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Diff for /OpenXM/doc/Papers/rims2004-noro-ohp.tex between version 1.1 and 1.2

version 1.1, 2004/12/11 09:12:23 version 1.2, 2005/12/18 13:41:12
Line 157  $\Rightarrow$ $r$ $B$N5U85$r7W;;$9$l$P(B, $h$ $B$N5
Line 157  $\Rightarrow$ $r$ $B$N5U85$r7W;;$9$l$P(B, $h$ $B$N5
 $B8=$o$l$kJQ?t$KBP$9$k4JLs2=$,9T$o$l$J$$$N$G(B, $B0lHL$KBg$-$JB?9`<0(B  $B8=$o$l$kJQ?t$KBP$9$k4JLs2=$,9T$o$l$J$$$N$G(B, $B0lHL$KBg$-$JB?9`<0(B
 $B$,78?t$K8=$o$l$k(B.  $B$,78?t$K8=$o$l$k(B.
   
 \item $h\in (\Q(\alpha_1,\ldots,\alpha_{n-1})[x_n]$ $B$H8+$J$9(B  \item $h\in (\Q(\alpha_1,\ldots,\alpha_{n-1}))[x_n]$ $B$H8+$J$9(B
   
 $B78?t=|;;$,BN1i;;$H$J$j(B, $B5U857W;;$,I,MW$H$J$k(B.  $B78?t=|;;$,BN1i;;$H$J$j(B, $B5U857W;;$,I,MW$H$J$k(B.
 \end{itemize}  \end{itemize}
Line 168  $\Rightarrow$ $r$ $B$N5U85$r7W;;$9$l$P(B, $h$ $B$N5
Line 168  $\Rightarrow$ $r$ $B$N5U85$r7W;;$9$l$P(B, $h$ $B$N5
   
 $BBe?tE*?t$N7W;;$K$O%b%8%e%i!<7W;;$,M-8z(B  $BBe?tE*?t$N7W;;$K$O%b%8%e%i!<7W;;$,M-8z(B
   
 [NORO96], [HOEIJ02]).  ([NORO96], [HOEIJ02]).
   
 \begin{itemize}  \begin{itemize}
 \item $BCf9q>jM>DjM}(B  \item $BCf9q>jM>DjM}(B
Line 209  Hensel lifting (1 step $B$"$?$j(B $O(d^2)$) $B$,(B
Line 209  Hensel lifting (1 step $B$"$?$j(B $O(d^2)$) $B$,(B
   
 \underline{$BDjM}(B}  \underline{$BDjM}(B}
   
 $F = \Q[\alpha_1,\ldots,\alpha_l] = \Q[T]/I$  $F = \Q[\alpha_1,\ldots,\alpha_l] = \Q[T]/I$  ($T=\{t_1,\ldots,t_l\}$)
   
 $I=\langle m_1(t_1),\ldots,m_l(t_1,\ldots,t_l)\rangle$  $I=\langle m_1(t_1),\ldots,m_l(t_1,\ldots,t_l)\rangle$
   
Line 230  $\Rightarrow$ $G=(G_F \setminus \Q[T]) \bmod I$ $B$O
Line 230  $\Rightarrow$ $G=(G_F \setminus \Q[T]) \bmod I$ $B$O
   
 $BDjM}$K$h$j(B, $F$ $B>e$N%0%l%V%J!<4pDl7W;;$O(B $\Q$ $B>e$N$=$l$K5"Ce(B  $BDjM}$K$h$j(B, $F$ $B>e$N%0%l%V%J!<4pDl7W;;$O(B $\Q$ $B>e$N$=$l$K5"Ce(B
   
 $B<B9T$r4Q;!$9$k$H(B $\cdots$ $B@8@.$5$l$kCf4V4pDl$NF,9`$N(B $t$ $BJQ?t$,$@$s$@$s>CLG(B  $B<B9T$r4Q;!$9$k$H(B, $B@8@.$5$l$kCf4V4pDl$NF,9`$N(B $t$ $BJQ?t$,$@$s$@$s>CLG(B
 = $BF,78?t$N5U857W;;$r(B S-$BB?9`<0$HC19`4JLs$G<B9T(B  
   
   $\Rightarrow$ $BF,78?t$N5U857W;;$r(B S-$BB?9`<0$HC19`4JLs$G<B9T(B
   
 $\Rightarrow$ S-$BB?9`<0$N?t$,A}Bg$7$F$$$k(B  $\Rightarrow$ S-$BB?9`<0$N?t$,A}Bg$7$F$$$k(B
   
 $BJ@32(B : $BITE,@Z$J=g=x$G(B S-$BB?9`<0$,=hM}$5$l$k2DG=@-$bA}$($k(B.  $BJ@32(B : $BITE,@Z$J=g=x$G(B S-$BB?9`<0$,=hM}$5$l$k2DG=@-$bA}$($k(B.
Line 314  typedef struct oDAlg {
Line 315  typedef struct oDAlg {
 \begin{itemize}  \begin{itemize}
 \item {\tt nd\_gr} $B$*$h$S(B {\tt nd\_gr\_trace} $B$r2~B$(B  \item {\tt nd\_gr} $B$*$h$S(B {\tt nd\_gr\_trace} $B$r2~B$(B
   
 $BF~NO$K:G>.B?9`<0$rDI2C$7$F<B9T(B + $B@55,7A$N(B monic $B2=(B  $BF~NO(B + $B:G>.B?9`<0$KBP$7<B9T(B + $B@55,7A$N(B monic $B2=(B
 $BF~NO$O(B {\tt Alg} $B7?$r78?t$K4^$`B?9`<0=89g$G$h$$(B.  
   
