Ruby Forum Ruby-dev > Numeric#scalar?

1.9 $B$N(B Numeric#scalar? $B$K$D$$$F!"E,Ev$G$J$$$N$G$O(B (real? 
$B$J$I$N$[$&$,$$(B
$B$$(B)$B!"$H$N0U8+$,$$$/$D$+$"$j$^$7$?$,!"$I$&$G$7$g$&!#$b$7JQ$($k$J$i:#$N$&(B
$B$A$+$J$H;W$$$^$9!#(B

scalar? $B$O!"(B2005-11-29 [ruby-dev:27871] 
$B$+$i;O$^$C$?5DO@$NCf$GF3F~$,7h(B
$B$^$C$?$h$&$G$9!#(B1.8 $B$K$OF3F~$5$l$F$$$^$;$s!#(B

$B$3$N$h$&$J0UL#$G=R8l$H$7$F(B scalar 
$B$N8l$,$D$+$o$F$$$kNc$O;W$$$D$+$J$+$C(B
$B$?$s$G$9$,!"$H$j$"$($:(B real $B$O!"(BCommon 
Lisp$B!"(BScheme$B!"(BFactor $B$KNc$,$"$j(B
$B$^$9!#(B

$B86$G$9!#(B

Tadayoshi Funaba $B$5$s$O=q$-$^$7$?(B:
> 1.9 $B$N(B Numeric#scalar? $B$K$D$$$F!"E,Ev$G$J$$$N$G$O(B (real? $B$J$I$N$[$&$,$$(B
> $B$$(B)$B!"$H$N0U8+$,$$$/$D$+$"$j$^$7$?$,!"$I$&$G$7$g$&!#$b$7JQ$($k$J$i:#$N$&(B
> $B$A$+$J$H;W$$$^$9!#(B
> 
> scalar? $B$O!"(B2005-11-29 [ruby-dev:27871] $B$+$i;O$^$C$?5DO@$NCf$GF3F~$,7h(B
> $B$^$C$?$h$&$G$9!#(B1.8 $B$K$OF3F~$5$l$F$$$^$;$s!#(B

$B$=$b$=$b$NF3F~$NF05!$,!"?t$NCf$GHf3S2DG=$J$b$N$r6hJL$7$?$$!"(B
$B$H$$$&$3$H$@$C$?$_$?$$$G$9$M!#(B

$B$d$O$j!"(Bscalar? $B$O$:$l$F$$$k$s$8$c$J$$$+$J!#(Breal? 
$B$NJ}$,$$$$(B
$B$H;W$$$^$9!#(B

$B$=$N$b$N$:$P$j!"(Bcomparable? $B$C$F$N$O$I$&$@$m$&!#(B

> $B$d$O$j!"(Bscalar? $B$O$:$l$F$$$k$s$8$c$J$$$+$J!#(Breal? $B$NJ}$,$$$$(B
> $B$H;W$$$^$9!#(B

$B$=$&46$8$^$9!#(B

scalar $B$,$"$l$P!"EvA3(B vector 
$B$b$H$J$j!"$I$C$A$J$N$+!"$H$$$&;v$b$"$j$^$9(B
$B$,!"$=$b$=$b$=$&$$$&;v$rLd$$$?$$$o$1$8$c$J$$$N$G!"$+$J$j0cOB46$,$"$j$^(B
$B$9$M!#<B:]$O!"(Breal 
$B$+$I$&$+CN$j$?$$$s$G$9!#$:$P$j$H8@$($P!"(Breal? $B$8$c$J(B
$B$$$+$H!#(B

$B2>$K!"=hM}7O>e$NI=8=$H$7$F:#$"$k$h$&$JJ#AG?t$H$OJL$K!"=c5u?t$N$h$&$J$b(B
$B$N$bO@M}E*$K$O:_$jF@$k$N$G$O$H;W$$$^$9$,!"$=$N>l9g!"(Bscalar? 
$B$OM-8z$G$9(B
$B$+(B?

$B@.@%$G$9!#(B

Tadayoshi Funaba wrote:
> 1.9 $B$N(B Numeric#scalar? $B$K$D$$$F!"E,Ev$G$J$$$N$G$O(B (real? $B$J$I$N$[$&$,$$(B
> $B$$(B)$B!"$H$N0U8+$,$$$/$D$+$"$j$^$7$?$,!"$I$&$G$7$g$&!#$b$7JQ$($k$J$i:#$N$&(B
> $B$A$+$J$H;W$$$^$9!#(B
> 
> scalar? $B$O!"(B2005-11-29 [ruby-dev:27871] $B$+$i;O$^$C$?5DO@$NCf$GF3F~$,7h(B
> $B$^$C$?$h$&$G$9!#(B1.8 $B$K$OF3F~$5$l$F$$$^$;$s!#(B

$BN.$l$O$4Mw$N>e$G6D$C$F$$$k$N$@$H$O;W$$$^$9$,!"$^$D$b$H$5$s$N(B
> $B%3%s%T%e!<%?8@8l$G$O(BReal$B$OEAE}E*$KIbF0>.?tE@$rI=8=$9$kC18l$H$7$F(B
> $BMQ$$$i$l$F$-$?$N$G@0?t$N%9!<%Q!<%/%i%9$NL>A0$K$O$U$5$o$7$/$J$$(B
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-dev/27923

$B$H$$$&<gD%$KBP$7$F==J,$JH?O@$,$J$$$h$&$K46$8$^$9!#(B
$B$b$&$A$g$C$HJd6/$7$?J}$,$h$m$7$$$N$G$O$J$$$G$7$g$&$+!#(B

> > $B%3%s%T%e!<%?8@8l$G$O(BReal$B$OEAE}E*$KIbF0>.?tE@$rI=8=$9$kC18l$H$7$F(B
> > $BMQ$$$i$l$F$-$?$N$G@0?t$N%9!<%Q!<%/%i%9$NL>A0$K$O$U$5$o$7$/$J$$(B
> http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-dev/27923

