Rational.rb, complex.rb and mathn.rb

rational e$B$He(B complex e$B$,AH$9~$$K$J$C$?$3$H$G!“e(Blib/mathn.rb
e$B$N0U5A$OGve(B
e$B$l$?LL$,$”$j$^$9!#e(B

rational e$B$He(B complex
e$B$,AH$9~$$K$J$k$H$$$&$3$H$O!“C1$K!”$=$l$i$,!"$I$se(B
e$B$J>l9g$be(B require
e$B$5$l$?>uBV$G$"$k!"$H$$$&$3$H$H$O0c$&$+$i$G$9!#e(B

require ‘mathn’ e$B$9$k$He(B (-8) ** Rational(1,2)
e$B$N7k2L$OJ#AG?t$K$J$j$^$9e(B
e$B$,!":#$d!":G=i$+$i$=$N$h$&$K$J$C$F$$$F$b$*$+$7$/$J$$$G$7$g$&!#e(B

e$B0lJ}$G!"e(Brequire ‘mathn’ e$B$7$F$be(B (-8.0) ** Rational(1,2)
e$B$de(B (-8) ** 0.5
e$B$N7k2L$OJ#AG?t$K$J$j$^$;$s!#e(B

e$B$D$^$j!“8=>u$Ne(B mathn e$B$K$OLdBj$J$j2]Bj$,$”$k$o$1$G$9!#e(B

e$B$D$E$/e(B

e$B8=;[email protected]$Ge(B rational.rb e$B$He(B complex.rb
e$B$r;D$7$F$$$k$N$O!"$=$l$,[email protected]$+$ie(B
e$B$G$9!#[email protected]$r=E;k$9$kN)>[email protected][email protected]$^$9!#$7$+$7!"9%$^e(B
e$B$7$/[email protected]$b0z$-7Q$$$G$7$^$&$+$b$7$l$^$;$s!#e(B

e$B$=$N5$$K$J$l$P!"e(Brational.rbe$B!"e(Bcomplex.rb
e$B$N$_$J$i$:!“e(Bmathn.rb e$B$b4]$4$He(B
e$B:o=|$9$k$3$H$b2DG=$G$7$g$&!#2>Dj$NOC$G$9$,!”$3$l$r9M$($k$3$H$K$h$C$F!"e(B
e$B2?$,LdBj$J$N$+H=$k$+$b$7$l$^$;$s!#e(B

e$B$^$:!“e(Brational.rb
e$B$K$O!”$b$O$dBg$7$?$b$N$O;D$C$F$$$^$;$s!#Hf3SE*0UL#$,e(B
e$B$"$k$N$O!"e(Bgcd (e$B5Z$Se(B lcm e$B$He(B gcdlcm) e$B$G$9!#e(B

gcd e$B$,$"$k$N$O!“e(Brational
e$B$G$D$+$&0Y$G$9!#@PDM$5$s$O!“MxMQ<T$,$D$+$C$Fe(B
e$B$b9=$o$J$$!”$H9M$($?$H;W$$$^$9$,!“4pK\E*$K$Oe(B rational
e$B$G$D$+$&0Y$KB8:_e(B
e$B$7$^$9!#$=$l0J30$K!“e(Bgcd e$B$,e(B rational.rb
e$B$K$”$kM}M3$O$J$$$G$7$g$&!#8+$?e(B
e$B$H$3$m!”$3$Ne(B gcd e$B$O$”$^$j4X?4$r=8$a$F$O$$$J$$$h$&$G$9!#e(B

e$B$I$l$/$i$$4X?4$,$J$$$+$H$$$($P!"$3$Ne(B gcd
e$B$,OCBj$K$J$k$N$,!"$b$C$Q$ie(B
rational e$B$NB.EY2~A1$K4X$9$k$K>l9g$G!"$=$N0Y$K$+$J$jAa$$;~4|$+$ie(B
gcd [email protected](B
e$B$1$G$bAH$9~$$K$7$?$i$I$&$+$H$$$&OC$OEY!9Ds0F$5$l$F$-$?$K$b4X$o$i$:!"e(B
e$B:#F|$^$GJ|CV$5$l$F$$$k$/$i$$$G$9!#e(B

