Complex/image

[ruby-math:00543] e$B$rFI$s$G!“e(Bimage e$B$O$d$a$Fe(B imag
e$B$KJQ99$7$?$i$I$&$+!”$De(B
e$B$$$G$Ke(B imaginary
e$B$NJLL>$rF3F~$7$?$i$I$&$+!"$H9M$($F$$$^$9!#<g4Q$G$O!"5ue(B
e$BIt$r;X$9$N$K$Oe(B imag e$B$,B?$/$F!"5)$Ke(B imaginarye$B!“e(Bim
e$B$,$”$kDxEY$H46$8$^$9!#e(B

e$B$^$?!“e(B#im e$B$K$D$$$F!”$`$7$me(B #i
e$B$G$$$$$s$8$c$J$$$+!"$H$$$&0U8+$,$"$j$^$9!#e(B
e$B$?$H$($P!“e(BSmalltalk e$B$G$ONc$,$”$j$^$9$M!#e(Bim
e$B$O!">/$J$$$G$9$,!"5uIt$r<($9e(B
e$B$?$a$K$b$D$+$o$l$k$N$G!“e(B(e$BFC$K5$$K$9$kDx$G$O$J$$$,e(B)
e$B<c43J6$i$o$7$$$H$3$me(B
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e$B$I$A$i$b$=$&$7$?$[$&$,$$$$$N$+$J!"$H;W$C$F$$$^$9$,!"$I$&$G$7$g$&!#e(B

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

In message “Re: [ruby-dev:36349] Complex/image”
on Wed, 17 Sep 2008 20:37:03 +0900, Tadayoshi F.
[email protected] writes:

|[ruby-math:00543] e$B$rFI$s$G!“e(Bimage e$B$O$d$a$Fe(B imag e$B$KJQ99$7$?$i$I$&$+!”$De(B
|e$B$$$G$Ke(B imaginary e$B$NJLL>$rF3F~$7$?$i$I$&$+!“$H9M$($F$$$^$9!#<g4Q$G$O!“5ue(B
|e$BIt$r;X$9$N$K$Oe(B imag e$B$,B?$/$F!“5)$Ke(B imaginarye$B!“e(Bim e$B$,$”$kDxEY$H46$8$^$9!#e(B
|
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|e$B$?$a$K$b$D$+$o$l$k$N$G!“e(B(e$BFC$K5$$K$9$kDx$G$O$J$$$,e(B) e$B<c43J6$i$o$7$$$H$3$me(B
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|
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e$B;d$O;?@.$7$^$9!#;d$N;?@.$,0UL#$,$"$k$+$I$&$+$O$H$b$+$/!#e(B

e$B$1$$$8$e!w$$$7$D$+$G$9e(B.

In [ruby-dev :36349 ] the message: "[ruby-dev:36349] Complex/image ",
on Sep/17 20:37(JST) Tadayoshi F. writes:

[ruby-math:00543] e$B$rFI$s$G!“e(Bimage e$B$O$d$a$Fe(B imag e$B$KJQ99$7$?$i$I$&$+!”$De(B
e$B$$$G$Ke(B imaginary e$B$NJLL>$rF3F~$7$?$i$I$&$+!"$H9M$($F$$$^$9!#<g4Q$G$O!"5ue(B
e$BIt$r;X$9$N$K$Oe(B imag e$B$,B?$/$F!"5)$Ke(B imaginarye$B!“e(Bim e$B$,$”$kDxEY$H46$8$^$9!#e(B

imagee$B$He(Bimage$B$N7o$G$9$,e(B, e$B8=9T$G$ON>J}Dj5A$5$l$F$$$k$1$Ie(B,
imagee$B$O:o=|$C$Fe(B
e$B$3$H$G$9$h$Me(B? e$B$b$&e(B, e$B:o=|$7$F$bNI$$5$$,$7$^$9e(B.
e$B$^$?$Oe(B, e$B2a5n$N8_49@-$r$H$Ce(B
e$B$Fe(B, e$B%o!<%K%s%0$r=P$9$+e(B…
e$B%o!<%K%s%0$r=P$9$h$&$K$J$C$F$+$i:o=|$,e(BRubye$BEe(B
e$B$K$O0lHLE
$N$h$&$G$9$,e(B.