$B$J$k$[$I!#(BReal 
$B$H$$$&%/%i%9$rF3F~$9$k$o$1$G$O$J$$$G$9$,!"KM$O!"(Breal $B$,(B
$BIbF0>.?tE@?t$@$H$$$&0U<1$O$+$J$jGv$$$h$&$G$9$M!#(BPascal 
$B$H$+;W$$=P$7$^$9!#(B
$B>/$78E=-$$0u>]$,$"$j$^$9!#(B

$B$9$G$K8@$$$^$7$?$,!"(BCommon Lisp$B!"(BScheme$B!"(BFactor 
$B$G$O$=$&$$$&0UL#$G$O$D(B
$B$+$o$l$F$$$^$;$s!#(B

Python $B$N&BHG$r8+$F$$$?$N$G$9$,!"(Bnumbers.py $B$H$$$&(B ABC 
$B$H8F$P$l$k%U%l!<(B
$B%`%o!<%/$r$D$+$C$?<BAu$N!"(BFraction (fractions.py) 
$B$H$$$&M-M}?t%i%$%V%i(B
$B%j$r$_$D$1$^$7$?!#(BScheme 
$B$K1F6A$r<u$1$F$$$k$i$7$$$G$9$,!"(Bnumbers.py $B$G(B
$B$O!"(BNumber > Complex > Real > Rational > Integral 
$B$H$$$&3,AX9=B$$K$J$C(B
$B$F$$$k$h$&$G$9!#(B

ruby $B$G$O!"(Breal 
$B$rIbF0>.?tE@?t$N0UL#$G$D$+$C$?;v$O$J$$$H;W$$$^$9!#(Bruby
$B$N(B Complex $B$G$O(B real 
$B$H$$$&8l$,$9$G$K;6!9$D$+$o$F$$$^$9$,!"$=$l$KBP$7$F(B
$B0cOB46$,$"$k!"$H$$$&$h$&$J0U8+$O8+$?$3$H$,$"$j$^$;$s!#(B

$B0J>e$N$h$&$JNc$b$"$j!"(Breal 
$B$@$H:.Mp$9$k!"$H$$$&Dx$N$b$N$G$O$J$$$H;W$$$^(B
$B$9!#(B

real? $B$@$1$G$J$/!"$$$C$=$N$3$H(B float? (Common Lisp $B$N(B floatp 
$BAjEv(B) $B$b:N(B
$BMQ$9$k<j$b$"$j$^$9!#$=$&$9$l$P$b$C$H%O%C%-%j$7$^$9!#(B

$B$?$@!":#2s!"(Breal? 
$B$r:NMQ$7$F$b$i$&$3$H$,<g4c$G$O$J$$$N$G!"B>$KBEEv$J$b(B
$B$N$,$"$l$P$=$l$G$b$$$$$7!"5?Ld$,$b$C$H$b$@$H;W$&$J$i!">/$J$/$H$b(B
scalar? 
$B$O8x<0$N$b$N$H$O$7$J$$!"$H$$$&7hCG$r$7$F$b$i$$$?$$$H;W$$$^$9!#(B

$B86$G$9!#(B

$B$3$3$G!"(Bscalar? $B$r5?Ld;k$9$kM}M3$rI|=,$9$k$H!"$?$H$($P!"!VJ#(B
$BAG?t@.J,(Bvector$B!W$H$$$&$b$N$,9M$($i$l$F!"$3$N%Y%/%H%k$K$H$C$F(B
$B$O!"J#AG?t$O(Bscalar$B$G$"$k!#$7$?$,$C$F!"(Bscalar? 
$B$r$b$C$FHf3S2D(B
$BG=$H$$$&0UL#$r;}$?$;$k$3$H$O!"$^$:$$$N$G$O$J$$$+!"$H$$$&$3$H(B
$B$G$9!#(B


> scalar $B$,$"$l$P!"EvA3(B vector $B$b$H$J$j!"$I$C$A$J$N$+!"$H$$$&;v$b$"$j$^$9(B
> $B$,!"$=$b$=$b$=$&$$$&;v$rLd$$$?$$$o$1$8$c$J$$$N$G!"$+$J$j0cOB46$,$"$j$^(B
> $B$9$M!#<B:]$O!"(Breal $B$+$I$&$+CN$j$?$$$s$G$9!#$:$P$j$H8@$($P!"(Breal? $B$8$c$J(B
> $B$$$+$H!#(B

real? $B$H$$$&$N$b$$$$$N$G$9$,!";d$O$+$9$+$K$:$l$F$$$k5$$b$9$k(B
$B$s$G$9$h$M!D!#$$$d!"(Breal?$B$G$$$$$s$G$9$,!#(B

ordered? $B$C$F$$$&$N$b;W$$$D$?$1$I!"$I$&$G$7$g$&!#(B

$B86$G$9!#(B

Tadayoshi Funaba $B$5$s$O=q$-$^$7$?(B:
>>> $B%3%s%T%e!<%?8@8l$G$O(BReal$B$OEAE}E*$KIbF0>.?tE@$rI=8=$9$kC18l$H$7$F(B
>>> $BMQ$$$i$l$F$-$?$N$G@0?t$N%9!<%Q!<%/%i%9$NL>A0$K$O$U$5$o$7$/$J$$(B
>> http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-dev/27923
> 
> $B$J$k$[$I!#(BReal $B$H$$$&%/%i%9$rF3F~$9$k$o$1$G$O$J$$$G$9$,!"KM$O!"(Breal $B$,(B
> $BIbF0>.?tE@?t$@$H$$$&0U<1$O$+$J$jGv$$$h$&$G$9$M!#(BPascal $B$H$+;W$$=P$7$^$9!#(B
> $B>/$78E=-$$0u>]$,$"$j$^$9!#(B

$BFC$K(B Rational $B$,AH$_9~$_$K$J$C$?$3$H$b$"$C$F!"(BRuby $B$G(B 
real $B$H(B
$B$$$&8l$KIbF0>.?tE@?t$N%K%e%"%s%9$r;}$?$;$k$3$H$O!"A4$/L5$/$J$k(B
$B$N$G$O$J$$$+$H;W$$$^$9!#(BRational $B$O5?$$$h$&$b$J$/(B real 
$B$@$+$i!#(B

