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version 1.3, 2002/12/09 02:09:23 version 1.4, 2002/12/09 04:23:05
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 % $OpenXM: OpenXM/doc/Papers/rims-2002-noro-ja.tex,v 1.2 2002/12/06 09:23:42 noro Exp $  % $OpenXM: OpenXM/doc/Papers/rims-2002-noro-ja.tex,v 1.3 2002/12/09 02:09:23 noro Exp $
 \documentclass[theorem]{jarticle}  \documentclass[theorem]{jarticle}
 %\usepackage{jssac}  %\usepackage{jssac}
 %\topmargin -0.5in  \topmargin -0.5in
 %\oddsidemargin -0.25in  \oddsidemargin 0in
 %\evensidemargin -0.25in  \evensidemargin 0in
 %  %
 %\textwidth 7in  \textwidth 6in
 %\textheight 9in  \textheight 9in
 %\columnsep 0.33in  \columnsep 0.33in
   
 \def\HT{{\rm HT}}  \def\HT{{\rm HT}}
 \def\HC{{\rm HC}}  \def\HC{{\rm HC}}
   \def\GF{{\rm GF}}
 \def\GCD{{\rm GCD}}  \def\GCD{{\rm GCD}}
 \def\tdeg{{\rm tdeg}}  \def\tdeg{{\rm tdeg}}
 \def\pp{{\rm pp}}  \def\pp{{\rm pp}}
Line 281  Hensel $B9=@.$K$*$$$F$O(B, $K[y]/(y^d)$ $B$r(B, $
Line 282  Hensel $B9=@.$K$*$$$F$O(B, $K[y]/(y^d)$ $B$r(B, $
 $BI.<T$NCN$kM#0l$N$b$N$O(B Maple $B$J$N$G(B, Maple $B$HHf3S$r9T$&(B. Maple $B$O(B,  $BI.<T$NCN$kM#0l$N$b$N$O(B Maple $B$J$N$G(B, Maple $B$HHf3S$r9T$&(B. Maple $B$O(B,
 $B$3$N5!G=$K4X$7$F$O(B, kernel $B$K$*$$$F@lMQ$NFC<l$J%G!<%?7?$rB?MQ$7$F(B  $B$3$N5!G=$K4X$7$F$O(B, kernel $B$K$*$$$F@lMQ$NFC<l$J%G!<%?7?$rB?MQ$7$F(B
 $B8zN($r>e$2$F$$$k$?$a(B, $BHf3S$9$k$3$H$O%"%s%U%'%"$G$O$J$$$H9M$($k(B.  $B8zN($r>e$2$F$$$k$?$a(B, $BHf3S$9$k$3$H$O%"%s%U%'%"$G$O$J$$$H9M$($k(B.
   $BNc$H$7$F$O(B, P.S. Wang $B$K$h$k(B, $B<g78?tLdBj$r5/$3$7$d$9$$B?9`<0$N(B
   $BNc(B (Asir $B$N(B {\tt lib/fctrdata} $B$N(B {\tt Wang[1]} $B$+$i(B
   {\tt Wang[15]} $B$rMQ$$$?(B. $B%^%7%s$O(B Athlon 1900+ $B$GC10L$OIC(B,
   $p$ $B$O(B, $B4pACBN$NI8?t$rI=$9(B. $BI=$G(B $N$ $B$O(B 60 $BICBT$C$F$bEz$($,(B
   $B$G$J$$$b$N(B, $F$ $B$O(B, Maple $B$,2?$i$+$NM}M3$G%(%i!<$r=P$7$F(B
   $B7W;;$G$-$J$+$C$?$b$N$rI=$9(B. Asir $B$K$*$$$F(B $p(n)$ $B$O(B, $n$ $B<!3HBg(B,
   $B$9$J$o$A(B $\GF(p^n)$ $B>e$G0x?tJ,2r$r9T$C$?$3$H$r<($9(B. 8 $BHV$NB?9`<0(B
   $B$N$h$&$KNc30E*$K;~4V$,$+$+$k$b$N$O$"$k$,(B, $B$*$*$`$M(B, Asir $B$,(B
   $BNI9%$J%Q%U%)!<%^%s%9$r<($7$F$$$k(B.
   
   \begin{table}[hbtp]
   \begin{center}
   % &  &  &  &  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
   {\normalsize
   \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}
   \caption{$B0x?tJ,2r(B (Maple7)}
   \end{table}
   
   \begin{table}[hbtp]
   \begin{center}
   % &  &  &  &  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
   {\normalsize
   \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}
   \caption{$B0x?tJ,2r(B (Asir)}
   \end{table}
 \section{$B$*$o$j$K(B}  \section{$B$*$o$j$K(B}
   
 $B:#8e$NM=Dj$H$7$F(B, $B<!$N$h$&$J$3$H$r9M$($F$$$k(B.  $B:#8e$NM=Dj$H$7$F(B, $B<!$N$h$&$J$3$H$r9M$($F$$$k(B.
Legend:
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  Added in v.1.4
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