(B
+\item 2 $BJQ?t$N0x?tJ,2r$K$*$$$F(B, [2] $B$G=R$Y$?(B, $BB?9`<0(B
 $B;~4V%"%k%4%j%:%`$r<+F0E*$KA*Br$7$F<B9T$9$k(B. 
 \end{itemize}
 \end{slide}
 
-\end{document}
+\begin{slide}{}
+\begin{center}
+\fbox{\fbc \large $BJ88%(B}
+\end{center}
+[1] Bernardin, L. (1997).
 
-\begin{thebibliography}{99}
-\bibitem{B97-2}
-Bernardin, L. (1997).
 On square-free factorization of multivariate polynomials over a finite
 field.
 {\em Theoret.\ Comput.\ Sci.\/} {\bf 187}, 105--116. 
 
-\bibitem{funny01}
-M. Noro and K. Yokoyama (2002).
+[2] M. Noro and K. Yokoyama (2002).
+
 Yet Another Practical Implementation of Polynomial Factorization
  over Finite Fields.
 Proceedings of ISSAC2002, ACM Press, 200--206.
-\end{thebibliography}
+\end{slide}
+\end{document}