> $B$3$3$G!"(Bscalar? $B$r5?Ld;k$9$kM}M3$rI|=,$9$k$H!"$?$H$($P!"!VJ#(B
> $BAG?t@.J,(Bvector$B!W$H$$$&$b$N$,9M$($i$l$F!"$3$N%Y%/%H%k$K$H$C$F(B
> $B$O!"J#AG?t$O(Bscalar$B$G$"$k!#$7$?$,$C$F!"(Bscalar? $B$r$b$C$FHf3S2D(B
> $BG=$H$$$&0UL#$r;}$?$;$k$3$H$O!"$^$:$$$N$G$O$J$$$+!"$H$$$&$3$H(B
> $B$G$9!#(B

scalar $B$HGX8e$K1#$l$F$$$k(B vector 
$B$H$$$&$b$N$r9M$($k$H!"7W;;5!$G$N>o<1$H(B
$B$b0c$&$H$$$&5$$,$7$^$9$M!#(B

ruby $B$G$b(B lib/matrix.rb $B$K(B Vector 
$B%/%i%9$,$"$j$^$9$,!"(Bvector $B$C$F$=$&$$(B
$B$&$b$N$@!"$C$F$$$&463P$,$"$j$^$9$h$M!#(Breal 
$B$,$I$&$3$&0JA0$K!"$^$:(B
scalar 
$B$,7W;;5!$G$N47=,$H$7$F$bE,@Z$G$J$$!"$H$$$&$3$H$K$J$j$^$9$+!#(B

ruby $B$N(B Matrix $B$d(B Vector $B$,(B Numeric 
$B$G$"$k$3$H$b9M$($i$l$J$/$b$J$/!"(B
scalar $B$@!"(Bvector 
$B$@$H$$$($P!"8m2r$,$J$$$o$1$G$O$J$$$G$7$g$&!#$=$NE@$G(B
$B$O!"(Bscalar $B$O(B real 
$B$KJ86g$r8@$($k$h$&$JN)GI$J$b$N$G$O$J$$$N$O3N$+$@$H;W(B
$B$$$^$9$M!#(B

> real? $B$H$$$&$N$b$$$$$N$G$9$,!";d$O$+$9$+$K$:$l$F$$$k5$$b$9$k(B
> $B$s$G$9$h$M!D!#$$$d!"(Breal?$B$G$$$$$s$G$9$,!#(B
> 
> ordered? $B$C$F$$$&$N$b;W$$$D$?$1$I!"$I$&$G$7$g$&!#(B

$B3N$+$K!":G=i$N5DO@$N$-$C$+$1$+$i9M$($l$P!"(Bcomparable? 
$B$J$s$+$O$O%:%P%j(B
$B$H$$$($k$+$b$7$l$^$;$s!#(Bordered $B$H$+!"(Bmagnitude 
$B$O4pK\E*$K$O!"(B
comparable $B$N8@$$49$($K6a$$$H;W$&$s$G$9$,!"$?$@!"(Bcomparable? 
$B$O!":#EY$O(B
Comparable $B%b%8%e!<%k$H$N4X78$,LdBj$K$J$j$=$&$G$9$7!"?t(B 
($B%*%V%8%'%/%H(B)
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$B$D$/$l$F$7$^$$$^$9$7!#(B

Python $B$N(B numbers.py $B$G(B Real 
$B$rMQ0U$7$F$$$k$N$H:,K\$OF1$8$J$O$:$G!":#$N(B
ruby $B$NOHAH$G$"$l$P(B real? 
$B$,I,MW$@$H$$$&$3$H$K$J$k$H;W$$$^$9!#2>Na!"L>(B
$BA0$,0c$C$F$$$?$H$7$F$b!"KM$+$i8+$k$HK\Ev$KI,MW$J$N$O!"(Breal? 
$B$G$7$g$&$M!#(B
$B%/%i%9$G$b$J$/!"@-<A$G$b$J$/$F!"$"$k<o7?$,I,MW$@$H;W$$$^$9!#(B

1.9.1 $B$^$G$K;~4V$,$J$$$N$G(B scalar? 
$B$@$12?$H$+$7$?$$$H;W$C$F$$$^$7$?$,!"(B
$BH?1~$,$h$/$J$$$N$GD|$a$F!"(B2.0 
$B$"$?$j$G:,K\E*$KN)$FD>$7$G$-$?$i$H;W$$$^(B
$B$9!#$H$j$"$($:!":#$N9M$($r>/$7=q$$$F$*$-$^$9!#(B

ruby $B$K$OCj>]E*$J%3!<%I$r=q$3$&$K$bF;6q$,$"$j$^$;$s!#$@$+$i!"(B
Complex.generic? $B$_$?$$$J$b$N$,=PMh$F$7$^$C$?$H;W$$$^$9!#(B

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$B$K$"$k$h$&$J(B
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$BF~$@$H;W$$$^$9!#(Bexact?$B!"(Binexact? 
$B$N$h$&$J$b$N$b4^$a$F$7$^$C$F!"(B
integer? $B$NDj5A$b>/$7JQ99$7$?$[$&$,$$$$$+$b$7$l$^$;$s!#(B

scalar? $B$,I,MW$@$H$9$l$P!"F1$8$h$&$J0UL#$G!"(Bcomplex? $B$d(B 
rational? $B$J$I(B
$B$bI,MW$@$H8@$($k$H;W$$$^$9!#$3$l$i$N0lO"$N=R8l$O$R$H$D$NBN7O$r7A:n$k$G(B
$B$7$g$&$,!"$=$N$h$&$JBN7O$+$i8@$($P!"(Bscalar? 
$B$OL>A0$,E,Ev$G$J$$$H9M$($^(B
$B$9!#(B

