HDTenEightyP/NetNews huggingface dataset:
From: ryu@sys.titech.ac.jp (ryu)
Subject: Re: Q in intutionistic math.
Organization: Tokyo Institute of Technology, Yokohama, Japan.
	<1992Oct31.052546.28018@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov2131119@sysipk.sys.titech.ac.jp>
	<1992Nov2.074326.17262@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov4105137@sysipk.sys.titech.ac.jp>
	<ISHIHARA.92Nov5101428@is15e0s10.jaist-east.ac.jp>
Date: Mon, 9 Nov 1992 00:55:03 GMT


$@$3$3$>$H$P$+$j$K!JL5CN$J!K<ALd$r%7%^%/%k3^(J(ryu@sys.titech.ac.jp)$@$G$9!#(J

In article <ISHIHARA.92Nov5101428@is15e0s10.jaist-east.ac.jp> ishihara@is15e0s10.jaist-east.ac.jp (Hajime Ishihara) writes:
 |   >>$@$G$b!"@P86$5$s$N@bL@$O$=$&$$$&OC$7$G$O$J$$$h$&$G$9$,!#(J
$@Cf(J$@N,(J
 |   >>[1] $@$,$$$($J$$$N$J$i$P!"(Jnot(A) or not(not(A)) $@$,0lHL$K=P$F$-$?$H$7$F$b(J
 |   >>$@JL$K:$$i$J$$$+(J$@$i$G$9!#(J
 |
 |$@3N$+!"(JA or not(A) <=> not(not(A)) -> A + not(A) or not(not(A)) $@$G$9!#(J
 |$@$^$?!"D>4Q<g5A(J($@L?Bj(J)$@O@M}$G(J not(A) or not(not(A)) $@$O0lHL$K$O=P$^$;$s!#(J

$@$"$j$,$H$&$4$6$$$^$9!#>.NS$5$s$+$i$b%U%)%m!<$r(J$@$$$?$@$-$^$7$?!#(J
$@$G!"Nc$N@P86$5$s$N$@$7$?%U%!%8!<%J=89g$O(J V^$@&8(J $@$N$I$N$X$s$K$"$k$s$G$7$g(J
$@$&$+!)(J

 |$@Nc$((J$@$P!"$"$k(J($@8EE5E*(J)$@DjM}$rD>4Q<g5A!V$G!W>ZL@$7$h$&$H$7$^$9!#(J
 |$@$H$3$m$,!"$I$&$d$C$F$_$F$b>ZL@$G$-$=$&$b$"(J$@$j$^$;$s!#(J
 |$@$3$&$$$&>l9g!">ZL@$G$-$J$$;v$r>ZL@$7$J$1$l$P$J$j$^$;$s!#(J
 |$@$5$i$K!"(J($@;d$O(J)$@$I$NDxEY>ZL@$7$K(J$@$/$$$N$+!)(J
 |
 | A or not(A) $@$/$i$$$+!)(J not(A) or not(not(A)) $@$/$i$$$+!)(J
 |$@$O$?$^$?(J not(not(A)) -> A $@$/$i$$$+!)(J $@$=$N$$$E$l$G$b$J$$$+!)(J
 |
 |$@$J$I$H9M$($F$7$^$$$^$9!#(J
 |$@$3$3$^$GMh$k$HD>4Q<g5A!V$r!W8&5f$7$F(J$@$$$k$3$H$K$J$j$^$;$s$+!)(J

$@%9%i%$%9$NOC$7$G$9$+!)(J
$@$=$l$O$$$/$i$J$s$G$b!VCf4VO@M}!W$J$N$G$O!"!"!"(J
From: hamao-k@fukushima-iri.go.jp (Kazuhide Hamao)
Newsgroups: fj.sci.math
Subject: Re: about Mathematica
Date: 10 Nov 92 00:09:58 GMT
	<OHTSU.92Nov8104514@mahler.gen.u-tokyo.ac.jp>
Distribution: fj
Organization: Fukushima Technology Centre, Koriyama Japan.

