Article View: fj.sci.math
Article #14283[Summary] r-adic (was: [Q] radix-r notation ?)
From: K.Nakano
Date: Mon, 01 Feb 1993 10:00
Date: Mon, 01 Feb 1993 10:00
120 lines
6279 bytes
6279 bytes
$BCfLn!w%*%j%s%Q%9!uAaBg$G$9!#(B
On Fri, 29 Jan 1993 02:13:04 GMT,
nakano@oscar.info.waseda.ac.jp (K.Nakano) said:
Nakano> $B!V#2?JK!$O(Bbinary notation$B!"#8?JK!$O(Boctal notation$B!"$N$h$&(B
Nakano> $B$KI=5-$9$k$h$&$G$9!#$3$N4p?t$r(Br$B$H$7$?;~$KF|K\8l$G$O!"(Br$B?JK!(B
Nakano> $B$H$$$&$$$$J}$,$G$-$k$H;W$&$s$G$9$,!"1Q8l$G$O$I$&I=5-$9$k$N(B
Nakano> $B$,@5$7$$$s$G$7$g$&$+!)!W(B
$B$H!"<ALd$7$?$H$3$m!"(B
$B%a!<%k$G!"(B
$B@DLZ$5$s!JAa0pEDBg3XM}9)3XIt?t3X2J;{ED8&5f<<!K(B
$B%K%e!<%9$G!"(B
$B1J9>$5$s!JEl9)Bg(B $BA|>pJs9)3X8&5f;\@_(B $B0B5o1!8&!K(B
$B0f>e$5$s!JBg:eI\N)9b@l!K(B
$B$K!"%j%W%i%$!C%U%)%m!<$7$F$$$?$@$-$^$7$?!#(B
$B$"$j$,$H$&$4$6$$$^$7$?!#(B
$B7k6I!"(Br-adic$B$G!V(Br$B?J$N!"(Br$B?JK!$N!W$H$$$&0UL#$K$J$k$h$&$G$9!#(B
$B$G$b!"$I$&H/2;$9$k$N$+$o$+$i$J$$(B(^_^;;$B$N$G!"$I$J$?$+65$($F(B
$B2<$5$$!#!J$^$?<ALd$7$F$7$^$C$?!#!K(B
$B$H$j$"$($:3:Ev$9$k1Q8l$O$o$+$j$^$7$?$N$G!"%5%^%i%$%:$5$;$F(B
$B$$$?$@$-$^$9!#$H$O$$$C$F$b!"3'$5$s$K$$$?$@$$$?>pJs$rNs5-$7(B
$B$F!"$=$N8e!"D4$Y$F$o$+$C$?$3$H$r<c43IU$12C$($?DxEY$G$9$,!#(B
----------- Summary Start -------------------------------------
g9l002@terada.info.waseda.ac.jp (AOKI Kazumaro) writes:
Aoki> $B@5$7$$$+$I$&$+$OITL@$G$9$,!"(B
Aoki> Neal Koblitz: A Course in Number Theory and Cryptography,
Aoki> pp.1, Springer--Verlag, 1987
Aoki> $B$G$O!"(B
Aoki> An integer n written to the base b is a notation for n of
Aoki> the form (d_{k-1}...d_1d_0)_b.
