===================================================================
RCS file: /home/cvs/OpenXM/doc/sci-semi2001/factor-resume.tex,v
retrieving revision 1.1
retrieving revision 1.3
diff -u -p -r1.1 -r1.3
--- OpenXM/doc/sci-semi2001/factor-resume.tex	2001/07/26 07:55:04	1.1
+++ OpenXM/doc/sci-semi2001/factor-resume.tex	2001/07/28 03:31:09	1.3
@@ -1,4 +1,4 @@
-%$OpenXM$
+%$OpenXM: OpenXM/doc/sci-semi2001/factor-resume.tex,v 1.2 2001/07/26 09:19:34 noro Exp $
 \documentclass[12pt]{jarticle}
 %\oddsidemargin -0.25in
 %\evensidemargin -0.25in
@@ -113,7 +113,7 @@ $a^2-4b = t^2$ ($t$ : $B@0?t(B) $B$H$+$1$k$+$I$&$+D
 \end{enumerate}
 
 $B$5$F(B, $BNc$($P(B $f(x) = x^2+11508x+28386587$ $B$r0x?tJ,2r$9$k>l9g(B, $B$I$NJ}K!(B
-$B$,$h$$$@$m$&$+(B. $B@52r$O(B $f(x)=(x+3581)(x+7927)$ $B$@$,(B,
+$B$,$h$$$@$m$&$+(B. $f(x)$ $B$O(B $f(x)=(x+3581)(x+7927)$ $B$HJ,2r$5$l$k$,(B,
 $28386587=3581\cdot 7927$ $B$H$$$&AG0x?tJ,2r$,!V4cNO!W$GJ,$+$k?M$OB?J,>/(B
 $B$J$$$H;W$&(B. $B<B:](B, $BB?9`<0$N0x?tJ,2r$KHf$Y$F(B, $B@0?t$NAG0x?tJ,2r$N$[$&$,$O(B
 $B$k$+$K:$Fq$JLdBj$G$"$k(B. $B$^$?(B, $BAG0x?tJ,2r$,4JC1$G$b(B, $BAG0x?t$,B?$9$.$k$H(B, 
@@ -151,8 +151,6 @@ $(a^2-4b)/4 = 4717584$ $B$,(B $2172^2$ $B$G$"$k$3$H
 $B$3$l$+$i=R$Y$kJ}K!$O(B, $B0x;R$N7A(B ($B<!?t(B)$B$r2>Dj$7$F(B, $B$=$N78?t$r6a;w$K(B
 $B$h$j5a$a$F$$$/J}K!$G$"$k(B. $B$3$N>l9g$K;X?K$H$J$k86M}$O(B
 $B!V@0?t(B $m$ $B$,(B 0 $\Leftrightarrow$ $m$ $B$O$I$s$J@0?t$G$b3d$j@Z$l$k!W(B
-$B$"$k$$$O(B
-$B!V@0?t(B $m$ $B$,(B 0 $\Leftrightarrow$ $m$ $B$O==J,Bg$-$$@0?t$G3d$j@Z$l$k!W(B
 $B$H$$$&$b$N$G$"$k(B. $B$3$l$rMQ$$$F(B, $B$?$H$($P(B
 
 \begin{enumerate}
@@ -164,7 +162,7 @@ $h_1$ $B$r8+$D$1$k(B. 
 
