Thread View: fj.sci.math
6 messages
6 total messages
Started by Masaru Shigesada
Wed, 04 Nov 1992 09:20
4ji-Houtei-Shiki
Author: Masaru Shigesada
Date: Wed, 04 Nov 1992 09:20
Date: Wed, 04 Nov 1992 09:20
44 lines
1812 bytes
1812 bytes
$@$O$8$a$^$7$F!"0B@nEE5!$NHKDj$H$$$&$b$N$G$9!#(J
$@$3(J$@$N#N#G$O>l0c$$$+$b$7$l$^$;$s$,$h$m$7$/$*4j$$$7$^$9!#(J
$@#4<!$NBe?tJ}Dx<0$K4X$9$k<ALd$G$9(J ^o^;$@!#(J
---
a x^4 + b x^3 + c x^2 + d x + e == 0
$@$r2r$/>l9g!"$^$:(J x = u - b/(4 a) $@$HCV$-49$($F4JLs7A(J
u^4 + p u^2 + q u + r == 0
$@$KD>$9!#$3$N4JLsJ}Dx<0$N:,$O!"$=$NJ,2rJ}Dx<0(J
t^3 + 2 p t^2 + (p^2 - 4 r) t - q^2 == 0
$@$N#3:,(J t1, t2, t3 $@$r;H$C$F!"(J
u1,2 = ( Sqrt[t1] $@!^(J ( Sqrt[t2] + Sqrt[t3] ))/2
u3,4 = (- Sqrt[t1] $@!^(J ( Sqrt[t2] - Sqrt[t3] ))/2
$@$N$h$&$KI=$9$3$H$,$G$-$k!#(J
---
$@$H!"$3$3$^$G$OD4$Y$k$3$H$,$G$-$?$N(J$@$G$9$,!"$3$NJ}K!$GNc$($P(J
x^4 + x^3 == 0
$@$r2r$/$H!"(Jx = 1/2, -1/2$@!J#3=E2r!K$K$J$C$F$7$^$$$^$9!#$I$3$+(J$@$G>l9gJ,$1(J
$@$,B-$j$J$$$N$G$7$g$&$+!#$3$l$K$D$$$F$N(J
i)$@2r7hK!!J$b$7$/$O$3$NJ}K!$,;}$DJL$NLdBjE@!K(J
$@$d!"(J
ii)$@FI$s$@$[$&$,$$$$=q@R(J
$@$J$I!">pJs$r$*BT$A$7$F$$$^$9!#(J
$@<B?t78?t$N#4<!J}Dx<0(J(a$@!b(J0)$@$K$D$$$F!"J#AG?t$r;H$o(J$@$:$K!";MB'1i;;$H;03Q4X(J
$@?t!&;X?t4X?t!&(Jsqrt[2]{ }$@!&(Jsqrt[3]{ }$@$r;H$C$F!"$9$Y$F$N<B?t2r$r5a$a$k$3(J
$@$H$rL\I8(J$@$H$7$F$$$^$9!#(J
$@!tD9!9$H<:Ni$7$^$7$?(J :-)
--
$@",",",",",",",",",",",",",",",",",",",(J
$@HKDj(J $@8-(J shige@tlab.yaskawa.co.jp
$@0B@nEE5!$D$/$P8&5f=j8&5fBh#4%0%k!<%W(J
$@",",",",",",",",",",",",",",",",","-",(J
Re: 4ji-Houtei-Shiki
Author: Yasuo Okabe
Date: Wed, 04 Nov 1992 13:34
Date: Wed, 04 Nov 1992 13:34
66 lines
2636 bytes
2636 bytes
In article <SHIGE.92Nov4182038@siva.tlab.yaskawa.co.jp>,
shige@tlab.yaskawa.co.jp (Masaru Shigesada) writes:
shige> $@#4<!$NBe?tJ}Dx<0(J$@$K4X$9$k<ALd$G$9(J ^o^;$@!#(J
shige> ---
shige> a x^4 + b x^3 + c x^2 + d x + e == 0
shige> $@$r2r$/>l9g!"$^(J$@$:(J x = u - b/(4 a) $@$HCV$-49$($F4JLs7A(J
u^4 + p u^2 + q u + r == 0
shige> $@$KD>$9!#(J
($@CfN,(J)
shige> $@$N(J$@#3:,(J t1, t2, t3 $@$r;H$C$F!"(J
shige> u1,2 = ( Sqrt[t1] $@!^(J ( Sqrt[t2] + Sqrt[t3] ))/2
shige> u3,4 = (- Sqrt[t1] $@!^(J ( Sqrt[t2] - Sqrt[t3] ))/2
shige> $@$N$h$&$KI=$9$3$H$,$G$-$k!#(J
shige> ---
$@!V%*%$%i!<$N2r(J$@K!!W$H8F$P$l$F$$$kJ}K!$G$9$M!#(J
shige> x^4 + x^3 == 0
shige> $@$r2r$/$H!"(Jx = 1/2, -1/2$@!J#3=E2r!K$K$J$C(J$@$F$7$^$$$^$9!#(J
~~~~~~~~~~~~~~~~~~~~~~
$@$3$N7k2L$,=P$kF;6Z$r<($7$FD:$1$^$9$+!)(J
shige> ii)$@FI$s$@$[$&$,$$$$=q@R(J
$@$H$7$F$O!"8=:_F~<j2DG=$+$I$&$+$OCN$j$^$;$s$,!"(J
$@Lp%vIt(J $@4`(J: $@?t(JIII$@J}<0%,%m%"(J$@$NM}O@(J ---$@%"%$%G%"$NJQA+$r$a$0$C$F(J---
$@8=Be?t3X<R(J (1976).