$@$I$&$b$*@$OC$K$J$C$F$^$9!#(J
$@IMHx(J$@!wJ!Eg8)%O%$%F%/%W%i%6(J  $@$G$9!#(J

  $@3'MM!"?'!9$H(JMathmatica$@$K$D$$$F%U%)%m!<$7$F$$$?$@$-M-Fq$&$4$6$$$^$9!#(J
$@AaB.F|K\8lHG$N%^%K%e%"%k$r9XF~$7$F$b$i$&$3$H$K$7$^$9!#(J

  $@$H$3$m$GBgDE$5$s$N>pJs$K$h$j;O$a$FCN$C$?$N(J$@$G$9$,!"1Q8lHG$N%=%U%H%+%P(J
$@!<$,$"$k$N$G$9$+!#(J2000$@1_0B$$$H$$$&$3$H$O(J7500$@1_$G$9$M!#$7$+$b@86($G#13d(J
$@0z$-(J$@$H$O!D!#:#;W$$$^$9$1$I!"Bg3X@86($N0RNO$OBg$-$$$G$9$M$'!##C#D$b0B$$(J
$@$7!D!#!JCOJ}$G$O7h$7$F0BGd$j$J$I$7(J$@$F$/$l$J$$!#!K(J

  $@$^$?:#8e!"B>$N;29M=q$K$D$$$F$d(JMathmatica$@$N;HMQK!$J$I$G2?$+$"$j$^$7$?(J
$@$i!"3'MM$h$m$7(J$@$/$*4j$$CW$7$^$9!#(J

  $@$=$l$G$O$^$?!#(J

$@!t;HMQ$7$F$$$k$N$O(JMathematica2.0 for SPARC$@$J$N$G$9$,!"(J2.1 for Mac
$@!t$H$N5!G=$N0c$$$C$F$"$k$s$G$9$+$M$'!D!#CN$i$J$$$s$G$9$1$I!#(J

  
--
******* $@J!Eg8)%O%$%F%/%W%i%6!!(J$@1~MQ5;=QIt!!EE;R1~MQ2J(J *******
     $@IMHxOB=((J       E-mai : hamao-k@fukushima-iri.go.jp
$@74;3;TJRJ?D.;z(J$@;3?@4\(J 7-2  Tel 0249-59-1911  Fax 0249-59-1761
Newsgroups: fj.sci.math
From: ryu@sys.titech.ac.jp (ryu)
Subject: Re: Q in intutionistic math.
Organization: Tokyo Institute of Technology, Yokohama, Japan.
	<1992Oct31.052546.28018@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov2131119@sysipk.sys.titech.ac.jp>
	<1992Nov2.074326.17262@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov4105137@sysipk.sys.titech.ac.jp>
	<ISHIHARA.92Nov5101428@is15e0s10.jaist-east.ac.jp>
	<RYU.92Nov9095504@sysipk.sys.titech.ac.jp>
	<ISHIHARA.92Nov11094303@is15e0s10.jaist-east.ac.jp>
Date: Wed, 11 Nov 1992 03:07:11 GMT


$@JY6/$rB3$1$k3^(J(ryu@sys.titech.ac.jp)$@$G$9!#(J

In article <ISHIHARA.92Nov11094303@is15e0s10.jaist-east.ac.jp> ishihara@is15e0s10.jaist-east.ac.jp (Hajime Ishihara) writes:
 |$@Cf4VO@M}$b4^$s$G$$$^$9$,!"8EE5O@M}$KL7=b$9$k$h$&$J8xM}$b(J
 |$@07$&$3$H$,$"$j$^$9$+$i!"@53N$K$$(J$@$&$HCf4V$G$O$"$j$^$;$s!#(J