$B>\$7$$;v$O!"$^$?;~4|$,Mh$?$H$-=q$1$l$P$H;W$$$^$9!#(B

$BA0ED$G$9!#(B

2008/09/06 8:04 Tadayoshi Funaba <tadf@dotrb.org>:
> 1.9.1 $B$^$G$K;~4V$,$J$$$N$G(B scalar? $B$@$12?$H$+$7$?$$$H;W$C$F$$$^$7$?$,!"(B
> $BH?1~$,$h$/$J$$$N$GD|$a$F!"(B2.0 $B$"$?$j$G:,K\E*$KN)$FD>$7$G$-$?$i$H;W$$$^(B
> $B$9!#$H$j$"$($:!":#$N9M$($r>/$7=q$$$F$*$-$^$9!#(B

1.9.1$B$,=P$?8e$G(Bscalar?$B$rGQ;_$9$k$N$O$"$^$jK>$^$7$/$J$$$H;W$$$^$9$N$G!"(B
$B$b$&$A$g$C$H$,$s$P$j$^$;$s$+(B?
# 2.0$B$J$s$F$$$D=P$k$s$@!"$H$$$&LdBj$b$"$j$^$9$7!D!#(B

$B$^$:!";d$N0U8+$r@h$K=R$Y$k$H!"(Breal?$B$K;?@.$G$9!#(B

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$B$N$G$9$,!":#$N$H$3$m$3$N%9%l%C%I$G$OL@3N$JH?BP0U8+$O=P$F$$$J$$$h$&$K;W$$(B
$B$^$9!#(B
comparable?$B$d(Bordered?$B$O?t$rI=$9%*%V%8%'%/%H$@$1$rBP>]$K9M$($k$H$h$$$h$&(B
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$B$3$3$O(BPascal$B$h$j$b(BLisp$B$KJo$&$3$H$K$7$F!"(Breal?$B$H$7$F$O$I$&$G$7$g$&$+(B? 
> $B$^$D$b$H$5$s(B
$B=R8l$@$H$=$s$J$KIbF0>.?tE@?t$N%$%a!<%8$O$J$$$h$&$K;W$$$^$9$7!#(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:36183] Re: Numeric#scalar?"
    on Sat, 6 Sep 2008 23:19:18 +0900, "Shugo Maeda" 
<shugo@ruby-lang.org> writes:

|$B$^$:!";d$N0U8+$r@h$K=R$Y$k$H!"(Breal?$B$K;?@.$G$9!#(B

|$B$3$3$O(BPascal$B$h$j$b(BLisp$B$KJo$&$3$H$K$7$F!"(Breal?$B$H$7$F$O$I$&$G$7$g$&$+(B? > $B$^$D$b$H$5$s(B
|$B=R8l$@$H$=$s$J$KIbF0>.?tE@?t$N%$%a!<%8$O$J$$$h$&$K;W$$$^$9$7!#(B

$B$O$$!#%/%i%9L>$G$J$1$l$PH?BP$7$^$;$s!#(B

$B86$G$9!#(B

> $BA0ED$G$9!#(B

> $B$^$:!";d$N0U8+$r@h$K=R$Y$k$H!"(Breal?$B$K;?@.$G$9!#(B
> 
> $B86$5$s$,!V$+$9$+$K$:$l$F$$$k5$$b$9$k!W$H$*$C$7$c$C$F$$$k$N$,$A$g$C$H5$$K$J$k(B
> $B$N$G$9$,!":#$N$H$3$m$3$N%9%l%C%I$G$OL@3N$JH?BP0U8+$O=P$F$$$J$$$h$&$K;W$$(B
> $B$^$9!#(B

$BHf3S$,$G$-$k$3$H$H<B?t$G$"$k$3$H$OF1CM$G$O$J$/$F!"(Breal$B$O8@$$(B
$B$9$.$J46$8$,$7$^$9!#(BNumeric$B$N2<$KHf3S$,$G$-$F$+$D<B?t$G$J$$?t(B
$B$r%i%$%V%i%j$H$7$F=q$/$3$H$O$"$j$($k$N$G$O$J$$$+!#(B

$B$,!"$=$N2DG=@-$,DY$5$l$F$b!"(Breal?$B$O(Bscalar?$B$h$j$$$$$H;W$&$N$G!"(B
real?$B$K;?@.$G$9!#(B

> $BHf3S$,$G$-$k$3$H$H<B?t$G$"$k$3$H$OF1CM$G$O$J$/$F!"(Breal$B$O8@$$(B
> $B$9$.$J46$8$,$7$^$9!#(BNumeric$B$N2<$KHf3S$,$G$-$F$+$D<B?t$G$J$$?t(B
> $B$r%i%$%V%i%j$H$7$F=q$/$3$H$O$"$j$($k$N$G$O$J$$$+!#(B

$B$=$&$$$&$N$"$k$s$G$9$+$M!#(B

$B$?$7$+$K!"$=$b$=$b$NH/C<$G$"$kHf3S1>!9$K94$k$HHyL/$H;W$&$+$b$7$l$^$;$s!#(B
$B$7$+$7!"0JA0$N5DO@$NCf$G$b$=$l$,K\<A$G$O$J$$!"$H$$$&$3$H$,L@$+$K$J$C$F(B
$B$$$?$H;W$$$^$9!#(B[ruby-dev:27928] 
$B$G$[$\7kO@$,=P$F$$$F!"$5$i$K(B
[ruby-dev:27940] $B$G(B real? $B$b=P$F$$$?$N$G$9$,!"(Bscalar? 
$B$K>y$C$?46$,$"$j(B
$B$^$9$M!#(B

real? 
$B$,$"$C$F$b$J$*$+$DHf3S1>!9$N=R8l$,M_$7$$$N$G$"$l$P!"0UL#$,$"$k$+(B
$B$b$7$l$^$;$s$,!"$$$E$l$K$7$F$b!"(Breal? 
$B$OI,MW$@$H;W$$$^$9!#$?$H$($P!"(B
Complex $B$N<BAu$G$O(B scalar? 
$B$r$D$+$C$F$$$^$9$,!"Hf3S$G$-$k$+$I$&$+$rCN$j(B
$B$?$$$o$1$G$O$J$$$N$G!#(B

$BA0ED$5$s$b;?@.$7$F$/$l$F!"$^$D$b$H$5$s$bH?BP$O$7$J$$!"$H$N$3$H$J$N$G!"(B
$B$"$H0l=54V$/$i$$$OMM;R$r8+$?$[$&$,$$$$$G$7$g$&$+!#(B

