===================================================================
RCS file: /home/cvs/OpenXM/doc/Papers/rims2002-noro.tex,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -p -r1.2 -r1.3
--- OpenXM/doc/Papers/rims2002-noro.tex	2002/12/09 04:23:05	1.2
+++ OpenXM/doc/Papers/rims2002-noro.tex	2003/12/13 12:52:12	1.3
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/doc/Papers/rims2002-noro.tex,v 1.1 2002/12/09 02:09:23 noro Exp $
+% $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
 
@@ -416,24 +416,26 @@ $p$ & 10 & 11 & 12 & 13 & 14 &  15 \\ \hline
 \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}