$@$"!"$J$k$[$I!#(J

 |$@$3$3$G!"D>4Q<g5A!V$G!W$H$+D>4Q<g5A!V$r!W$H$$$&$H$-!"$I$s$J(J$@!VD>4Q<g5A!W$r(J
 |$@;X$7$F$$$k$N$G$7$g$&$+!)(J
 |$@;d$O!V9-$$0UL#$G$N9=@.<g5A!WDxEY$K9M$($F$$$^$7$?!#(J

$@$=$N!V(J$@9-$$0UL#$G$N9=@.<g5A!W$H$$$&$b$N$N@5BN$,!"%$%a!<%8$,!"$J$s$+A4A3(J
$@DO$a$J$$$s$G$9!#(J
Bishop $@$H$+$rFI$`$7(J$@$+$J$$$s$G$7$g$&$+!)(J
From: shingo@ipc02.rtri.or.jp (Shingo MATSUMOTO)
Newsgroups: fj.sci.math
Subject: intuitionism & constructivism (Re: Q in int. math.)
Date: 12 Nov 92 08:27:41 GMT
Reply-To: shingo@ipc02.rtri.or.jp (Shingo MATSUMOTO)
Distribution: fj
Organization: Railway Technical Research Institute

$@$^$D$b$H!w?t3X2J%/%:%l(J

In article <ISHIHARA.92Nov11130128@is15e0s10.jaist-east.ac.jp> ishihara@is15e0s10.jaist-east.ac.jp (Hajime Ishihara) writes:
|   >>$@$=$N!V9-$$0UL#$G$N9=@.<g5A!W$H$$$&$b$N$N@5BN$,!"%$%a!<%8$,!"$J$s$+A4A3(J
|   >>$@DO$a$J$$$s$G$9!#(J
|   >>Bishop $@$H$+$rFI$`$7$+$J$$$s$G$7$g$&$+!)(J

| Brouwer$@$ND>4Q<g5A!"(JMarkov$@$N9=@.<g5A$H(JBishop$@$N9=@.E*?t3X$r%$%a!<%8$7$F$$$^$9!#(J

$@!V9-$$0UL#$G$N9=@.<g5A!W$H(J
$@!V69$$0UL#$G$N9=@.<g5A!W$N0c$$$H$$$&$N$O(J
$@7?!J=89g!K$rDj5A$9$k$H$-$K(J
impredicative$@$G$b$h$$$N$+(J
predicative$@$G$J$1$l$P$$$1$J$$$N$+(J
$@$H$$$&$3$H$G$9$+!)(J

$@$3$3$G(Jpredicative$@$J7?Dj5A$H$O!"$9$G$K$"$k7?$N$_$rMQ$$$F?7$?$J7?$rDj5A$9$k$3$H!#(J
impredicative$@$J7?Dj5A$O!"7?$rF0$/JQ?t$rMQ$$$k$+$i!"(Jpredicative$@$J$b$N$h$j6/NO!#(J

$@!t>\$7$$$3$H$O!"@lLg2H$N>.NS@h@8$K2r@b$r8f4j$$$7$?$$!#(J(^^;)

$@!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!](J
$@!!!!!!!!!!E4E4E4E4!!!!!!>>K\??8c(J (Shingo Matumoto)$@!!!!!!!!!!!!!!!!!!!!!!!!!!!!(J
$@!!!!!!!!!!E4!!!!!!E4!!!!(Jshingo@ipc02.rtri.or.jp$@!!!!!!!!!!!!!!(J $@!!!!!!!!!!!!!!!!(J
$@!!!!!!!!!!E4!!E4E4!!!!!!")#1#8#5!!El5~ET9qJ,;{;T8wD.#2!]#8!]#3#8!!!!!!!!!!!!!!(J
$@!!E4!!!!!!E4!!!!E4!!!!!!E4F;Am9g5;=Q8&5f=j!!M"Aw%7%9%F%`I>2A8&5f<<!!!!!!!!!!!!(J
$@!!!!E4E4E4!!!!!!!!E4!!!!#0#4#2#5!]#7#3!]#7#3#0#6!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(J
$@!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!]!](J
Newsgroups: fj.sci.math
From: ryu@sys.titech.ac.jp (ryu)
Subject: Re: Q in intuitionistic math.
Organization: Tokyo Institute of Technology, Yokohama, Japan.
Distribution: fj
Date: Fri, 13 Nov 1992 16:46:31 GMT