Aoki> $B$H$$$&I=5-$rMQ$$$F$$$^$9!#(B
Aoki> $B6&N)=PHG$N!V?t3XOB1Q!&1QOB<-E5!W$G$O!"(B
Aoki> a-adic a$B?J$N(B
Aoki> a-adic integer a$B?J@0?t(B
Aoki> $B$H$$$N$b$"$j$^$9!#(B
$B6&N)=PHG!V?t3X1QOB!&OB1Q<-E5!W!J(BISBN(?) 3541-110160-1371$B!K(B
$B$G$9$M!#1J9>$5$s$N5-;v$K$b!V>.>>M&:n@h@8$N<-E5!W$H$7$F=P$F(B
$B$-$^$9$M!#$3$N<-E5$r8+$k$H!"1QOB$NJ}$G!"(B
-adic suf. $B!V(B-$B?J$N!"(B-$B?JK!$N!"!D$rK!$H$9$k!W$N0U!#(B
$BOB1Q$NJ}$G!"(B
-sin $B?J(B -adic
$B$H!"$"$j$^$7$?$N$G!"$3$l$@$J!"$H;W$C$?$o$1$G$9!#(B
$B$?$@$3$N(B-adic$B$H$$$&C18l!J@\Hx<-!K$O!"(BWebster's$B$G$b(BOxford
English Dictionary$B$G$b8+$D$1$k$3$H$,$G$-$^$;$s$G$7$?!#$=$l(B
$B$G$I$&H/2;$9$k$+$o$+$i$J$$$s$G$9$,!"$3$l$C$F$=$s$J$KFC<l$J(B
$BC18l$J$s$G$7$g$&$+!)!d!d$I$J$?$+$4B8CN$NJ}!#(B
In article <NAGAE.93Jan29173933@ipc5.an.isl.titech.ac.jp>,
nagae@an.isl.titech.ac.jp (Takanori Nagae) writes:
Nagae> D. Knuth$B@h@8$O(Bpositional number system$B$J$>$H$$$C$F$^$7$?!%(B
positional notation$B!a0L<h$j5-?tK!!"$H$"$j$^$7$?!#(B
$B4dGH>pJs2J3X<-E5!J(BISBN 4-00-080074-4$B!K(B
Nagae> $B>.>>M&:n@h@8$N<-E5$K$O(Br-adic$B$H$G$F$^$9!%(B
Nagae> r-radix$B$H$+(Br-ary$B$H$+(Br-tuple$B$H$$$&$b$N$"$C$?$h$&$J5$$,$7$^$9!%(B
n-ary relation$B$G(Bn$B9`4X78!"(Bp-ary$B$G(Bp$BCM!"(Bn-tuple$B$G(Bn$BAH!"$H$"$j$^$7$?!#(B
$B4dGH?t3X<-E5!J(BISBN 4-00-080016-7$B!K(B
Nagae> $B!t(B r-radix$B$d(Br-adic$B$@$H(Br$B$,J#AG?t$G$b$$$$$H$3$m$,%_%=$G$9$M!%(B
Nagae> $B!t(B multiple radix arithmetic$B$H$$$&$N$b$"$j$^$7$F!%!%!%(B
Nagae> $B!t(B $B$d$d!%$*$h$S$G$J$$!%(B
Nagae> $B$=$&$$$($P!$(Bnumber system$B$N$3$H$r(Barithmetic$B$H$b$$$&$s$G$9$h$M!%(Bnumber
Nagae> system$B$b(Bcomplex number system$B$H$$$&$H$-$K$OBN(B($B=89g!)(B)$B$N$3$H$i$7$$$7!%(B
Nagae> $B$H$3$m$G!$(Bradix-2 $B$H$$$&$h$&$J=q$-J}$O$"$k$s$G$7$g$&$+!%$b$7$"$k$H$9$l(B
Nagae> $B$P!$(B2-radix$B$NJ}$N$h$&$J5$$,$7$^$9!%(B
$B$=$&$G$9$M!#(Bradix-r$B$H=q$$$F$7$^$C$?$N$O!"!V4p?t(B-1$B$NJd?t!W(B
$B$r(Bradix-minus-one complement$B$H=q$/$H<-=q$K$"$C$?$N$r8+$D$1(B
$B$?$b$N$@$+$i!"!I$J$s$@!"(Bradix$B$N8e$m$K(Br$B$r$D$1$l$P$$$$$s$8$c(B
$B$J$$!I$HAa9gE@$7$?$+$i$@$C$?$N$G$7$?!#(B(^.^;; r$B0l8l$J$N$@$+(B
$B$i!"(Br-radix$B$HA0$K$D$/$N$,Ev$?$jA0$G$9$M!#$?$@(B2-radix$B$N$h$&(B
$B$J=q$-J}$,$"$k$+$I$&$+$O$o$+$j$^$;$s!#(B