gcd e$B$K$D$$$F$O!"<N$F$k$+!"e(Bruby
e$BK\BN$K5[<}$9$k$+$I$A$i$+$K$J$j$^$9e(B (e$B%ae(B
e$B%=%C%I7A<0$+!"4X?t7A<0$+$N$$$E$l$+$Ge(B)e$B!#e(B

complex.rb e$B$G$O!“e(BMath
e$B4X?t$NCV$-49$($,$”$j$^$9!#$3$l$O$?$V$s<N$F$i$l$Je(B
e$B$$$H;W$$$^$9!#e(B

e$BK\BN$K5[<}$9$k>l9g$$$/$D$+$NA*Br$,$"$k$H;W$$$^$9!#$?$H$($P!“e(Bpython
e$B$Je(B
e$B$I$G$O!“e(Bmath e$B$NB>$K!“e(Bcmath e$B$,$”$j$^$9!#e(Bruby
e$B$G$b!”$=$N$h$&$J7A$G<h$j$3e(B
e$B$`$3$H$,2DG=$G$7$g$&!#[email protected]!”$3$N>l9g!“e(Bsqrt(aRational)
e$B$r$I$3$G0z$-<u$1e(B
e$B$k$N$+!”$H$$$C$?$3$H$,LdBj$K$J$k$+$b$7$l$^$;$s!#$^$?!"e(Bruby
e$B$NBg%/%i%9e(B
e$B<g5Ae(B (e$B%/%i%9$G$O$J$$$,e(B)
[email protected]$^$J$$$+$b$7$l$^$;$s!#e(B

e$B$"$k$$$O!"e(B(e$B:#8=:_e(B complex.rb [email protected]$H$-$N$h$&$Ke(B)
Math e$B$N4X?t$rCVe(B
e$B$-49$($F!“J#AG?t0h$K$^$G3HBg$9$k$3$H$b2DG=$G$9!#B.EY$O<c43CY$/$J$k$+$be(B
e$B$7$l$^$;$s!#e(Bruby e$B$Ne(B Math e$B%b%8%e!<%k$O!“e(BTime
e$B$HF1MM$Ke(B ruby e$B$N$*$1$ke(B
Unix/C
e$B<g5A$N8=$l$H;W$o$l$k$N$G!”[email protected]}@-$r0];}$7$h$&$H$9$k$H!”$3$Ne(B
e$B<j$O$D$+$($J$$$+$b$7$l$^$;$s!#e(B

mathn e$B$G$O!“e(B** e$B$He(B sqrt
e$B$r:FDj5A$7$F$”$j!"@PDM$5$s<+$i$$$o$l$k$h$&$K!"e(B
e$B$J$+$J$+J#;($=$&$G$9$,!“e(B** e$B$OJ#AG?tBP1~!“e(Bsqrt e$B$Oe(B
complex.rb e$B$G$b:FDj5Ae(B
e$B$7$F$$$^$9$,!“e(Bmathn
e$B$G$OM-M}?t$K$bBP1~$9$k!”$H$$$&$3$H$G$”$k$H;W$$$^$9!#e(B
** e$B$He(B sqrt e$B$OB8:_0U5A$,HyL/$9$.$k$N$G!”$$$E$l$K$7$F$be(B
mathn.rb e$B$+$i$Oe(B
e$BE15n$9$k$7$+$J$$$H;W$$$^$9!#e(B

mathn.rb e$B$G$O!“1i;;;Re(B / e$B$NCV$-49$($,$”$j$^$9$,!"$3$N5!G=$re(B
ruby e$BK\BN$Ke(B
e$BAH$_9~$`$3$H$b2DG=$G$O$J$$$+$H;W$$$^$9!#e(Bruby e$B$K!"%*%W%7%g%se(B
m e$B$rDI2C$7!"e(B
ruby -m e$B$H$7$?>l9g$O!"e(Bmathn
e$B$N$h$&$K1i;;;R$rCV$-49$($^$9!#$3$l$O<BAu$Ne(B
e$BLL$G$bET9g$,$$$$$+$b$7$l$^$;$se(B (e$B8=CJ3,$G$Oe(B matrix
e$B$N$3$H$OD|$a$J$1$l$Pe(B
e$B$J$j$^$;$se(B)e$B!#e(B