$@<+J,$N4*0c$$$K$d$C$H5$IU$$$?(J$@3^!J(Jryu@sys.titech.ac.jp$@!K$G$9!#(J
$@!t$/$@$i$J$$%]%9%H$r>/$7%-%c%s%;%k$7$F$^$9!#(J

In article <526@keu02.rtri.or.jp> shingo@ipc02.rtri.or.jp (Shingo MATSUMOTO) writes:
 |$@D>4Q<g5A$G$O(J{0,1}$@$NItJ,=89g$,#4$D$G$"(J$@$k$H(J
 |$@H=Dj$G$-$J$$$N!#(J
 |$@JL$KB>$NItJ,=89g$,$J$$$H$$$&$3$H$G$O(J
 |$@0f>e;a$NM}2r$O@5$7$$$N!#(J
 |$@$=$N$3$H$,(J$@D>4Q<g5A$G$OH=Dj$G$-$J$$$@$1!#(J

$@$($($H!"0f>e$5$s$O!V#4$D$N$&$A$N$I$l$G$"$k$+$,7h$a$i$l$J$$$+$i!W$J$s$F(J
$@$$$C$F$?$h$&$J5$$,$7$?$s$G!"M>7W$J$3$H$r=q$$$F$7$^$$$^$7$?!#5-210c$$$@$C(J
$@$?$i$4$a$s$J$5$$!#(J
$@$K$7$F$b(J$@!VH=Dj$G$-$J$$!J#4$D$G$"$k$H$$$&!K$3$H!"$rM}2r$7$?!W$H$O!)(J

 |> z in y -> z in {0,1} $@$rK~$?$9(J y $@$,%?%"(J$@%"%"%/%5%s!V:_$k!W$+$i$8$c$"$J$+$C(J
 |> $@$?$C$1!)$H$$$&$N$,!"$=$b$=$b8@$$$?$+$C$?$3$H$G$9!#(J
 |> $@!t:G=i$C(J$@$+$i$3$&8@$($PNI$+$C$?$s$@!#(J
 |
 |$@$?$/$5$s$J$s$+$J$$$h!#$=$l$3$=!V8m2r!W(J

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$@$9$k$H!"(J
[x in A] = A(0) cup [x=0] $@$G(J [x in {0}'] = 1 cup [x=0] $@$G$9$h$M!#(J
$@$9$k$H!"(J
forall x [x in A -> x in {0}'] = 1 $@$K8+$($^$;$s$+!)(J
$@$G$b$C$F#1$G$b$$$$$s$G$7$g!#$=$&$$$&0UL#$G$b%V!<%kCM%b%G%k$H0l=o$J$s$G(J
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 |$@$"!"%o%+%C%?$h!#(J
 |$@MW$O!">ZL@$G$-$J$$$C$F$3$H$O!"(J$@8D?t$,0c$&%b%G%k$,$"$k$+$i$@$m$C$F(J
 |$@$$$$$?$$$o$1$G$7$g!#(J

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 |$@$3$l$O!"$=$l$H$O(J$@0c$&$N!#(J
 |$@>e$N$h$&$J$3$H$O!"8EE5O@M}>e$G9M$($F$k$+$i!"D>4Q<g5A>e$^$G1dD9$7$?$i(J
 |$@%@%a$J$N!#(J

$@$($C!)(J V^$@&8(J $@$O8EE5O@M}$G:n$C$F$^$9$h!#(J

 |> $@!t$*<j?t$r$*$+$1$7$F$*$j$^$9$,!"$^$"!"$3$l$b!V9=@.<g5A?t3X$NIa5Z(J$@$N$?$a!W(J
 |> $@!t$@$H;W$C$F$$$?$@$1$l$P!"!"!"(J
 |
 |$@FbMF$+$i$9$k$H!"$H$F$b$=$&$O$*$b$($s$,!#(J(^^;)