 \item $g_1$, $h_1$ $B$,@52r$KBP1~$7$F$$$l$P(B, $BE,Ev$J(B $k$ $B$N$H$3$m$G$[$s$H$K3d$j@Z$l$k$@$m$&(B. 
 \end{enumerate}
-$B$H$$$&%?%$%W$N%"%k%4%j%:%`$r9=@.$9$k$N$G$"$k(B. $B8@$$$+$($k$H<!$N$h$&$K$J$k(B. 
+$B$H$$$&%?%$%W$N%"%k%4%j%:%`$r9=@.$9$k(B. $B8@$$$+$($k$H<!$N$h$&$K$J$k(B. 
 $B0J2<(B, $B4JC1$N$?$a(B $f(x)$ $B$*$h$S$=$N0x;R$N78?t$OA4$F@5$G$"$k$H$9$k(B. 
 $B$^$:(B, $f(x)$ $B$N3F78?t$r(B $p$-$B?J?t$GI=$7(B, $B3F(B $p^k$ $B$4$H$K$^$H$a$F(B
 $$f(x) = a_0(x)+p \cdot a_1(x)+p^2\cdot a_2(x)+\cdots$$
@@ -250,9 +248,9 @@ $tr \equiv 2 \bmod 3$}\\
 \noindent
 $B$r0UL#$9$k$,(B, $B$3$l$i$O%Z%"$H$7$F$OF1$8$b$N$G$"$k(B.
 $b_0=x^2+1$, $c_0=x^2+x+2$ $B$H$9$k$H3N$+$K(B
-$$f \equiv b_0c_0 \bmod 3$$ $B$,@.$jN)$D(B. 
+$f \equiv b_0c_0 \bmod 3$ $B$,@.$jN)$D(B. 
 $B$b$H$N<0$KLa$k$H(B, 
-$$gh \equiv (b_0+3b_1)(c_0+3c_1) \equiv 3^2$$ $B$h$j(B
+$$gh \equiv (b_0+3b_1)(c_0+3c_1) \bmod 3^2$$ $B$h$j(B
 $$f-gh \equiv a_0-b_0c_0+3(a_1-(c_0b_1+b_0c_1)) \bmod 3^2$$
 $a_0\equiv b_0c_0 \bmod 3$ $B$h$jN>JU$r(B 3 $B$G3d$k$H(B
 $$(f-gh)/3 \equiv (a_0-b_0c_0)/3+(a_1-(c_0b_1+b_0c_1)) \bmod 3$$$B$5$F(B, 
@@ -282,12 +280,21 @@ $2r+t \equiv 0 \bmod 3$}\\
 
 \noindent
 $B$3$l$G(B $$f \equiv (b_0+3b_1)(c_0+3c_1) \bmod 3^2$$ $B$H$J$k(B $b_1$, $c_1$
-$B$,5a$^$C$?$3$H$K$J$k(B. $B0J2<F1MM$K(B $$b_i = qx+r, c_i = sx+t$$ 
+$B$,5a$^$C$?$3$H$K$J$k(B. $B<!$O(B $a_2$, $b_2$, $c_2$ $B$^$G$H$C$F(B $\bmod 3^3$ $B$G8+$H(B, 
+$$f \equiv a_0+3a_1+3^2a_2 \equiv (b_0+3b_1+3^2b_2)(c_0+3c_1+3^2c_2) \bmod 3^3$$
+$B$h$j(B	
+$$((a_0+3a_1)-(b_0+3b_1)(c_0+3c_1))+3^2(a_2-(c_0b_2+b_0c_2)) \equiv 0 \bmod 3^3$$
+($3^3$ $B$G3d$j@Z$l$k9`$O<N$F$?(B.) $B@hF,ItJ,$O(B $3^2$ $B$G3d$j@Z$l$k$N$G(B,
+$BN>JU$r(B $3^2$ $B$G3d$k$H(B
+$$((a_0+3a_1)-(b_0+3b_1)(c_0+3c_1))/3^2+(a_2-(c_0b_2+b_0c_2)) \equiv 0 \bmod 3$$
+$b_2 = qx+r, c_2 = sx+t$ $B$H$*$/$H(B, $k=1$ $B$HF1MM$N(B $(q,r,s,t)$ $B$NO"N)0l<!(B
+$B9gF1<0$,F@$i$l$k(B. 
+$B0J2<F1MM$K(B $b_i = qx+r, c_i = sx+t$ 
 ($i=2,3,\ldots$) $B$H$*$$$F(B $(q,r,s,t)$ $B$NO"N)0l<!9gF1<0$r=g<!(B
 $B2r$$$F$$$1$P(B
 $$f \equiv (b_0+\ldots+3^{k-1}b_{k-1})(c_0+\ldots+3^{k-1}c_{k-1\
 }) \bmod 3^k$$
-$B$9$J$o$A(B$$f \equiv g_kh_k \bmod 3^k$$ $B$H$J$k(B $g_k$, $h_k$ $B$,7h$^$k(B. 
+$B$9$J$o$A(B$f \equiv g_kh_k \bmod 3^k$ $B$H$J$k(B $g_k$, $h_k$ $B$,7h$^$k(B. 
 \begin{table}[hbtp]
 \label{gh}
 \begin{center}
@@ -424,8 +431,8 @@ $k > 1$ $B$GI,MW$H$J$k(B $v_0$, $w_0$ $B$,B8:_$9$k$
 