Nagae> $B$"$H!$(B2-state$B%^%k%3%U$J$s$H$+$H$+!$(B3-dimensional$B$H$+!%!%!%(B
Nagae> $B!t(B $B:G6a!$(B$\theta$-threshold$B$H$+(Br-radius$B$H$+(Br-connective$B$J$I$H$$$&C18l(B
Nagae> $B!t(B $B$r>!<j$K:n$C$F$$$k$N$G$9$4$/5$$K$J$k!%!%!%(B
$B$H$$$&$o$1$G!";d$NAa9gE@$N$;$$$G$9$+$i!"$*5$$K$J$5$i$:$K!#(B
$B!t$@$C$F%"%a%j%+5"$j$N@hGZ$,!V(Bradix-r$B$G$o$+$k!W$C$F$$$C$F(B
$B!t$/$l$?$b$s$@$+$i!#!J8@$$Lu(B(^.^;;;$B!K(B
In article <1993Jan29.091241.10516@kudpc.kyoto-u.ac.jp>,
f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi) writes:
Inoue> r-adic $B$G$$$$$s$8$c$J$$$+$H;W$&$N$G$9$,!"0c$&$+$bCN$l$^$;$s$M!#(B
$B$H$j$"$($:!"=q$-J*$KI,MW$@$C$?$N$G(Br-adic$B$r;H$&$3$H$G2r7h$7(B
$B$^$7$?!#(B
$B$G!"8e3X$N$?$a$J$s$G$9$,!"$J$s$HFI$s$G$$$i$C$7$c$$$^$9$+!)(B
----------- Summary End -------------------------------------
$B0J>e!"3'$5$s!"$*Ez$($"$j$,$H$&$4$6$$$^$7$?!#(B
$B$*0~MM$GL\E*$O2L$?$9$3$H$,$G$-$?$s$G$9$,!"(B-adic$B$NFI$_J}$b(B
$BCN$j$?$$$N$G!"$4B8CN$NJ}$,$$$i$C$7$c$C$?$i$*CN$i$;2<$5$$!#(B
$B:\$C$F$$$k<-=q$r65$($F$$$?$@$1$k$H$"$j$,$?$$$G$9!JC5$7J}$,(B
$B0-$$$@$1$N$h$&$J5$$,$9$k$1$I!K!#$*4j$$$7$^$9!#(B
--
$BCfLn(B $B7C0l(B $B%*%j%s%Q%98w3X9)6H3t<02q<R(B $B4pAC8&5fIt%=%U%H%&%'%"8&5f<<(B
Tel +81-426-91-7111 Fax +81-426-91-5709
$BAa0pEDBg3X(B $BM}9)3XIt(B $B@.ED!&3^868&5f<<(B [$BEE5$9)3X@l96(B D1]
Tel +81-3-3209-6323 Fax +81-3-3232-3594
_______nakano@oscar.info.waseda.ac.jp__________HCC02247(NIFTY)_______
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X-Google-Language: Japanese,JIS X-Google-Thread: f4956,55136ef391d494c5,start X-Google-Attributes: gidf4956,public X-Google-ArrivalTime: 1993-02-01 02:00:36 PST Newsgroups: fj.sci.math Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!sun-barr!sh.wide!wnoc-tyo-news!toumon!toumon!nakano From: nakano@oscar.info.waseda.ac.jp (K.Nakano) Subject: [Summary] r-adic (was: [Q] radix-r notation ?) X-Nntp-Posting-Host: oscar13.oscar.info.waseda.ac.jp Message-ID: <NAKANO.93Feb1190036@oscar13.oscar.info.waseda.ac.jp> Sender: news@toumon.waseda.ac.jp (News Maintainer) Organization: Narita-Kasahara Lab., Department of Electric Engineering, School of Science and Engineering, WASEDA University Distribution: fj Date: Mon, 1 Feb 1993 10:00:36 GMT Lines: 121