🚀 go-pugleaf

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In article <OKABE.92Nov4223444@sole.kutsuda.kuis.kyoto-u.ac.jp> okabe@kutsuda.kuis.kyoto-u.ac.jp (Yasuo Okabe) writes:
 >>shige>   $@#4<!$NBe?tJ}Dx<0$K4X$9$k<A(J$@Ld$G$9(J ^o^;$@!#(J
 >>$@!V%*%$%i!<$N2rK!!W$H8F$P$l$F$$$kJ}K!$G$9$M!#(J
 >>shige> 	x^4 + x^3 == 0
 >>shige> $@$r2r(J$@$/$H!"(Jx = 1/2, -1/2$@!J#3=E2r!K$K$J$C$F$7$^$$$^$9!#(J
 >>		    ~~~~~~~~~~~~~~~~~~~~~~
 >>$@$3$N7k2L$,=P$kF;(J$@6Z$r<($7$FD:$1$^$9$+!)(J

$@$?$7$+$K2#Ce$G$7$?!J>P!K!#$=$l$G$O!"!"!"(J
----
	x^4 + x^3 == 0					(i)

 x = u - 1/4$@$HCV$-49$($k!#(J

	u^4 + p u^3 + q u + r == 0			(ii)
	p = -3/8, q = 1/8, r = -3/256			(iii)

$@J,2r(J$@J}Dx<0(J t^3 + 2 p t^2 + (p^2 - 4 r) t - q^2 == 0 $@$H$=$N:,$O!"(J

	t^3 - 3/4 t^2 + 3/16 t - 1/64 == 0		(iv)
			  (t - 1/4)^3 == 0
				    t == 1/4

$@$h$C$F!"(J(ii)$@$N:,$O!"(J

	u = 1/2 {sqrt(1/4) + sqrt(1/4) + sqrt(1/4)} = 3/4
	u = 1/2 {sqrt(1/4) - sqrt(1/4) - sqrt(1/4)} = -1/4 ... $@#3=E:,(J

(i)$@$N:,$O!"(J

	x = 3/4 - 1/4 = 1/2, -1/4 - 1/4 = -1/2
----
$@J,2rJ}Dx<0$,(J x^4 - x^3 == 0 $@$r2r$/$H$-$HF1$8$@$C$?$N$G>l9gJ,$1$,B-(J$@$j$J(J
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$@!t!V<a2`$K@bK!!W$O%D%i%$$b$N$,$"$j$^$9(J :-)

 >>shige> ii)$@FI$s$@$[$&$,$$(J$@$$=q@R(J
 >>$@$H$7$F$O!"8=:_F~<j2DG=$+$I$&$+$OCN$j$^$;$s$,!"(J
 >>
 >>	   $@Lp%vIt(J $@4`(J: $@?t(JIII$@J}<0%,%m%"$NM}O@(J ---$@%"%$%G%"$NJQA+$r$a$0$C$F(J---
 >>		   $@8=Be?t3X<R(J (1976).
 >>
 >>$@$r$*4+$a$7$F$*$-$^$9!#(J

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--
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