 \item $BAw?.B&$O80$G0E9f2=$7(B, $B<u?.B&$O80$GI|9f2=$9$k(B. 
 
-$B80$O0l$D$G0E9f2=(B/$BI|9f2=$K;H$($k(B. $B$b$A$m$s(B, $B0E9f2=$K;H$C$?80$r;}$C$F$$(B
-$B$J$1$l$PI|9f$G$-$J$$$h$&$J0E9fJ}<0$rMQ$$$F$$$k$H$9$k(B. $B$3$N$h$&$J0E9f$O(B
+$B80$O0l$D$G0E9f2=(B/$BI|9f2=$K;H$&(B. $B$b$A$m$s(B, $B0E9f2=$K;H$C$?80$r;}$C$F$$(B
+$B$J$1$l$PI|9f$G$-$J$$$h$&$J0E9fJ}<0$rMQ$$$k(B. $B$3$N$h$&$J0E9f$O(B
 $B6&DL800E9f$H8F$P$l$k(B.
 \end{enumerate}
 $B$3$3$GLdBj$,0l$D$"$k(B. $B0E9f2=$5$l$F$$$J$$(B, $BE{H4$1$NDL?.O)$r;H$C$F(B
@@ -517,7 +524,7 @@ Knuth, D.E., The Art of Computer Programming, Vol. 2.
 Seminumerical Algorithms, Third ed. Addison-Wesley (1998).
 
 \bibitem{NORO}
-$BLnO$(B $B@59T(B, $B7W;;5!Be?t(B. Rokko Lectures in Mathematics 9, $B?@8MBg3XM}3XIt(B
+$BLnO$(B, $B7W;;5!Be?t(B. Rokko Lectures in Mathematics 9, $B?@8MBg3XM}3XIt(B
 $B?t3X65<<(B (2001).
 
 \bibitem{ASIR}
@@ -533,7 +540,43 @@ Seminumerical Algorithms, Third ed. Addison-Wesley (19
 $B$b>\$7$/=R$Y$F$$$k(B. $BB>$NJ88%$K$D$$$F$O(B, $B$3$l$i$NK\$NJ88%I=$r;2>H$7$F$[(B
 $B$7$$(B.  \cite{ASIR} $B$O%U%j!<$J7W;;5!Be?t%7%9%F%`(B($B?t<0=hM}%7%9%F%`(B)$B$G(B,
 \cite{NORO} $B$K=q$+$l$?%"%k%4%j%:%`$O$[$\<BAu$5$l$F$$$k(B. $B<B:]$K$I$NDxEY(B
-$B;H$$$b$N$K$J$k$+;n$7$F$_$F$[$7$$(B.
+$B;H$$$b$N$K$J$k$+;n$7$F$_$F$[$7$$(B.\\
 