$@$r$*4+$a$7$F$*$-$^$9!#(J
shige> $@<B?t78?t$N(J$@#4<!J}Dx<0(J(a$@!b(J0)$@$K$D$$$F!"J#AG?t$r;H$o$:$K!";MB'1i;;$H;03Q4X(J
shige> $@?t!&;X?t4X?t!&(Jsqrt[2]{ }$@!&(Jsqrt[3]{ }$@$r;H$C$F!"$9$Y$F$N<B?t2r$r5a$a$k$3(J
shige> $@$H$rL\I8$H$7$F$$$^$9!#(J
$@$3$NL\I8$N$?$a$J$i!"2<5-$N!V%U%'(J$@%i%j$N2rK!!W$NJ}$,E,$7$F$$$k$+$b$7$l$^$;$s!#(J
$@4JLs7A(J
u^4 + p u^2 + q u + r = 0
$@$KBP$7!"#3<!J}Dx<0(J
t^3 - p t^2 + 4 r t + ( 4pr - q^2 ) = 0
$@$r9M$($k!#$3$N#3<!J}Dx<0$N0l$D$N:,$r(J t_0 $@$H$9$k$H!"(J
t_0 \neq p $@$N$H$-!"4JLs7A#4<!J}Dx<0$O!"F1CM$JJ}Dx<0(J
( u^2 + t_0 / 2 )^2 = \{ \sqrt{t_0-p} u - q / ( 2 \sqrt{t_0-p} ) \}
$@$KJQ7A$7$F2r$1$k!#(Jt_0 = p $@$N$H$-$O(J q = 0 $@$G(J
u^4 + p u^2 + r = 0
$@$G2r$1$k!#(J($@>e5-(J$@J88%;2>H(J)
-----
$@2,It<wCK!w5~ETBg3X9)3XIt>pJs9)3X65<<7W;;5!%=%U%H%&%'%"9V:B(J
Re: 4ji-Houtei-Shiki
Author: Yasuo Okabe
Date: Thu, 05 Nov 1992 01:28
Date: Thu, 05 Nov 1992 01:28
23 lines
1536 bytes
1536 bytes
$@4V0c$C$F$^$7$?!#$4$a$s$J$5$$(J (_o_)
In article <OKABE.92Nov4223444@sole.kutsuda.kuis.kyoto-u.ac.jp>,
okabe@kutsuda.kuis.kyoto-u.ac.jp (Yasuo Okabe) writes:
$@;d(J> u^4 + p u^2 + q u + r = 0
$@;d(J> $@$KBP$7!"#3<!J}Dx<0(J
$@;d(J> t^3 - p t^2 + 4 r t + ( 4pr - q^2 ) = 0
$@;d(J> $@$r9M(J$@$($k!#$3$N#3<!J}Dx<0$N0l$D$N:,$r(J t_0 $@$H$9$k$H!"(J
$@;d(J> t_0 \neq p $@$N$H$-!"4JLs7A#4<!J}Dx<0$O!"F1CM$JJ}Dx(J$@<0(J
$@!ND{@5!O(J ( u^2 + t_0 / 2 )^2 = \{ \sqrt{t_0-p} u - q / ( 2 \sqrt{t_0-p} ) \}^2
$@",(J
$@$3$3$N<+>h$r=q$-Mn$H$7$F$^$7$?!#(J
$@;d(J> $@$KJQ7A$7$F2r$1$k!#(J
-----
$@2,It<wCK!w5~ETBg3X9)3XIt>pJs9)3X(J$@65<<7W;;5!%=%U%H%&%'%"9V:B(J
Re: 4ji-Houtei-Shiki
Author: Masaru Shigesada
Date: Fri, 06 Nov 1992 02:22
Date: Fri, 06 Nov 1992 02:22
56 lines
2494 bytes
2494 bytes
$@HKDj!w0B@nEE5!$G$9!#AaB.$N%U%)%m!<$r$"$j$,$H$&$4$6$$(J$@$^$9!#$4JV;v$,CY(J
$@$/$J$C$F?=$7Lu$"$j$^$;$s!#(J
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
$@$$$N$+$J$H;W$C$?$N$G$9!#(J
$@!t!V<a2`$K@bK!!W$O%D%i%$$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