$@$=$G$9(J$@$M!#(J

$@$G!":#EY$3$=!"%[%s%H$K:#EY$3$=!"??LLL\$J<ALd!#(J
$@JL$K(J V^$@&8(J $@$C$F!V40A4!W$8$c$"$J$$$s$G$7$g!)(J
From: koji@aries.sk.tsukuba.ac.jp (Koji Yamada)
Newsgroups: fj.sci.math
Subject: Extension of Monmole's problem ( Re: Two questions )
Date: 5 Nov 92 09:51:13 GMT
Distribution: fj
Organization: College/Institute of Socioeconomic Planning, University of Tsukuba, Tsukuba Ibaraki 305, Japan

$BC^GHBg3X$N;3ED$H$$$$$^$9!#(B

$B%&%A$NJ}$G$3$l0JA0$N5-;v$rB?>/<h$j$3$\$7$?0Y!"(B
$BOC$7$NA08e4X78$,>\$7$/$o$+$j$^$;$s$,(B

In article <1992Nov2.034639.15505@kudpc.kyoto-u.ac.jp> f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi) writes:
>
>  $B0f>e!wBg:eI\N)9b@l$G$9!#(B
>
>
>$BLdBj!##N8D$NM9JXJ*$HF1?t$NIuE{$,$"$k!#1n$,>!<j$KM9JXJ*$rIuE{$K$D$a$F$$(B
>$B$/;~!"@5$7$$08@h$KFO$/M9JXJ*$N4|BTCM$O2?DL$+!#!J3FIuE{$KM9JXJ*$O$R$H$D(B
>$BF~$k!#1n$K$O08L>$OFI$a$J$$!#!K(B
>

$BKM$OEz$rCN$i$J$$$N$G$9$,!"(B
$B$3$l$O%b%s%b!<%k$NLdBj$N3HD%$G$9$M!#$9$J$o$A(B
$B@5$7$/FO$/M9JXJ*$,#0DL$G$"$k3NN($,(B

            k
    N   (-1)
   $B&2(B  ------
   k=0   k!


$B$G!"(BN $B"*(B $B!g$H$7$?;~!">e$N3NN($O(B 1/e $B$G$9$h$M!#(B
$B$G$9$+$i!";d$O<!$N$h$&$J?dB,$rN)$F$?$N$G$9$,!"(B

   N $B"*(B $B!g(B $B$H$7$?;~!"@5$7$$08@h$KFO$/M9JXJ*$N?t$O(B
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$B$3$l$O@5$7$$$N$G$7$g$&$+!)(B
$B87L)$J2rEz!"Kt$O>e<j$J2r<a$r$4B8CN$NJ}$O$I$&$>65$($F2<$5$$!#(B
$B59$7$/$*4j$$$7$^$9!#(B

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$B;3ED(B $B9@;J(B
$BC^GHBg3X(B $BBg3X1!<R2q9)3X8&5f2J7P1D9)3X@l96Bh#2G/<!(B
-- 
Koji Yamada <koji@aries.sk.tsukuba.ac.jp>
Newsgroups: fj.sci.math
From: okabe@kutsuda.kuis.kyoto-u.ac.jp (Yasuo Okabe)
Subject: Re: 4ji-Houtei-Shiki
Reply-To: okabe@kutsuda.kuis.kyoto-u.ac.jp
Organization: Dept. of Information Science, Kyoto University, JAPAN
	<OKABE.92Nov4223444@sole.kutsuda.kuis.kyoto-u.ac.jp>
	<SHIGE.92Nov6112242@vega.tlab.yaskawa.co.jp>
Distribution: fj
Date: Fri, 6 Nov 1992 08:25:56 GMT