+\noindent
+{\large\bf $BG[I[(B CD $B$K$D$$$F(B}
+\begin{enumerate}
+\item
+Windows $BHG(B Asir $B$K$O%$%s%9%H!<%i$,$"$j$^$;$s(B. $B$$$-$J$j5/F0$G$-$^$9(B.
+Asir $B$r5/F0$9$k$K$O(B, CDROM $B>e$N(B $B%U%)%k%@(B {\tt asir} $B$r3+$-(B,$B$5$i$K(B {\tt
+bin} $B%U%)%k%@$r3+$-(B {\tt asirgui} $B%"%$%3%s$r%@%V%k%/%j%C%/$7$^$9(B.  $B%^(B
+$B%K%e%"%k(B({\tt index.html}), $BF~Lg=q(B({\tt index-asir-book.html})$B$J$I$b(B 
+CDROM $B$K$$$l$F$"$j$^$9(B.  Asir $B$N%[!<%`%Z!<%8$O(B, \\
+{\tt http://www.math.kobe-u.ac.jp/Asir/asir.html} $B$G$9(B. {\tt asirgui} $B$O(B 
+$B%G%9%/%H%C%W$X%3%T!<$9$k$HF0$-$^$;$s(B.  $B%^%$%I%-%e%a%s%H$X$N%3%T!<$O(B($BB?(B
+$BJ,(B)$BBg>fIW$G$9(B.  $B$?$@$7(B {\tt asir} $B%U%)%k%@A4BN$r%3%T!<$9$kI,MW$,$"$j$^(B
+$B$9(B.  ({\tt asirgui} $B$OF|K\8l$N%Q%9L>$,$"$k$H%H%i%V%k$r5/$3$90Y(B.  $B%G%9(B
+$B%/%H%C%W$OF|K\8l$N%Q%9L>$rMxMQ$7$F$$$k(B.)
+
+\item
+Asir $B$O%^%7%sL>$,F|K\8l$N>l9g(B, $BF0:n$,$*$+$7$/$J$j$^$9(B.
+$B<+J,$N%3%s%T%e!<%?$N%^%7%sL>$rD4$Y$k$K$O(B, $B%G%9%/%H%C%W$N(B
+$B%M%C%H%o!<%/%3%s%T%e!<%?%"%$%3%s$r%/%j%C%/$7$F2<$5$$(B.
+LAN $B$K@\B3$5$l$F$$$J$$>l9g$O(B, 1 $BBf$@$1%3%s%T%e!<%?$,I=<($5$l$^$9$,(B,
+$B$=$NL>A0$,<+J,$N%3%s%T%e!<%?$NL>A0$G$9(B.
+
+\item
+CDROM $B>e$N(B {\tt povwin3} $B$r%@%V%k%/%j%C%/$9$k$H(B, ray tracer povray $B$N(B
+$B%$%s%9%H!<%k$,;O$^$j$^$9(B.  povray $B$NF|K\8l$N@bL@=q$H$7$F$O(B, $B%"%9%-!<=P(B
+$BHG6I$N!V(BPOV-Ray $B$G$O$8$a$k%l%$%H%l!<%7%s%0!W(B $B>.<<F|=P<yCx(B 
+(ISBN4-7561-1831-3) $B$,$"$j$^$9(B. \\
+{\tt http://hp.vector.co.jp/authors/VA000449/pov/} $B$r$_$k$H(B povray $B$K$D$$$F(B
+$B$N$$$m$s$J>pJs$rF@$k$3$H$,2DG=$G$9(B.
+
+\item 
+$B?@8MBg3X?t3X65<<$N(B web page $B$KCV$$$F$"$k(B, $B6JLL$N2hA|=8$r<}O?$7$F$"$j$^(B
+$B$9(B.\\
+{\tt web-math-kobe-u} $B%U%)%k%@$r3+$$$?$N$A(B, {\tt index.html} $B$r%@(B
+$B%V%k%/%j%C%/$7$F(B,$BI=<($5$l$?%Z!<%8$N(B Mathematical Diversion $B$r3+$-$^$9!#(B
+\end{enumerate}
 \end{document}