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e$B$?$a$K$b$D$+$o$l$k$N$G!“e(B(e$BFC$K5$$K$9$kDx$G$O$J$$$,e(B) e$B<c43J6$i$o$7$$$H$3$me(B
e$B$b$”$j$^$9!#e(B

e$B$o$?$7$be(B, Numeric#im e$B$K$3$@$o$j$^$;$s$,e(B, e$B$=$NEv;~e(B,
ie$B$K$9$k$+e(Bime$B$K$9$k$+e(B
e$B$OG:$s$@$N$O;v<B$G$9e(B. e$B$"$^$j$K$b%a%=%C%IL>$,C;$$$G$9$7e(B.

1.i -> (0+1i)

e$B$K$J$k$N$Oe(B Complexe$BCN$C$F$$$k?M$O$J$C$H$/$G$7$g$&$,e(B,
e$B$J$8$_$N$J$$?M$K$Oe(B
e$B$I$&$+$H;W$C$?$o$1$G$9e(B.

Numeric#im e$B$re(B Numeric#i e$B$K$9$k$C$FOC$Ge(B, Complex
e$BFbIt$KJD$8$F$J$$$N$Ge(B,
e$B>>K$5$s$H$+B>$NJ}$N0U8+$rJ9$$$?J}$,NI$5$=$&$G$9e(B.

__
---------------------------------------------------->> e$B@PDMe(B
e$B7=<ye(B <<—
---------------------------------->> e-mail: [email protected] <<—

imagee$B$He(Bimage$B$N7o$G$9$,e(B, e$B8=9T$G$ON>J}Dj5A$5$l$F$$$k$1$Ie(B, imagee$B$O:o=|$C$Fe(B
e$B$3$H$G$9$h$Me(B? e$B$b$&e(B, e$B:o=|$7$F$bNI$$5$$,$7$^$9e(B. e$B$^$?$Oe(B, e$B2a5n$N8_49@-$r$H$Ce(B
e$B$Fe(B, e$B%o!<%K%s%0$r=P$9$+e(B… e$B%o!<%K%s%0$r=P$9$h$&$K$J$C$F$+$i:o=|$,e(BRubye$BEe(B
e$B$K$O0lHLE
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e$B$d$O$j$3$l$b:o=|$H$$$&;v$K$J$k$H;W$$$^$9$,!":#$N$H$3$mG0$N$?$ae(B
lib/complex.rb e$B$KJLL>Ey$r;D$9$3$H$K$7$F$$$^$9!#e(B

e$B$o$?$7$be(B, Numeric#im e$B$K$3$@$o$j$^$;$s$,e(B, e$B$=$NEv;~e(B, ie$B$K$9$k$+e(Bime$B$K$9$k$+e(B
e$B$OG:$s$@$N$O;v<B$G$9e(B. e$B$"$^$j$K$b%a%=%C%IL>$,C;$$$G$9$7e(B.

1.i → (0+1i)

e$B$K$J$k$N$Oe(B Complexe$BCN$C$F$$$k?M$O$J$C$H$/$G$7$g$&$,e(B, e$B$J$8$_$N$J$$?M$K$Oe(B
e$B$I$&$+$H;W$C$?$o$1$G$9e(B.

http://blog.s21g.com/articles/664

e$B$3$l$r8+$k$H!"4N?4$N$o$+$C$F$[$7$$?M$K$be(B #im
e$B$NB8:_$,M}2r$5$l$F$$$J$$$he(B
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e$B$G!“e(B
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e$B$H$+$”$C$?$iIT;W5D$K;W$&?M$O$$$k$+$b$7e(B
e$B$l$^$;$s$M!#e(B

e$B$1$$$8$e!w$$$7$D$+$G$9e(B.

In [ruby-dev :36372 ] the message: "[ruby-dev:36372] Re: Complex/image
", on Sep/18 20:05(JST) Tadayoshi F. writes:

e$B$d$O$j$3$l$b:o=|$H$$$&;v$K$J$k$H;W$$$^$9$,!":#$N$H$3$mG0$N$?$ae(B
lib/complex.rb e$B$KJLL>Ey$r;D$9$3$H$K$7$F$$$^$9!#e(B

e$B$O$$e(B.