$@$3$l$rFI$`$N(J$@$,@h$N$h$&$G$9$M!#$H$j$"$($:$O!"$I$&$b$"$j$,$H$&$4$6$$$^$7(J
$@$?!#(J
--
$@",",",",",",",",",",",",",",",",",(J$@",",(J
$@HKDj(J $@8-(J shige@tlab.yaskawa.co.jp
$@0B@nEE5!$D$/$P8&5f=j8&5fBh#4%0%k!<%W(J
$@",",",",",",",",",",",(J$@",",",",",","-",(J
Re: 4ji-Houtei-Shiki
Author: Masaru Shigesada
Date: Fri, 06 Nov 1992 07:35
Date: Fri, 06 Nov 1992 07:35
51 lines
2656 bytes
2656 bytes
$@HKDj!w0B@nEE5!(J$@$G$9!#$J$s$H$^$!!"$O$:$+$7$$!#(J
| >>shige> $@#4<!$NBe?tJ}Dx<0$K4X$9$k<ALd$G$9(J ^o^;$@!#(J
| >>$@!V%*%$%i!<(J$@$N2rK!!W$H8F$P$l$F$$$kJ}K!$G$9$M!#(J
| >>shige> x^4 + x^3 == 0
| >>shige> $@$r2r$/$H!"(Jx = 1/2, -1/2$@!J#3(J$@=E2r!K$K$J$C$F$7$^$$$^$9!#(J
| >> ~~~~~~~~~~~~~~~~~~~~~~
| >>$@$3$N7k2L$,=P$kF;6Z$r<($7$FD:$1$^$9$+(J$@!)(J
$@!'(J
| x^4 + x^3 == 0 (i)
|
| x = u - 1/4$@$HCV$-49$($k!#(J
|
| u^4 + p u^3 + q u + r == 0 (ii)
| p = -3/8, q = 1/8, r = -3/256 (iii)
|
|$@J,2rJ}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
$@$3$3$G!";d$,2r<a$r4V0c$($F$$$?$h$&$G(J$@$9!#(Jsqrt(t1), sqrt(t2), sqrt(t3) $@$H$7$F!"(J
sqrt(t1)sqrt(t2)sqrt(t3) = - q/8 = - 1/64
$@$H$J$k$b$N$rA*(J$@$P$J$1$l$P$J$j$^$;$s$G$7$?!#7+$jJV$7$K$J$j$^$9$,!"(J
{ 1/2, 1/2, -1/2 } $@$^$?$O(J { -1/2, -1/2, -1/2 }
$@$r;H$($P!"4JN,J}Dx<0$N:,$O(J -3/4 $@$H(J 1/4 $@$K$J$j$^$9!#(J
$@!t;d$,8+$?J88%$G$O!""e(J $@$H(J $@J?J}:,$,$O$C$-$j6hJL$5(J$@$l$F$J$+$C$?$N$G!"$3$N(J
$@!t$h$&$J4V0c$$$r$7$F$7$^$$$^$7$?!#J88%$N$;$$$K$9$k$o$1$G$O$"$j$^$;$s$,!#(J
$@!t8x<0(J$@$r;H$&$H$-$O!"$=$NF3=PK!$^$GCN$C$F$J$1$l$P$J$i$J$+$C$?$s$G$9$M!#(J
$@5.=E$J$*;~4V$r3d$$$F$$$?$@$$$?>e$K!"(J$@LLGr$$K\$r>R2p$7$F2<$5$C$?2,It@h@8(J
$@$K$O!"=E$M$F$*Ni$r?=$7>e$2$^$9!#$I$&$b$"$j$,$H$&$4$6$$$^$7$?!#$=$l(J$@$+$i!"(J
$@@h$N;d$N5-;v$K<:Ni$K$"$?$kI=8=$,$"$C$?$+$b$7$l$^$;$s$,!"7h$7$FB>0U$O$"(J
$@$j$^$;$s!#$*5$$K>c$j$^$7(J$@$?$i$*OM$S?=$7>e$2$^$9!#(J
--
$@",",",",",",",",",",",",",",",",",",",(J
$@HKDj(J $@8-(J shige@tlab.yaskawa.co.jp
$@0B@nEE5!$D$/$P8&5f=j8&5fBh#4%0%k!<%W(J
$@",",",",",",",",",",",",",",",",","-",(J
