===================================================================
RCS file: /home/cvs/OpenXM/doc/compalg/num.tex,v
retrieving revision 1.1.1.1
retrieving revision 1.3
diff -u -p -r1.1.1.1 -r1.3
--- OpenXM/doc/compalg/num.tex	2000/03/01 02:25:51	1.1.1.1
+++ OpenXM/doc/compalg/num.tex	2000/10/03 01:44:03	1.3
@@ -1,3 +1,4 @@
+%$OpenXM: OpenXM/doc/compalg/num.tex,v 1.2 2000/03/28 02:02:30 noro Exp $
 \chapter{$B@0?t(B}
 
 \section{$B@0?t$NI=8=(B}
@@ -154,6 +155,16 @@ $w_{i+j}$, $c$ $B$,>o$K(B $B$ $B?J(B 1 $B7e$H$J$k
 2 $B7e$N?t$G$"$k(B. $B$h$C$F(B $t_h$, $t_l$ $B$O(B $B$ $B?J(B 1 $B7e$H$J$j(B, $B5"G<E*$K(B,
 $w_{i+j}$, $c$ $B$,>o$K(B $B$ $B?J(B 1 $B7e$H$J$k$3$H$,J,$+$k(B. $B$?$@$7(B, $u_iv_j$ 
 $B$N7W;;$K$OG\@:EY@0?t>h;;$,I,MW$H$J$k(B.
+
+$B$3$N%"%k%4%j%:%`$G$O(B, $BF~NO$N7e?t$N@Q(B $mn$ $B$KHfNc$9$k<j4V$,$+$+$k(B. $B7e?t(B
+$B$NBg$-$$?t$N@Q$N<j4V$r8:$i$99)IW$H$7$F(B Karatsuba $BK!$*$h$S(BFFT $BK!$,$"$k(B. 
+$B$3$l$i$N$&$A(B, $BB?9`<0$K4X$9$k(B Karatsuba $BK!$K$D$$$F$O(BSection \ref{kara} 
+$B$G=R$Y$k$,(B, $B@0?t$KBP$7$F$bA4$/F1MM$N%"%k%4%j%:%`$,E,MQ$G$-$k(B. ($B$ $B?J(B
+$B@0?t$O(B, $B$ $B$K4X$9$kB?9`<0$H$_$J$;$k$3$H$KCm0U(B.)  $B0lHL$K(B, Karatsuba $BK!(B
+$B$O$$$/$i$+$N(B overhead $B$rH<$&$?$a(B, $B<B:]$K$O(B, $B$"$k7e?t(B ($B$7$-$$CM(B)
+$B$r@_Dj$7$F(B, $B$7$-$$CM0J>e$N7e?t$G$O(B Karatsuba $BK!(B, $B$=$l0J2<$G$O$3$3$G=R(B
+$B$Y$?%"%k%4%j%:%`$rE,MQ$9$k$3$H$G(B, $B$5$^$6$^$J7e?t$N?t$KBP$7$F9bB.$J(B
+$B<BAu$,F@$i$l$k(B. 
 
 \section{$B=|;;(B}
 $B@0?t=|;;$b4pK\$OI.;;$HF1MM$G(B, $B>&$N>e0L$N7e$+$i5a$a$F$$$/(B.