Numeric#iで虚数を簡単に使う - Hello, world! - s21g

e$B$3$l$r8+$k$H!"4N?4$N$o$+$C$F$[$7$$?M$K$be(B #im e$B$NB8:_$,M}2r$5$l$F$$$J$$$he(B
e$B$&$G!#e(B

e$B$=$&$G$9$M$'e(B(^^;;;;

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e$B$$$&$$$&$b$N$,$"$l$P$$$i$J$$$C$F$$$&46$8$O$7$^$9!#e(B

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e$BJ#AG?t%j%F%i%k$”$C$F$bNI$$$G$9$M$'e(B.

Pythone$B$O5u?t%j%F%i%k$G$9$+e(B, Rubye$B$bF1$8$GNI$$$H;W$$$^$9$,e(B,
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Pythone$B$G$be(B, e$B$5$9$,$Ke(B, e$BIbF0>.?tE@%j%F%i%k$Ge(B, `.’

e$B$He(B `,’ e$B$r5U$K$O$7$Fe(B

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e$B$"$He(B, e$BJQ?t$Ge(Bie$B$H$+e(Bje$B$H$+$h$/;H$&$N$Ge(B,
e$B$=$l$b5$$K$7$^$7$?e(B. e$B$?$@e(B, Numeric
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e$B$l$^$;$s$,e(B.

__
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e$B7=<ye(B <<—
---------------------------------->> e-mail: [email protected] <<—

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

In message “Re: [ruby-dev:36386] Re: Complex/image”
on Fri, 19 Sep 2008 13:19:10 +0900, [email protected]
(e$B@PDM7=<ye(B) writes:

|>e$B$d$O$jJ#AG?t%j%F%i%k!“5u?t%j%F%i%k$NBe$j!”$C$FB&LL$b$"$j$=$&$J$N$G!"$=e(B
|>e$B$$$&$$$&$b$N$,$"$l$P$$$i$J$$$C$F$$$&46$8$O$7$^$9!#e(B
|
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e$B@K$7$$!#%*%i%s%@?M$G$9!#e(B

e$B$1$$$8$e!w$$$7$D$+$G$9e(B.

In [ruby-dev :36387 ] the message: "[ruby-dev:36387] Re: Complex/image
", on Sep/19 16:53(JST) Yukihiro M. writes:

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

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1/2

e$B$H$+e(B? e$B$3$C$A$O$9$0$K$O$^$H$^$i$J$=$&e(B(^^;

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(1/2) e$B$de(B (1+2i) e$B$N$h$&$K%+%C%3Fb$K6uGr$J$7$KB3$1$?>l9g$O!"e(B
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In message “Re: [ruby-dev:36391] Re: Complex/image”
on Fri, 19 Sep 2008 18:04:41 +0900, [email protected]
(e$B@PDM7=<ye(B) writes:

|>e$B$G$9$M!#e(B1.9.1e$B$K$O4V$K9g$$$=$&$K$J$$$G$9$,!#e(B
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  • e$B%a%=%C%Ie(Bime$B$He(Bimage

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

In message “Re: [ruby-dev:36396] Re: Complex/image”
on Fri, 19 Sep 2008 21:14:43 +0900, Tadayoshi F.
[email protected] writes:

|e$B8=;~E@$GH=CG$,$D$+$J$$$h$&$J$i!“0lC6:o=|$7$Fe(B2.0 e$B$K8~$1$F$N:n6H$G!“B>$Ne(B
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e$B!V0lC6:o=|$7$F!W$H$$$&$N$O$I$3$^$G:o=|$9$k$C$F$3$H$G$7$g$&$+!#e(B

  • e$B%a%=%C%Ie(Bim
  • e$B%a%=%C%Ie(Bime$B$He(Bimage
  • e$BJ#AG?tA4Ite(B
  • e$BJ#AG?t$HM-M}?te(B

e$B!V0lC6:o=|$7$F!W$H$$$&$N$O$I$3$^$G:o=|$9$k$C$F$3$H$G$7$g$&$+!#e(B

  • e$B%a%=%C%Ie(Bim
  • e$B%a%=%C%Ie(Bime$B$He(Bimage
  • e$BJ#AG?tA4Ite(B
  • e$BJ#AG?t$HM-M}?te(B

e$B$=$l$K$7$F$b!"$I$&FI$s$G$bJ#AG?t$HM-M}?t$r:o=|$9$k$h$&$K$O2r<a$G$-$J$$e(B
e$B$H;W$&$s$G$9$,!":o=|$7$?$1$l$P:o=|$9$l$P$$$$$H;W$$$^$9!#$^$D$b$H$5$s$,e(B
e$BH=CG$9$l$P$$$$$3$H$J$N$G!#e(B