mathn.rb e$B$G$Oe(B Prime
e$B$b$"$j$^$9$,!"$3$l$O<N$F$k$+!"$I$3$+$K0$9e(B
(lib/prime.rb e$B$J$Ie(B) [email protected]$H;W$$$^$9!#e(B

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

In message “Re: [ruby-dev:34107] Re: rational.rb, complex.rb and
mathn.rb”
on Sat, 22 Mar 2008 15:59:28 +0900, Tadayoshi F.
[email protected]lid writes:

|lib/rational.rb e$B$O$J$/$9!#e(B
|
| gcd e$B$O!"$I$&$7$F$b;D$7$?$1$l$P!“e(Bruby e$BK\BN$K5[<}$9$k$+!“JLES!“e(B
| lib/gcd.rb (?) e$B$J$I$KCV$-$^$9!#e(B
|
|lib/complex.rb e$B$b$J$/$9!#e(B
|
| Math e$B$rJ#AG?tBP1~HG$GCV$-49$($F$7$^$$$^$9!#e(B
| e$B4pK\E*$K$O!”:#$”[email protected]$re(B C e$B$KD>$7$Fe(B math.c e$B$KH?1G$5$;[email protected]$1$G$9!#e(B
| e$B$b$A$m$s!”$b$C$H8zN([email protected]:EYLL$G!“M%$l$?$b$N$,$”$l$P!"$=$l$r$D$+$C$F$be(B
| e$B$$$$$G$9!#e(B

e$B$$$:$l$b;[email protected]$G$9$,!"EvLL$O6u$Ne(Brational.rbe$B$He(Bcomplex.rbe$B$r;D$7e(B
e$B$F$*$$$F$[$7$$$G$9!#7Y9p$r=P$9$N$b$h$$$+$b$7$l$^$;$s!#e(B

|lib/mathn.rb e$B$O;D$7$F$b$$$$!#e(B
|
| e$B$1$I!"Cf?H$O!"e(Brequire ‘matrix’ e$B$He(B / e$B$NCV$-49$($He(B Unify [email protected]$1$Ke(B
| e$B$7$^$9!#e(B** e$B$de(B sqrt e$B$N:FDj5A$O!"[email protected]$15b$<h$C$F<N$F$^$9!#e(B
| Prime e$B$O;D$7$?$1$l$P!"e(B lib/prime.rb (?) e$B$J$I$KCV$-$^$9!#e(B
| ruby -m [email protected]
$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

mathne$B$r;D$9$3$H$K$O;[email protected]$7$^$9!#$G$b!"e(Bruby
-me$B$C$F$J$s$G$9$+$M!#e(B

e$B$G!"$+$J$jA*Br;h$r9J$C$?C!$-Bf$G$9!#e(B

lib/rational.rb e$B$O$J$/$9!#e(B

gcd e$B$O!"$I$&$7$F$b;D$7$?$1$l$P!"e(Bruby
e$BK\BN$K5[<}$9$k$+!"JLES!"e(B
lib/gcd.rb (?) e$B$J$I$KCV$-$^$9!#e(B

lib/complex.rb e$B$b$J$/$9!#e(B

Math e$B$rJ#AG?tBP1~HG$GCV$-49$($F$7$^$$$^$9!#e(B
e$B4pK\E*$K$O!":#$"[email protected]$re(B C e$B$KD>$7$Fe(B math.c
e$B$KH?1G$5$;[email protected]$1$G$9!#e(B
e$B$b$A$m$s!"$b$C$H8zN([email protected]:EYLL$G!“M%$l$?$b$N$,$”$l$P!"$=$l$r$D$+$C$F$be(B
e$B$$$$$G$9!#e(B