   $BF~NO$O(B {\tt Alg} $B7?$r78?t$K4^$s$G$h$$(B ($BMW(B monic $B2=(B)
   
 \item $BFbItI=8=(B  \item $BFbItI=8=(B
   
 $BBe?tE*?t$O(B, $B85$NB?9`<0JQ?t$HF1Ey(B, $B@55,2=7W;;$OM-M}?tBN>e$G(B  $BBe?tE*?t$O(B, $B85$NB?9`<0JQ?t$HF1Ey(B, $B@55,2=7W;;$OM-M}?tBN>e$G(B
Line 324  $\Rightarrow$ $B78?t$N(B content $B=|5n$,<+F0E*$KE,
Line 326  $\Rightarrow$ $B78?t$N(B content $B=|5n$,<+F0E*$KE,
   
 \item monic $B2=(B  \item monic $B2=(B
   
 $B$N:]$K$N$_(B, $BK\Mh$N78?t$,Be?tE*?t(B ({\tt DAlg $B7?(B}) $B$H(B  monic $B2=$N:]$K$N$_(B, $BK\Mh$N78?t$,Be?tE*?t(B ({\tt DAlg}$B7?(B) $B$H(B
 $B$7$F<h$j=P$5$l(B, $B5U857W;;$J$I$,9T$o$l$k(B.  $B$7$F<h$j=P$5$l(B, $B5U857W;;$J$I$,9T$o$l$k(B.
   
 \item weight  \item weight
Line 375  f_5&=&((c_2+\omega )c_1+\omega c_5)c_0+c_3c_2c_1+c_4c_
Line 377  f_5&=&((c_2+\omega )c_1+\omega c_5)c_0+c_3c_2c_1+c_4c_
 f_6&=&(c_1+\omega )c_0+c_2c_1+c_3c_2+c_4c_3+c_5c_4+\omega c_5\\  f_6&=&(c_1+\omega )c_0+c_2c_1+c_3c_2+c_4c_3+c_5c_4+\omega c_5\\
 f_7&=&c_0+c_1+c_2+c_3+c_4+c_5+\omega  f_7&=&c_0+c_1+c_2+c_3+c_4+c_5+\omega
 \end{eqnarray*}}  \end{eqnarray*}}
 $Cyc$: cyclic-7 $B$N(B $c_6$ $B$K(B 1 $B$N86;O(B 7 $B>h:,$rBeF~(B  $Cyc$: cyclic-7 $B$N(B $c_6$ $B$K(B 1 $B$N86;O(B 7 $B>h:,(B $\omega$ $B$rBeF~(B
   
 \underline{$\Q(\omega)$ $B>e$G$N(B GB $B7W;;(B}: $B@F<!2=(B trace $B%"%k%4%j%:%`$K$h$j(B 22 $BIC(B  \underline{$\Q(\omega)$ $B>e$G$N(B GB $B7W;;(B}: $B@F<!2=(B trace $B%"%k%4%j%:%`$K$h$j(B 22 $BIC(B
 (monic $B2=$K(B 2.2 $BIC(B ($B5U857W;;(B 0.2$BIC(B))  (monic $B2=$K(B 2.2 $BIC(B ($B5U857W;;(B 0.2$BIC(B))
Line 436  FGLM $B$d(B RUR $B$N7W;;$NBe?tBN>e$X$N3HD%(B
Line 438  FGLM $B$d(B RUR $B$N7W;;$NBe?tBN>e$X$N3HD%(B
   
 $BBe?tBN$NI=8=$r(B {\tt DP} $B$+$i(B, $B$h$j8zN($h$$(B  $BBe?tBN$NI=8=$r(B {\tt DP} $B$+$i(B, $B$h$j8zN($h$$(B
 $B<BAu$KJQ99$9$k(B  $B<BAu$KJQ99$9$k(B
   
   \item Dynamic evaluation
   
   $BI,$:$7$b4{Ls$G$J$$B?9`<0$K$h$k3HBg$r5v$9(B
   
   $\Rightarrow$ $B5U857W;;$K<:GT$9$l$P(B, $B78?t4D$,J,2r$G$-$k(B.
 \end{itemize}  \end{itemize}
   
 \end{slide}  \end{slide}
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