Re: 4ji-Houtei-Shiki
Author: Yasuo Okabe
Date: Fri, 06 Nov 1992 08:25
Date: Fri, 06 Nov 1992 08:25
70 lines
2862 bytes
2862 bytes
In article <SHIGE.92Nov6112242@vega.tlab.yaskawa.co.jp>,
shige@tlab.yaskawa.co.jp (Masaru Shigesada) writes:
shige> x^4 + x^3 == 0 (i)
shige> x = u - 1/4$@$HCV$-49$($k!#(J
shige> u^4 + p u^3 + q u + r == 0 (ii)
$@",$3$3$O(J2$@$G$9$M(J$@!#(J
shige> p = -3/8, q = 1/8, r = -3/256 (iii)
shige> $@J,2rJ}Dx<0(J t^3 + 2 p t^2 + (p^2 - 4 r) t - q^2 == 0 $@$H$=$N:,$O!"(J
shige> t^3 - 3/4 t^2 + 3/16 t - 1/64 == 0 (iv)
shige> (t - 1/4)^3 == 0
shige> t == 1/4
$@$3$3$^$G$O$h$$$G$9$,!"(J
shige> $@$h$C$F!"(J(ii)$@$N:,$O!"(J
shige> u = 1/2 {sqrt(1/4) + sqrt(1/4) + sqrt(1/4)} = 3/4
shige> u = 1/2 {sqrt(1/4) - sqrt(1/4) - sqrt(1/4)} = -1/4 ... $@#3=E(J$@:,(J
$@$3$3$,BLL\$G$9!#855-;v$N(J
$@$3$N4JLsJ}Dx<0$N:,$O!"$=$NJ,2rJ}Dx<0(J
t^3 + 2 p t^2 + (p^2 - 4 r) t - q^2 == 0
$@$N#3:,(J t1, t2, t3 $@$r;H$C$F!"(J
u1,2 = ( Sqrt[t1] $@!^(J ( Sqrt[t2] + Sqrt[t3] ))/2
u3,4 = (- Sqrt[t1] $@!^(J ( Sqrt[t2] - Sqrt[t3] ))/2
$@$N$h$&$KI=$9$3$H$,$G$-$k!#(J
$@$K$*$$$F!"(JSqrt[t?] $@$OJ#AG?t$N0UL#$NJ?J}:,$G$9$+$i!"(Jt? $@$,@5$N<B?t$@$+$i$H(J
$@$$$C$F(J Sqrt[t?] $@$,@5$G$"$k(J$@$H$$$&$o$1$G$O$"$j$^$;$s!#Be$o$j$K(J
t1, t2, t3 $@$NJ?J}:,$NCf$G!"$=$N@Q$,(J -q $@$H$J$k$b$N$r(J
Sqrt[t1], Sqrt[t2], Sqrt[t3] $@$H$9$k(J
$@$H$$$&$h$&$J>r7o$,$D$-$^$9!#(J
$@$3$NNc$G$9$H!"(Jt=1/4 $@$KBP$7!"$=$NJ?J}:,$G!"@Q$,(J -1/8 $@$K$J$k#3?t(J
1/2, 1/2, -1/2
$@$rA*$S!"(J
u_1 = ( 1/2 + ( 1/2 - 1/2 ) ) )/2 = 1/4
u_2 = ( 1/2 - ( 1/2 - 1/2 ) ) )/2 = 1/4
u_3 = (-1/2 - ( 1/2 + 1/2 ) ) )/2 = -3/4
u_4 = (-1/2 + ( 1/2 - 1/2 ) ) )/2 = 1/4
(i)$@$N:,$O!"(J
x = 1/4 - 1/4 = 0 ($@#3=E:,(J), -3/4 - 1/4 = -1
$@$G!"$a$G$?$/5a$^$j$^$9!#(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).
shige> $@$3(J$@$l$rFI$`$N$,@h$N$h$&$G$9$M!#(J
$@0J>e$O$9$Y$F$3$NK\$N<u$1Gd$j$G$9(J:-)
-----
$@2,It<wCK!w5~ETBg3X9)3XIt>pJs9)(J$@3X65<<7W;;5!%=%U%H%&%'%"9V:B(J
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