lib/mathn.rb e$B$O;D$7$F$b$$$$!#e(B

e$B$1$I!"Cf?H$O!"e(Brequire ‘matrix’ e$B$He(B / e$B$NCV$-49$($He(B
Unify [email protected]$1$Ke(B
e$B$7$^$9!#e(B** e$B$de(B sqrt
e$B$N:FDj5A$O!"[email protected]$15b$<h$C$F<N$F$^$9!#e(B
Prime e$B$O;D$7$?$1$l$P!"e(B lib/prime.rb (?) e$B$J$I$KCV$-$^$9!#e(B
ruby -m [email protected]
$9$l$P!"e(Blib/mathn.rb
e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

e$B$3$l$r<B:]$d$k$d$i$J$$$K4X$o$i$:!"[email protected]$&[email protected]$C$?$H;W$&$N$G!"e(B
e$B$3$3$^$G$G!"e(Bcomplexe$B!"e(Brational
e$BAH$9~$$N=i4|E*$JLrL$O2L$;$?$H;W$$$^$9!#e(B

[email protected]>;3OB9-$G$9!#e(B

At Sat, 22 Mar 2008 16:49:20 +0900,
Yukihiro M. wrote:

| ruby -m [email protected]_$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

mathne$B$r;D$9$3$H$K$O;[email protected]$7$^$9!#$G$b!"e(Bruby -me$B$C$F$J$s$G$9$+$M!#e(B

–enablee$B$de(B–disablee$B$,$"$k$N$G!"e(Bruby
–enable=mathe$B$H$+$G$7$g$&$+!#e(B

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

In [ruby-dev :34107 ] the message: "[ruby-dev:34107] Re: rational.rb,
complex.rb and mathn.rb ", on Mar/22 15:59(JST) Tadayoshi F.
writes:

lib/rational.rb e$B$O$J$/$9!#e(B

gcd e$B$O!"$I$&$7$F$b;D$7$?$1$l$P!"e(Bruby e$BK\BN$K5[<}$9$k$+!"JLES!"e(B
lib/gcd.rb (?) e$B$J$I$KCV$-$^$9!#e(B

rational.c e$B$NCf$Ke(B gcd e$B<B:]$K$O$"$k$o$1$G$9$h$Me(B?
e$B$=$l$r;H$($k$h$&$K$7$?e(B
e$B$iNI$$$H;W$&$N$G$9$,e(B? e$B$D$^$je(B,
rubye$BK\BN$K5[<}$C$F$3$H$G$9$,e(B.

lib/complex.rb e$B$b$J$/$9!#e(B

Math e$B$rJ#AG?tBP1~HG$GCV$-49$($F$7$^$$$^$9!#e(B
e$B4pK\E*$K$O!":#$"[email protected]$re(B C e$B$KD>$7$Fe(B math.c e$B$KH?1G$5$;[email protected]$1$G$9!#e(B
e$B$b$A$m$s!"$b$C$H8zN([email protected]:EYLL$G!“M%$l$?$b$N$,$”$l$P!"$=$l$r$D$+$C$F$be(B
e$B$$$$$G$9!#e(B

e$B$3$l$O$3$l$GNI$$5$$,$7$^$9e(B.

[email protected](B, e$B:#$^[email protected]$,5$$K$J$i$J$$$o$1$G$b$J$$$G$9$,e(B,
e$B:#$^$GNc30$,5/$3$Ce(B
e$B$F$$$?>lLL$Ge(BComplexe$B$,5"$C$F$/$k$3$H$K$J$j$^$9$N$Ge(B…
e$B8_49%b!<%I$K$9$ke(B
e$B2?$+$rMQ0U$7$?J}$,NI$$$+$be(B.

