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Article #14288

Re: [Summary] r-adic (was: [Q] radix-r notation ?)

#14288
From: Takanori Nagae
Date: Tue, 02 Feb 1993 06:57
43 lines
3152 bytes
In article <NAKANO.93Feb2103624@oscar13.oscar.info.waseda.ac.jp>
    nakano@oscar.info.waseda.ac.jp (K.Nakano) writes:
|In article <1kk95pINN51g@flop.ENGR.ORST.EDU>, 
|takikawm@jade.CS.ORST.EDU (TAKIKAWA MASAMI) writes:
|
|TAKIKAWA> Knuth $@@h@8$O!"(Jradix 2 $@$H$+(J radix r $@$H$+=q$$$F$$$^$9!#$-$C$H(J
|TAKIKAWA> $@H`(J$@$NMQK!$G$O!"L>;l$H$7$F$N(J r $@?JK!$H$$$&$N$O(J radix r $@$H=q$$(J
|TAKIKAWA> $@$F!"7AMF;l!J$H$$$&$h$jL>;l$NO"B3!K(J$@$H$7$F$O!"(Jradix-r $@$H=q$/(J
|TAKIKAWA> $@$s$G$7$g$&!#Nc$($P!"(Jradix-r arithmetic $@$H$+!#(J

$@$"$"$C!%K\Ev$G$9$M(J$@!%(J
Positional notation using base b (alternatively called radix b)...
$@!t(J                        ^^^^$@$J(J$@$<(Ja$@$b(Jthe$@$b$$$i$J$$$s$@!%!%!%$d$C$Q$j7A(J
$@!t(J $@MF;l$_$?$$$J$b$N$J$N$@$m$&$+!%%M%$%F%#%V$N$d$k$3$H$O$h$/$o$+(J$@$i$s!%(J

$@!t(J $@<j85$K$O%3%T!<$7$+$J$/$F=qL>$,@53N$K$o$+$i$J$$$s$G$9$,!$(J
$@!t(J D.E.Knuth: Seminumerical Algorithms, Addison Wesley$@$H$$$&$d$D$G!$(J
$@!t(J $@$?$V$s(JThe art of computer programming$@$H$$$&%7%j!<%:$NFs4,L\$G$9(J$@!%(J 
$@!t(J $@$3$NCf$N(J4.1 Positional number systems$@$H$$$&%;%/%7%g%s$K:\$C$F$^$9!%(J

|$@$J$k$[$I!"(Jradix r$@$H$+(Jradix-r$@$H$$$&=q$-J}$b$G$-$k$s$G$9$M!#(J

$@$J$s$+5,B'@-$,$"$C$?$iCN$j$?$$$G$9$h$M!%(J

|$@$@$C$?$i8l46$+$i$$$($P(J$@KM$O$3$A$i$NJ}$,9%$-$G$9!#!J%^%k%3%`(J
|X$@$_$?$$$G!"$C$FA4A34X78$J$$$+!#<:Ni$7$^$7$?!#(J(^.^;;$@!K(J

$@$&$o$C(J^^;
f(x)$@$H$+(Jsqrt-2$@$H$+$$$$$^$9$b$s$M!%(J

$@$H$3$m$G!$$3$N(JKnuth$@$NK\$b$=$&$J$s$G$9$1$I!$;DG0$J$,$i;d$O(Jr-adic$@$H$$$&(J
$@8@MU$,<B:]$K=q@R$dO@J8$NCf$G;H$o$l$F$$$k$N$r8+$?$3$H$,$J$$$s$G$9$h!%$$(J
$@$m$$$mC5$7$F$O$_$?$s$G$9(J$@$,!%$d$C$Q$j(JKnuth$@$_$?$$$K!$(J

a number system obtained by using the base i-1...

$@$N$h$&$KD9$C$?$i$7$/=q(J$@$/$N$,!vNI$$1Q8l!v$J$N$@$m$&$+!%(J

$@!t(J $@$7$+$7!$(Jby using$@$H(Jby$@$H(Jusing$@$O$$$C$?$$$I$3$,0c$&$s$@$m$&!$$J$I$H9M(J$@$((J
$@!t(J $@=P$9$H@Z$j$,$J$$!%#N#G$b0c$$$=$&!%!%(J
--
   $@1J9>(J $@9'5,(J <nagae@an.isl.titech.ac.jp>
   $@El9)Bg(J $@A|>p(J$@Js9)3X8&5f;\@_(J $@0B5o1!8&(J
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References: <NAKANO.93Feb1190036@oscar13.oscar.info.waseda.ac.jp> <1kk95pINN51g@flop.ENGR.ORST.EDU> <NAKANO.93Feb2103624@oscar13.oscar.info.waseda.ac.jp>

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From: nagae@an.isl.titech.ac.jp (Takanori Nagae)
Newsgroups: fj.sci.math
Subject: Re: [Summary] r-adic (was: [Q] radix-r notation ?)
Message-ID: <NAGAE.93Feb2155752@momo.an.isl.titech.ac.jp>
Date: 2 Feb 93 06:57:52 GMT
References: <NAKANO.93Feb1190036@oscar13.oscar.info.waseda.ac.jp>
 <1kk95pINN51g@flop.ENGR.ORST.EDU>
 <NAKANO.93Feb2103624@oscar13.oscar.info.waseda.ac.jp>
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In-reply-to: nakano@oscar.info.waseda.ac.jp's message of 2 Feb 93 01:36:24 GMT