$BA0ED$G$9!#(B

2008/09/07 1:25 Shin-ichiro HARA <sinara@blade.nagaokaut.ac.jp>:
> $BHf3S$,$G$-$k$3$H$H<B?t$G$"$k$3$H$OF1CM$G$O$J$/$F!"(Breal$B$O8@$$(B
> $B$9$.$J46$8$,$7$^$9!#(BNumeric$B$N2<$KHf3S$,$G$-$F$+$D<B?t$G$J$$?t(B
> $B$r%i%$%V%i%j$H$7$F=q$/$3$H$O$"$j$($k$N$G$O$J$$$+!#(B

$B$J$k$[$I!"86$5$s$N?4G[$OM}2r$G$-$^$7$?!#(B

$B2>$K>-Mh$=$&$$$C$?MW5a$,$"$C$F(Bcomparable?$B$rF3F~$7$?$H$7$F$b!"$=$N;~$K(B
real?$B$r:o=|$9$Y$-$@$H$$$&$3$H$K$J$k0Z$l$,$J$1$l$P!":#2s(Breal?$B$rF3F~$7$?(B
$B$H$7$F$bBg$-$JLdBj$O$J$$$h$&$K;W$$$^$9!#$I$&$G$7$g$&$+!#(B

$B:XF#$H?=$7$^$9!#(B

On Sun, 7 Sep 2008 01:25:19 +0900
Shin-ichiro HARA <sinara@blade.nagaokaut.ac.jp> wrote:

> $B$9$.$J46$8$,$7$^$9!#(BNumeric$B$N2<$KHf3S$,$G$-$F$+$D<B?t$G$J$$?t(B
> $B$r%i%$%V%i%j$H$7$F=q$/$3$H$O$"$j$($k$N$G$O$J$$$+!#(B

($B0lIt$N<B?t(BNumeric$B$H(B)$B!VHf3S$,$G$-$J$/$F$+$D<B?t$G$"$k!W?tCM$N%i%$%V%i%j$r=q$$$F(B
$B$$$k<T$G$9!#(B

$BCx:n$N%i%$%V%i%j$O!">.?t$r@53N$KI=$;$k$N$r%&%j$H$7$F$$$^$9!#$=$N@-3J$r=E$s$8$F!"(B
$BIT@53N$G$"$k(BFloat$B$H$NHf3S$N;~$O!"0U?^$7$FNc30$,>e$,$k$h$&$K$J$C$F$$$^$9!#(B

$BNc$($P(BBigDecimal("1.1")$B$G$O!"(B1.1$B$r@53N$KI=$;$^$9$,!"(BFloat$B$N(B1.1$B$G$O$=$&$H$O8B$j(B
$B$^$;$s!#$=$N$?$a!"$;$C$+$/(BBigDecimal$B$rMQ$$$F@53N$K1i;;$7$?7k2L$b!":G8e$K$=$l$r(B
$B$&$C$+$j(BFloat$B$HHf3S$7$F$7$^$&$H!"7k2L$OL5;D$J$b$N$H$J$C$F$7$^$$$^$9!#(B
Float$B$O%j%F%i%k$H$7$F4JC1$K=q$1$k$N$G!"$&$C$+$j$,5/$3$j$d$9$$$h$&$G$9!#(B

$B$3$N$h$&$J8m$j$OC1$J$k2>@b$G$O$J$/!"(B1.8$B$N%j%j!<%9$N8e$K<B:]2?EY$b7+$jJV$75/$-!"(B
ruby-talk$B$KEj9F$5$l$F$$$kHa7`$G$9!#:G6a$G$O(B [ruby-talk:312713] 
$B$,$"$j$^$7$?!#(B

$B$=$N$h$&$JM}M3$,$"$C$F!"Cx:n%i%$%V%i%j$G$O(BFloat$B$H$NHf3S$,IT2DG=$G$9(B($BHf3S$9$k$J$i$P(B
to_f$B$r;H$C$F$+$i$*9%$-$K$I$&$>!"$H$$$&%9%?%s%9$G$9(B)$B!#$=$N$?$a!"%i%$%V%i%j$K(B1.9$BBP1~$r(B
$B@9$j9~$b$&$H$7$F$$$k<+J,$K$H$C$F$O!"86$5$s$N!V$"$j$($k$N$G$O$J$$$+!W$H$$$&4mW|$O:#(B
$B8=:_5/$3$C$F$$$kLdBj$G$9!#(B

$B$H$$$&$3$H$G!">e5-$N$h$&$J%b%N$N<BAu<T$H$7$F$O!"(Bcompareble? 
$B$NJ}$,$$$/$i$+<+A3$K(B
$B46$8$^$9!#(Breal? 
$B$NG\0J>e$ND9$5$,$"$j$^$9$,!"$=$l$[$IIQHK$K;H$&$b$N$G$O$J$$$N$G!"(B
$B$$$$$N$+$J$H$$$&5$$,$7$^$9!#(B

$BA0ED$G$9!#(B

2008/09/08 17:29 Tadashi Saito <shiba@mail2.accsnet.ne.jp>:
>> $B$9$.$J46$8$,$7$^$9!#(BNumeric$B$N2<$KHf3S$,$G$-$F$+$D<B?t$G$J$$?t(B
>> $B$r%i%$%V%i%j$H$7$F=q$/$3$H$O$"$j$($k$N$G$O$J$$$+!#(B
>
> ($B0lIt$N<B?t(BNumeric$B$H(B)$B!VHf3S$,$G$-$J$/$F$+$D<B?t$G$"$k!W?tCM$N%i%$%V%i%j$r=q$$$F(B
> $B$$$k<T$G$9!#(B
(snip)
> $B$=$N$h$&$JM}M3$,$"$C$F!"Cx:n%i%$%V%i%j$G$O(BFloat$B$H$NHf3S$,IT2DG=$G$9(B($BHf3S$9$k$J$i$P(B
> to_f$B$r;H$C$F$+$i$*9%$-$K$I$&$>!"$H$$$&%9%?%s%9$G$9(B)$B!#$=$N$?$a!"%i%$%V%i%j$K(B1.9$BBP1~$r(B
> $B@9$j9~$b$&$H$7$F$$$k<+J,$K$H$C$F$O!"86$5$s$N!V$"$j$($k$N$G$O$J$$$+!W$H$$$&4mW|$O:#(B
> $B8=:_5/$3$C$F$$$kLdBj$G$9!#(B