lib/mathn.rb e$B$O;D$7$F$b$$$$!#e(B

e$B$1$I!"Cf?H$O!"e(Brequire ‘matrix’ e$B$He(B / e$B$NCV$-49$($He(B Unify [email protected]$1$Ke(B
e$B$7$^$9!#e(B** e$B$de(B sqrt e$B$N:FDj5A$O!"[email protected]$15b$<h$C$F<N$F$^$9!#e(B
Prime e$B$O;D$7$?$1$l$P!"e(B lib/prime.rb (?) e$B$J$I$KCV$-$^$9!#e(B
ruby -m [email protected]
$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

e$B$G$-$l$Pe(B, e$B$3$N$^$^;D$7$F$*$$$FM_$7$$$J$!e(B.
e$BLdBj$,$"$k$H$$$&$+CfESH>C<$Je(B
e$B$H$3$m$,$"$k$N$OG’$a$^$9e(B. e$B$3$l$O$3$l$G4hD%$k$H$$$&$3$H$Ge(B.

[email protected](B:

ruby -m [email protected]_$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

e$B$Ge(B, “/” e$B$rCV$-49$($k$H$$$&$N$G$"$l$Pe(B,
e$BOC$OJQ$o$C$F$/$k$H;W$$$^$9$,e(B.

e$B$3$l$r<B:]$d$k$d$i$J$$$K4X$o$i$:!"[email protected]$&[email protected]$C$?$H;W$&$N$G!"e(B
e$B$3$3$^$G$G!"e(Bcomplexe$B!"e(Brational e$BAH$9~$$N=i4|E*$JLrL$O2L$;$?$H;W$$$^e(B
e$B$9!#e(B

e$B;d$+$i$$$&$N$b2?$J$s$G$9$,e(B, e$B$"$j$,$H$&$4$6$$$^$7$?e(B.

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

e$B86$G$9!#e(B

e$B;d$be(B Complex e$B$NAH$9~$$Oe(B Rational
e$B$H$OHf3S$K$J$i$J$$$/$i$$!";EMM$,7h$ae(B
e$B$K$/$$$N$G!“AH$9~$>C6KE*[email protected]$C$?$s$G$9$,!”$b$&F~$l$k$H7h$a$F$7$^$C$?$s$Ge(B
e$B$9$h$M!)e(B

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

In [ruby-dev :34107 ] the message: "[ruby-dev:34107] Re: rational.rb,
complex.rb and mathn.rb ", on Mar/22 15:59(JST) Tadayoshi F.
writes:

lib/rational.rb e$B$O$J$/$9!#e(B

gcd e$B$O!"$I$&$7$F$b;D$7$?$1$l$P!"e(Bruby e$BK\BN$K5[<}$9$k$+!"JLES!"e(B
lib/gcd.rb (?) e$B$J$I$KCV$-$^$9!#e(B

e$B;d$b!"e(BInteger e$B$N%a%=%C%I$H$7$FAH$_9~$s$G$[$7$$$G$9!#e(B

e$B$F$$$?>lLL$Ge(BComplexe$B$,5"$C$F$/$k$3$H$K$J$j$^$9$N$Ge(B… e$B8_49%b!<%I$K$9$ke(B
e$B2?$+$rMQ0U$7$?J}$,NI$$$+$be(B.

e$BFq$7$$$G$9$M!#$d$C$Q$j%G%U%)%k%H$G$O!"e(Bsqrt(-1)
e$B$ONc30$8$c$J$$$+$J!#e(B

lib/mathn.rb e$B$O;D$7$F$b$$$$!#e(B

e$B$1$I!"Cf?H$O!"e(Brequire ‘matrix’ e$B$He(B / e$B$NCV$-49$($He(B Unify [email protected]$1$Ke(B
e$B$7$^$9!#e(B** e$B$de(B sqrt e$B$N:FDj5A$O!"[email protected]$15b$<h$C$F<N$F$^$9!#e(B
Prime e$B$O;D$7$?$1$l$P!"e(B lib/prime.rb (?) e$B$J$I$KCV$-$^$9!#e(B
ruby -m [email protected]
$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

e$B$G$-$l$Pe(B, e$B$3$N$^$^;D$7$F$*$$$FM_$7$$$J$!e(B. e$BLdBj$,$"$k$H$$$&$+CfESH>C<$Je(B
e$B$H$3$m$,$"$k$N$OG’$a$^$9e(B. e$B$3$l$O$3$l$G4hD%$k$H$$$&$3$H$Ge(B.