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

In message “Re: [ruby-dev:36405] Re: Complex/image”
on Sat, 20 Sep 2008 09:14:47 +0900, Tadayoshi F.
[email protected] writes:

|> e$B!V0lC6:o=|$7$F!W$H$$$&$N$O$I$3$^$G:o=|$9$k$C$F$3$H$G$7$g$&$+!#e(B
|>
|> * e$B%a%=%C%Ie(Bim
|> * e$B%a%=%C%Ie(Bime$B$He(Bimage
|> * e$BJ#AG?tA4Ite(B
|> * e$BJ#AG?t$HM-M}?te(B
|
|e$B$=$l$K$7$F$b!“$I$&FI$s$G$bJ#AG?t$HM-M}?t$r:o=|$9$k$h$&$K$O2r<a$G$-$J$$e(B
|e$B$H;W$&$s$G$9$,!”:o=|$7$?$1$l$P:o=|$9$l$P$$$$$H;W$$$^$9!#$^$D$b$H$5$s$,e(B
|e$BH=CG$9$l$P$$$$$3$H$J$N$G!#e(B

e$B$9$$$^$;$s!“;d$O$3$N5DO@A4BN$r%U%)%m!<$7$F$J$$$s$GJ8L.$J$7$Ge(B
e$BFI$s$G$^$9$+$i!#;d$,:o=|$7$?$$$H$+$=$&$$$&B>0U$O$”$j$^$;$s!#e(B

#im e$B$O:o=|$5$;$F$b$i$*$&$H;W$$$^$9!#BeBX$N%a%=%C%I$O$"$j$^$;$s!#e(B
e$BM}M3$O!"e(B

  1. Complex#im
    e$B$O!"$d$O$j5uIt$r;2>H$9$k%a%=%C%I$K8+$($k!#$3$l$O?t3X$N47e(B
    e$B=,$K1h$C$F$$$F!"<B:]$=$N$h$&$J<BAuNc$,$$$/$D$+$"$k!#e(B

  2. Numeric#im e$B$O$o$+$jFq$$;v$KJQ$j$J$$!#BeBX0F$Ne(B #i
    e$B$O$h$jC;$+$$$N$,Fqe(B
    e$BE@e(B
    (e$B$@$,$"$k<o$N@5E}@-$,$"$C$F!"H=$k?M$K$OH=$k$H;W$o$l$ke(B)e$B!#e(B

  3. #im e$B$be(B #i
    e$B$bHyL/$@$H$9$l$P!“L5M}$KMQ0U$9$kDx$N$b$N$G$O$J$$e(B (e$B$J$$$H:$e(B
    e$B$k$H$$$&$b$N$G$b$J$$e(B)e$B!#6a$$>-Mh!”%j%F%i%k$,MQ0U$5$l$k2DG=@-$b$"$j!"$=$Ne(B
    e$B>l9g!"B8:_0U5A$,Gv$l$F$7$^$&!#e(B

ruby 1.8 e$B$Ge(B Numeric
e$B$K$"$k%a%=%C%I$G:G$bC;$$$b$N$O!"e(Babse$B!"e(Bdive$B!"e(Bquo
e$B$G$9e(B
e$B$,e(B (e$B1i;;;R$O=|$/e(B)e$B!“e(B#im
e$B$O$3$l$i$h$j$b99$KC;$+$$$G$9!#$7$+$b2r$j0W$5$G$O!“e(B
e$B$`$7$me(B #i
e$B$h$j$bNt$k$H;W$o$l$^$9!#AH$9~$$H$7$F?75,$”$D$+$$$Ne(B Complex
e$B$N$?$a$K$”$($F$3$l$r7Q>5$9$k0UL#$O$J$$$H;W$$$^$9!#e(B

e$B$b$7!";D$9$b$C$H$b$JM}M3$,$"$l$PI|3h$5$;$^$9!#e(B