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Diff for /OpenXM/doc/compalg/num.tex between version 1.1.1.1 and 1.3

version 1.1.1.1, 2000/03/01 02:25:51 version 1.3, 2000/10/03 01:44:03
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   %$OpenXM: OpenXM/doc/compalg/num.tex,v 1.2 2000/03/28 02:02:30 noro Exp $
 \chapter{$B@0?t(B}  \chapter{$B@0?t(B}
   
 \section{$B@0?t$NI=8=(B}  \section{$B@0?t$NI=8=(B}
Line 154  $$ t=w_{i+j}+u_iv_j+c \le (B-1)+(B-1)^2+B-1 = B^2-1$$
Line 155  $$ t=w_{i+j}+u_iv_j+c \le (B-1)+(B-1)^2+B-1 = B^2-1$$
 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,  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, $u_iv_j$  $w_{i+j}$, $c$ $B$,>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.  $B$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{$B=|;;(B}  \section{$B=|;;(B}
 $B@0?t=|;;$b4pK\$OI.;;$HF1MM$G(B, $B>&$N>e0L$N7e$+$i5a$a$F$$$/(B.  $B@0?t=|;;$b4pK\$OI.;;$HF1MM$G(B, $B>&$N>e0L$N7e$+$i5a$a$F$$$/(B.

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