e$B:#2s!"e(Bmathn.rb e$B$Ge(B aRational**aRational e$B$,e(B Rational
e$B$GI=8=$G$-$k$H$-$O!"e(B
Rational
e$B$rJV$9$h$&$K6E$C$?:n$j$K$J$C$F$k$N$K5$IU$-$^$7$?!#$$$^$5$i!#e(B
e$B$9$P$i$7$$!#e(B

[email protected]!"@PDM$5$s$OAG0x?tJ,2r$r;H$C$F$$$k$1$I!"$b$&$A$g$C$HB.$$J}K!$,$"$ke(B
e$B$+$b$7$l$^$;$s$M!#e(B1/2
e$B>[email protected]$H!"@0?t$N9bB.$KJ?J}:,$r5a$a$kJ}K!$,!"e(B
ruby/math e$B$N$I$3$+$Ge(B isqrt
e$B$H$+$$$&L>A0$GDs0F$5$l$F$$$?$7!"[email protected]?t$Ne(B
1/n
e$B>h$b%K%e!<%H%sK!$r;H$C$FB.$/5a$a$k$3$H$,$G$-$k$H;W$$$^$9!#B?J,J#AG?te(B
e$BCM$G$bF1MM$K=PMh$F!"e(B(-8)**Rational(1,3) e$B$re(B Complex(0,
Rational(2)) e$B$K$Ge(B
e$B$-$k$N$G$O$J$$$+!#e(B

e$B$G$b!“AH$9~$$G$=$3$^$G$9$k$N$O!”$d$j$9$.$G$9$M!#e(B

e$B$3$l$r<B:]$d$k$d$i$J$$$K4X$o$i$:!"[email protected]$&[email protected]$C$?$H;W$&$N$G!"e(B
e$B$3$3$^$G$G!"e(Bcomplexe$B!"e(Brational e$BAH$9~$$N=i4|E*$JLrL$O2L$;$?$H;W$$$^e(B
e$B$9!#e(B

e$B;d$+$i$$$&$N$b2?$J$s$G$9$,e(B, e$B$"$j$,$H$&$4$6$$$^$7$?e(B.

e$B;d$+$i$b!#$U$J$P$5$s!"$"$j$,$H$&$4$6$^$7$?!#e(B

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In message “Re: [ruby-dev:34130] Re: rational.rb, complex.rb and
mathn.rb”
on Tue, 25 Mar 2008 21:56:25 +0900, Tadayoshi F.
[email protected] writes:

|> e$BFq$7$$$G$9$M!#$d$C$Q$j%G%U%)%k%H$G$O!"e(Bsqrt(-1) e$B$ONc30$8$c$J$$$+$J!#e(B
|
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e$BC&$9$k$H$$$&$N$,7|G0$H$$$($P7|G0$G$9$M!#e(BPythone$B$G$be(B

math.sqrt(-1)

e$B$Oe(B ValueError: math domain error
e$B$K$J$j$^$9!#$G$O!"e(BRubye$B$G$O$Ie(B
e$B$&[email protected]$($P!“e(Blibme$B$H$N4XO”@-$O:#8eD>@\E*$G$J$$$H7h$a$l$Pe(B
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                            e$B$^$D$b$He(B e$B$f$-$R$me(B /:|)

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

In message “Re: [ruby-dev:34125] Re: rational.rb, complex.rb and
mathn.rb”
on Tue, 25 Mar 2008 18:12:10 +0900, Shin-ichiro HARA
[email protected] writes:

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Tadayoshi F. e$B$5$s$O=q$-$^$7$?e(B:

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Tadayoshi F. e$B$5$s$O=q$-$^$7$?e(B:

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(2) Math.sqrt(-8) e$B$O!"Nc30H/@8e(B

e$B$G$I$&$G$7$g$&$+!#e(B(2) e$B$NM}M3$O!VEAE}$N0];}!W$G$9!#e(B(1)
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e$B<2C+$G$9!#e(B

-------- Original Message --------
Subject: [ruby-dev:34140] Re: rational.rb, complex.rb and mathn.rb
From: Nobuyoshi N. [email protected]
To: ruby developers list [email protected]
Date: Wed Mar 26 2008 18:20:01 GMT+0900

(1+e$B"ee(B3i)(1+e$B"ee(B3i) = 1+(-3)+2e$B"ee(B3i = -2+2e$B"ee(B3i = -2(1-e$B"ee(B3i)
-2(1-e$B"ee(B3i)
(1+e$B"ee(B3i) = -2(1-(-3)) = -8

e$B$G$7$g$&!#$J$<<B?t2r$h$j$b5u?t2r$,M%@h$5$l$k$N$+$O5?Ld$G$9$,!#e(B

e$B6K:BI8I=<($r$7$?$H$-$K!"3QEY$,0lHV>.$5$$$+$i$G$O$J$$$G$7$g$&$+!#e(B

[email protected]$G$9!#e(B

At Wed, 26 Mar 2008 02:17:39 +0900,
Shin-ichiro HARA wrote in [ruby-dev:34134]:

(expt -8 1/3) ;=> #C(1.0 1.7320508)

e$B$"$"!"$J$k$[$I!#e(B-8 e$B$Ne(B3e$B>h:,$O!"e(B1+e$B"ee(B3i e$B$G$9$+!#e(B

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e$B$G$J$/$J$k$1$I!”$=$NJ}$,$$$$$N$+$J!#e(B

(1+e$B"ee(B3i)(1+e$B"ee(B3i) = 1+(-3)+2e$B"ee(B3i = -2+2e$B"ee(B3i =
-2(1-e$B"ee(B3i)
-2(1-e$B"ee(B3i)
(1+e$B"ee(B3i) = -2(1-(-3)) = -8

e$B$G$7$g$&!#$J$<<B?t2r$h$j$b5u?t2r$,M%@h$5$l$k$N$+$O5?Ld$G$9$,!#e(B

e$B86$G$9!#e(B

(1+e$B"ee(B3i)(1+e$B"ee(B3i) = 1+(-3)+2e$B"ee(B3i = -2+2e$B"ee(B3i = -2(1-e$B"ee(B3i)
-2(1-e$B"ee(B3i)
(1+e$B"ee(B3i) = -2(1-(-3)) = -8

e$B$G$7$g$&!#e(B

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e$B$G$I$&$G$7$g$&$+!#e(B(2) e$B$NM}M3$O!VEAE}$N0];}!W$G$9!#e(B(1) e$B$O!“[email protected]$,$J$$e(B
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e$B$d$C$Q$jFq$7$$$J$"!#e(B

e$B$d$O$j$A$0$O$0$J46$8$,$7$^$9$M!#e(B

ruby e$B$G$O!“F1$8?tCM$re(B Rational e$B$G$be(B Complex
e$B$G$bI=8=$G$-!”$^$?!“4X?t7Ae(B
e$B<0!”%a%=%C%I7A<0!“1i;;;R4V$G0c$$$,$”$C$F!"$5$i$Ke(B mathn
e$B$b$"$C$F!"$"$A$3e(B
e$B$AJ,CG$5$l$F$$$k$h$&$K46$8$^$9!#e(B

e$B$3$N0F$r:NMQ$7$?$H$7$F!"e(B

Math.sqrt(Rational(1,4)) #=> Rational(1, 2)
Math.sqrt(4) #=> 2

e$B$N$h$&$J$3$H$r$7$?$$>l9g!"$I$&$$$&BP1~$K$J$k$s$G$7$g$&$M!#e(B

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

e$B%a%$%k$,:xAn$7$F$$$^$9$,e(B…

In [ruby-dev :34129 ] the message: "[ruby-dev:34129] Re: rational.rb,
complex.rb and mathn.rb ", on Mar/25 20:15(JST) Tadayoshi F.
writes:

[email protected](B, e$B:#$^[email protected]$,5$$K$J$i$J$$$o$1$G$b$J$$$G$9$,e(B, e$B:#$^$GNc30$,5/$3$Ce(B
e$B$F$$$?>lLL$Ge(BComplexe$B$,5"$C$F$/$k$3$H$K$J$j$^$9$N$Ge(B… e$B8_49%b!<%I$K$9$ke(B
e$B2?$+$rMQ0U$7$?J}$,NI$$$+$be(B.
Math.fsin e$B$N$h$&$J$N$r:n$C$F!"e(Brequire ‘fmath’ e$B$H$+$9$k$He(B Math.sin e$B$,e(B
fsin e$B$GCV$-49$($i$l$k$h$&$Je(B?

[email protected]$H;W$$$^$9$,e(B,
e$B$=$l0JA0$NCJ3,$G$b$a$F$$$^$9$+$i$M$'e(B…

lib/mathn.rb e$B$O;D$7$F$b$$$$!#e(B

e$B$1$I!"Cf?H$O!"e(Brequire ‘matrix’ e$B$He(B / e$B$NCV$-49$($He(B Unify [email protected]$1$Ke(B
e$B$7$^$9!#e(B** e$B$de(B sqrt e$B$N:FDj5A$O!"[email protected]$15b$<h$C$F<N$F$^$9!#e(B
Prime e$B$O;D$7$?$1$l$P!"e(B lib/prime.rb (?) e$B$J$I$KCV$-$^$9!#e(B
ruby -m [email protected]
$9$l$P!"e(Blib/mathn.rb e$B$b$$$i$J$$$+$b$7$l$^$;$s!#e(B

e$B$3$N$^$^!"$H$$$&$3$H$O!“e(B** e$B$de(B sqrt e$B$b$=$N$^$^!“e(BPrime e$B4XO”$b$=$N$^$^!”$He(B
e$B$$$&$3$H$G$9$h$M!#e(B

e$B$G$9$Me(B.

e$B$*$=$i$/!“e(B** e$B$de(B sqrt e$B$G!“e(Bruby e$BK\BN$G$ODs6!$G$-$J$$2?$+$,$”$k!”$H$$$&$3e(B
e$B$H$G$9$h$M!#$=$l$O$I$s$J$b$N$G!"2?8N!"e(Bruby e$BK\BN$G$ODs6!$G$-$J$$$N$G$7$ge(B
e$B$&$+!#e(B

e$B$(!<$He(B.

e$B$7$^$9!#e(B** e$B$de(B sqrt e$B$N:FDj5A$O!"[email protected]$15b$_<h$C$F<N$F$^$9!#e(B

e$B$H$$$&$N$Oe(B, rubye$BK\BN$Ge(B
mathne$B$GDj5A$7$F$$$k$h$&$J$b$N$rDs6!$7$h$C$F$3$He(B
[email protected]$C$?$N$G$9e(B? e$B$=$l$J$ie(B, e$BA4A30U5A$O$J$$$G$9e(B.

[email protected](B, e$B86$5$s$b$*$C$7$c$C$F$$$k$h$&$Ke(B,
e$B$$$^$Ne(BMathne$B$Ne(B**e$B$rAH$9~$$K$9$ke(B
e$B$N$OL5M}$,$"$k$h$&$J5$$b$7$J$$$G$b$J$$$G$9$,e(B.

matrix e$B$O!"$=$l$rC1BN$GMxMQ$G$-$^$9$,!“e(BPrime e$B$Oe(B / e$B$NCV$-49$($J$I$H0l=oe(B
e$B$KDs6!$5$l$F$$$^$9!”$3$l$OIT2DJ,$J4X78$G$"$k!"$H$$$&$3$H$G$7$g$&$+!#e(B

e$B$=$l$Oe(B, e$BJ,$1$F$b$h$$$H;W$$$^$9e(B.

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

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