$B@53N$K$O86$5$s$,!V$"$j$($k$N$G$O$J$$$+!W$H;W$C$F$$$kLdBj$H$O0c$$$^$9$h$M!#(B
$B86$5$s$,7|G0$7$F$$$k$N$O!VHf3S$,$G$-$F$+$D<B?t$G$J$$?t!W%1!<%9$G$"$C$F!"(B
$B!VHf3S$,$G$-$J$/$F$+$D<B?t$G$"$k!W%1!<%9$G$O$J$$$N$G!#(B

> $B$H$$$&$3$H$G!">e5-$N$h$&$J%b%N$N<BAu<T$H$7$F$O!"(Bcompareble? $B$NJ}$,$$$/$i$+<+A3$K(B
> $B46$8$^$9!#(Breal? $B$NG\0J>e$ND9$5$,$"$j$^$9$,!"$=$l$[$IIQHK$K;H$&$b$N$G$O$J$$$N$G!"(B
> $B$$$$$N$+$J$H$$$&5$$,$7$^$9!#(B

$B$h$/$o$+$i$J$+$C$?$N$G$9$,!":XF#$5$s$N:n$i$l$F$$$k%/%i%9$G$O(Bcomparable?$B$O(B
false$B$rJV$9$3$H$K$J$k$N$G$7$g$&$+(B?
$B$b$7!"$=$&$@$H$9$k$H!"$?$H$($P(Bx$B$H(By$B$,$=$N%/%i%9$N%$%s%9%?%s%9$@$C$?$H$7$F!"(BComplex(x, 
y)
$B$,0J2<$N$h$&$J%(%i!<$K$J$k$H;W$&$N$G$9$,!"$=$l$O0U?^$5$l$?$3$H$G$7$g$&$+(B?

irb(main):001:0> Complex(x, y)
ArgumentError: not a real

$B$b$7>e5-$N$h$&$J5sF0$r0U?^$5$l$F$$$J$+$C$?$H$9$k$H!"$d$O$j:#2s8!F$$5$l$F$$$k5!G=$N(B
$BL>A0$H$7$F$O(Breal?$B$NJ}$,$h$jE,@Z$@$C$?$j$7$J$$$G$7$g$&$+!#(B

Yugui$B$G$9!#(B

Shugo Maeda $B$5$s$O=q$-$^$7$?(B:
> $B@53N$K$O86$5$s$,!V$"$j$($k$N$G$O$J$$$+!W$H;W$C$F$$$kLdBj$H$O0c$$$^$9$h$M!#(B
> $B86$5$s$,7|G0$7$F$$$k$N$O!VHf3S$,$G$-$F$+$D<B?t$G$J$$?t!W%1!<%9$G$"$C$F!"(B
> $B!VHf3S$,$G$-$J$/$F$+$D<B?t$G$"$k!W%1!<%9$G$O$J$$$N$G!#(B
> 
>> $B$H$$$&$3$H$G!">e5-$N$h$&$J%b%N$N<BAu<T$H$7$F$O!"(Bcompareble? $B$NJ}$,$$$/$i$+<+A3$K(B
>> $B46$8$^$9!#(Breal? $B$NG\0J>e$ND9$5$,$"$j$^$9$,!"$=$l$[$IIQHK$K;H$&$b$N$G$O$J$$$N$G!"(B
>> $B$$$$$N$+$J$H$$$&5$$,$7$^$9!#(B

$BD6<B?t$,$"$j$^$9$h!#!VHf3S$,$G$-$F$+$D<B?t$G$J$$?t!W$G$9!#(B
Ruby$B<BAu$b$"$j$^$9!#0l1~!"(BComplex$B$H:.$<$F;H$($J$/$O$J$$$h$&$G$9!#(B
http://www.math.kobe-u.ac.jp/~kodama/tips-HyperReal.html

Comparable$B$G$"$k$H$$$&$N$ODj5A$NLdBj$G$9!#J#AG?t$@$C$F<+A3$J=g=x$,Dj$^$i(B
$B$J$$$@$1$G<-=q<0$N$h$&$KWs0UE*$J=g=x$rM?$($F$d$k$3$H$O$G$-$k$o$1$G$9!#(B
$BI,MW$G$"$l$P<+J,$N@UG$$G(BComplex#<=>$B$rDj5A$9$k$N$O>!<j$@$h!"$H$$$&$N$,(B
Ruby$B%i%$%V%i%j$H$7$F$ONI$5$=$&$K;W$$$^$9!#(B


$B$J$N$G!"%i%$%V%i%jB&$G5,Dj$NH=JLK!$H$7$F(Bcomparable?$B$rM?$($k$N$O0cOB46$,(B
$B$"$j$^$9!#$G!"(Bscalar?$B$O99$KJQ$@$H$$$&$N$O86$5$s$N$*$C$7$c$k$H$*$j$H;W$$(B
$B$^$9!#J#AG%Y%/%H%k$NN)>l$,$J$$!#(B

$B$H$j$"$($:!"(Bscalar?$B$r(Breal?$B$K$7$F!"$=$N8e$K(Bexact?/inexact?$B$r8!F$$9$k$N$,(B
$BNI$$$N$G$O$J$$$G$7$g$&$+!#(Bcomparable?$B$+$I$&$+$O(Bscalar?$B@-$H(Bexact?$B@-$K=>$C(B
$B$F%"%W%j%1!<%7%g%s!&%I%a%$%s$N@-<A$K1~$8$FDj$^$k$3$H$G$9!#(B


$B$H$3$m$G!"(BPrecision$B$O$I$&$J$C$F$k$s$G$7$g$&!#%i%$%V%i%j$N<BAu$r8+$k$K$O(B
$B$"$^$j?tCM%*%V%8%'%/%H$N1i;;$K9W8%$7$F$$$k$h$&$K;W$($^$;$s$,!#(B

> $B$=$N$h$&$JM}M3$,$"$C$F!"Cx:n%i%$%V%i%j$G$O(BFloat$B$H$NHf3S$,IT2DG=$G$9(B($BHf3S$9$k$J$i$P(B
> to_f$B$r;H$C$F$+$i$*9%$-$K$I$&$>!"$H$$$&%9%?%s%9$G$9(B)$B!#$=$N$?$a!"%i%$%V%i%j$K(B1.9$BBP1~$r(B
> $B@9$j9~$b$&$H$7$F$$$k<+J,$K$H$C$F$O!"86$5$s$N!V$"$j$($k$N$G$O$J$$$+!W$H$$$&4mW|$O:#(B
> $B8=:_5/$3$C$F$$$kLdBj$G$9!#(B

$BA0ED$5$s$N;XE&$N$h$&$K!"$=$l<+BN$,Hf3S$G$-$k$+$I$&$+$H0c$&$H;W$&$N$G$9(B
$B$,!"$=$&$$$&;XF3$C$]$$;v$r$7$?$j$9$k$N$O!"$J$s$@$+(B BigDecimal 
$BE*$J46$8(B
$B$,$7$^$9$M!#$J$s$J$i7Y9p=P$7$F$b$$$$$o$1$G$9$7!#(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:36216] Re: Numeric#scalar?"
    on Mon, 8 Sep 2008 21:15:14 +0900, "Yugui (Yuki Sonoda)" 
<yugui@yugui.jp> writes:

|$B$H$3$m$G!"(BPrecision$B$O$I$&$J$C$F$k$s$G$7$g$&!#%i%$%V%i%j$N<BAu$r8+$k$K$O(B
|$B$"$^$j?tCM%*%V%8%'%/%H$N1i;;$K9W8%$7$F$$$k$h$&$K;W$($^$;$s$,!#(B

$B$4$H$1$s$5$s$,MJ8n$7$J$$$J$i!">-Mh:o=|$7$?$$$H$3$m$G$9!#(B

Common Lisp $B$N(B realp $B$H(B Scheme $B$N(B real?$B!"9,$$(B 
real $B$K$D$$$F$O!"$I$A$i$b(B
$B$=$l$[$I$N:9$,$J$$$G$9$,!"$H$j$"$($:!"(Breal? $B$K$O(B 
($B$?$H$($P!"(Br6rs $B$K=`$8(B
$B$?$H$7$F(B) $BIbF0>.?tE@?t$NL58BBg>.!"(BNaN 
$B$b4^$^$l$k!"$H$$$&$h$&$J$3$H$O3N(B
$BG'$7$F$*$$$?$[$&$,$$$$$G$9$+$M!#(B

> $B$H$3$m$G!"(BPrecision$B$O$I$&$J$C$F$k$s$G$7$g$&!#%i%$%V%i%j$N<BAu$r8+$k$K$O(B
> $B$"$^$j?tCM%*%V%8%'%/%H$N1i;;$K9W8%$7$F$$$k$h$&$K;W$($^$;$s$,!#(B

$BKM$b4^$a$F!"$"$^$j0U5A$rM}2r$G$-$F$$$J$$$+$b!#(B

$B$"$i$?$a$FH?O@$J$I$J$1$l$P!"?tF|Cf$K(B scalar? $B$+$i(B real? 
$B$KJQ99$7$F$7$^(B
$B$*$&$+$H;W$$$^$9!#(B

$B:XF#$H?=$7$^$9!#(B

On Mon, 8 Sep 2008 20:35:34 +0900
"Shugo Maeda" <shugo@ruby-lang.org> wrote:

> $B@53N$K$O86$5$s$,!V$"$j$($k$N$G$O$J$$$+!W$H;W$C$F$$$kLdBj$H$O0c$$$^$9$h$M!#(B
> $B86$5$s$,7|G0$7$F$$$k$N$O!VHf3S$,$G$-$F$+$D<B?t$G$J$$?t!W%1!<%9$G$"$C$F!"(B
> $B!VHf3S$,$G$-$J$/$F$+$D<B?t$G$"$k!W%1!<%9$G$O$J$$$N$G!#(B

$B$=$&$G$9$M!#(B

> $B$h$/$o$+$i$J$+$C$?$N$G$9$,!":XF#$5$s$N:n$i$l$F$$$k%/%i%9$G$O(Bcomparable?$B$O(B
> false$B$rJV$9$3$H$K$J$k$N$G$7$g$&$+(B?
> $B$b$7!"$=$&$@$H$9$k$H!"$?$H$($P(Bx$B$H(By$B$,$=$N%/%i%9$N%$%s%9%?%s%9$@$C$?$H$7$F!"(BComplex(x, y)
> $B$,0J2<$N$h$&$J%(%i!<$K$J$k$H;W$&$N$G$9$,!"$=$l$O0U?^$5$l$?$3$H$G$7$g$&$+(B?
> 
> irb(main):001:0> Complex(x, y)
> ArgumentError: not a real

$B<+J,$NCf$G$O!"(Bx $B$H(B y 
$B$,3F!9(BFloat$B$HCx:n%/%i%9$G$J$1$l$P!"%(%i!<$K$J$i$J$$$G(B
$BM_$7$$$G$9!#(BFloat($B$H!"$=$l$r%a%s%P$H$7$FJ];}$9$k(BComplex$BEy(B)$B$H$O:.$<$F7W;;$7$?$/(B
$B$J$$!"$H$$$&$3$H$G$9!#(B

$B!D!D$H$9$k$H!"K\Bj$+$i$O$=$l$^$9$,!"<+J,$N%/%i%9$G$O(BNumeric#real?$B$r$I$&<BAu$7$?$i(B
$B$$$$$N$G$7$g$&$+(B?

> $B$b$7>e5-$N$h$&$J5sF0$r0U?^$5$l$F$$$J$+$C$?$H$9$k$H!"$d$O$j:#2s8!F$$5$l$F$$$k5!G=$N(B
> $BL>A0$H$7$F$O(Breal?$B$NJ}$,$h$jE,@Z$@$C$?$j$7$J$$$G$7$g$&$+!#(B

$B@5D>!"<+J,$G$b:#$N5DO@$,M}2r$7$-$l$F$$$J$$5$$,$7$F$-$^$7$?!#$H$j$"$($:!"(Breal?$B$H(B
$B$$$&L>A0$KH?BP$N0U;V$O!":#$"$j$^$;$s!#(B

On Mon, 8 Sep 2008 21:15:14 +0900
"Yugui (Yuki Sonoda)" <yugui@yugui.jp> wrote:

> $B$H$j$"$($:!"(Bscalar?$B$r(Breal?$B$K$7$F!"$=$N8e$K(Bexact?/inexact?$B$r8!F$$9$k$N$,(B
> $BNI$$$N$G$O$J$$$G$7$g$&$+!#(Bcomparable?$B$+$I$&$+$O(Bscalar?$B@-$H(Bexact?$B@-$K=>$C(B
> $B$F%"%W%j%1!<%7%g%s!&%I%a%$%s$N@-<A$K1~$8$FDj$^$k$3$H$G$9!#(B

$B<+J,$O(Bexact/inexact$B$K$D$$$F$NM}2r$,$[$\3'L5$G$9$N$G!"(Byugui$B$5$s$N>e5-J8LL$r85$K(B
$BJY6/$7$^$9!"$H$$$&$H$3$^$G$7$+8@$($^$;$s!#(B($B$4$a$s$J$5$$!#(B)
# 
$B$7$+$7$*$=$i$/!"$=$l$,<+J,$NM_$9$k$H$3$m$G$"$m$&!"$H$$$&5$$,$7$F$$$^$9!#(B

> $B$H$3$m$G!"(BPrecision$B$O$I$&$J$C$F$k$s$G$7$g$&!#%i%$%V%i%j$N<BAu$r8+$k$K$O(B
> $B$"$^$j?tCM%*%V%8%'%/%H$N1i;;$K9W8%$7$F$$$k$h$&$K;W$($^$;$s$,!#(B

$B<+:n$N%/%i%9$G$O!"4{B8(BNumeric$B$H$N?FOB@-$r9M$($F@_7W$7$F$$$?$N$GEvA3!"(BPrecision
$B<~$j$N<BAu$b$7$h$&$H:G=i$O;W$C$F$$$^$7$?!#$,!":n<T$4K\?M$,$k$S$^$G!V1xE@!W(B
$B!V;H$$F;$,$J$$!W$H$*$C$7$c$C$F$k$N$G!"$3$l$+$i:n$k%b%@%s$J%W%m%@%/%H$H$7$F$O!"(B
$B<BAu$r>J$/$3$H$K$7$^$7$?!#(B

http://jp.rubyist.net/magazine/?0011-Hotlinks#l17

$BA0ED$G$9!#(B

2008/09/16 18:58 Tadashi Saito <shiba@mail2.accsnet.ne.jp>:
> $B$J$$!"$H$$$&$3$H$G$9!#(B
>
> $B!D!D$H$9$k$H!"K\Bj$+$i$O$=$l$^$9$,!"<+J,$N%/%i%9$G$O(BNumeric#real?$B$r$I$&<BAu$7$?$i(B
> $B$$$$$N$G$7$g$&$+(B?

Complex()$B$N;~E@$G$=$&$$$&%A%'%C%/$r$9$k$N$O(B($B>/$J$/$H$b:#$NOHAH$G$O(B)$BL5M}$@$H(B
$B;W$&$N$G!"(Breal?$B$O(Btrue$B$rJV$9$N$,$h$$$N$G$O$J$$$G$7$g$&$+!#(B
# 
true$B$rJV$5$J$$$H!"(BFloat$B$,2p:_$7$J$$7W;;$G$b4|BTDL$j$KF0$+$J$/$J$C$F$7$^$&(B
# $B$N$G!#(B
$BNc30$,5s$,$k$N$O!":XF#$5$s$N%/%i%9$N%$%s%9%?%s%9$H(BFloat$B%$%s%9%?%s%9$H$N4V$G(B
$B<B:]$K1i;;$,9T$o$l$k;~$^$GCY1d$5$l$k$3$H$K$J$k$H;W$$$^$9!#(B

$B:XF#$H?=$7$^$9!#(B

On Tue, 16 Sep 2008 21:38:30 +0900
"Shugo Maeda" <shugo@ruby-lang.org> wrote:

> > $B!D!D$H$9$k$H!"K\Bj$+$i$O$=$l$^$9$,!"<+J,$N%/%i%9$G$O(BNumeric#real?$B$r$I$&<BAu$7$?$i(B
> > $B$$$$$N$G$7$g$&$+(B?
> 
> Complex()$B$N;~E@$G$=$&$$$&%A%'%C%/$r$9$k$N$O(B($B>/$J$/$H$b:#$NOHAH$G$O(B)$BL5M}$@$H(B
> $B;W$&$N$G!"(Breal?$B$O(Btrue$B$rJV$9$N$,$h$$$N$G$O$J$$$G$7$g$&$+!#(B
> # true$B$rJV$5$J$$$H!"(BFloat$B$,2p:_$7$J$$7W;;$G$b4|BTDL$j$KF0$+$J$/$J$C$F$7$^$&(B
> # $B$N$G!#(B

$B$J$k$[$I!"$=$l$OLdBj$J$N$G!"(Breal? 
#=>true$B!"$G<BAu$9$k$3$H$K$7$^$9!#(B
$B$"$j$,$H$&$4$6$$$^$9!#(B

> $BNc30$,5s$,$k$N$O!":XF#$5$s$N%/%i%9$N%$%s%9%?%s%9$H(BFloat$B%$%s%9%?%s%9$H$N4V$G(B
> $B<B:]$K1i;;$,9T$o$l$k;~$^$GCY1d$5$l$k$3$H$K$J$k$H;W$$$^$9!#(B

$B$3$l$G$bLdBj$J$5$=$&$G$9!#(B