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
Newsgroups: fj.sci.math,fj.questions.misc
From: mino@hep1.esb.yamanashi.ac.jp (Hidetoshi MINO)
Subject: rank of a tensor
X-Nntp-Posting-Host: hep1.esb.yamanashi.ac.jp
Organization: Yamanashi University, Yamanashi, Japan
Distribution: fj
Date: Sat, 14 Nov 1992 07:03:15 GMT


$BH~G;!w;3M|Bg$H?=$7$^$9!#$3$N(B NG $B=iEj9F$G$9!#(B
$B!J(B fj.sci.math $B$H(B fj.questions.misc $B$K%/%m%9%]%9%H$7$F$^$9!#!K(B
$B(B
$B(B  $B!V#33,0J>e$N%F%s%=%k$N%i%s%/$r5a$a$kJ}K!!J%"%k%4%j%:%`!K!W(B
$B(B
$B$K$D$$$F$I$J$?$+65$($F$$$?$@$1$J$$$G$7$g$&$+!#(B
$B(B
$B;d$,<+NO$GD4$Y$?HO0O!J@lLg30$J$N$GD4$YJ}$bE,@Z$G$O$J$$$N$G$7$g$&$,!K(B
$B$G$O(B $B$=$NMM$JJ}K!$OL$$@8+$D$+$C$F$$$J$$$N$G$O$J$$$+$H;W$o$l$k$N$G$9$,!"(B
$B$I$&$J$N$G$7$g$&$+!)(B
$B(B
$BG0$N$?$a!"$3$3$G$$$&%F%s%=%k$N(B "$B%i%s%/(B" $B$H$O(B
$B(B
$B(B   $B$"$k%F%s%=%k$r%Y%/%H%k$N%F%s%=%k@Q$NOB$GI=$7$?>l9g$K(B
$B(B   $B$I$l$@$1?t>/$J$$9`$GI=$;$k$+$H$$$&LdBj$r9M$($?;~$N!"(B
$B(B   $B$=$N:G>.9`?t(B
$B(B
$B$G$9!#(B
$B%F%s%=%k$,#23,$N>l9g$O(B "$B9TNs(B" $B$N%i%s%/$K0lCW$7$^$9$N$G!"(B
$B$=$N5a$a$+$?$O9b9;$N?t3X$G$d$kDL$j$G$9$,!"#33,0J>e$N(B
$B>l9g$O$$$+$K!)$H$$$&$N$,5?Ld$J$N$G$9!#(B
$B(B
$B;29M$K$J$kJ88%$J$I$b;XE&$7$F$$$?$@$1$k$H9,$$$KB8$8$^$9!#(B
$B$I$&$+!"$h$m$7$/$*4j$$$7$^$9!#(B
$B(B
$B(B-- 
    $B;3M|Bg3X(B $BEE;R>pJs9)3X2J(B           $BH~G;!!1Q=S(B 
                                      mino@hep1.esb.yamanashi.ac.jp
From: ishihara@is15e0s10.jaist-east.ac.jp (Hajime Ishihara)
Subject: Re: Q in intutionistic math.
Organization: Japan Advanced Institute of Science and Technology Hokuriku,
	Ishikawa, Japan
	<1992Oct31.052546.28018@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov2131119@sysipk.sys.titech.ac.jp>
	<1992Nov2.074326.17262@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov4105137@sysipk.sys.titech.ac.jp> <ISHIHARA.92Nov5101428@
	<SATOSHI.92Nov11151829@whale.ryukoku.ac.jp>
Date: Thu, 12 Nov 1992 00:18:57 GMT


$@@P86!wKLN&@hC<Bg$G$9!#(J

In article <SATOSHI.92Nov11151829@whale.ryukoku.ac.jp> satoshi@whale.ryukoku.ac.jp (Satoshi Kobayashi) writes:


   >> |$@Nc$($P!"$"$k(J($@8EE5E*(J)$@DjM}$rD>4Q<g5A!V$G!W>ZL@$7$h$&$H$7$^$9!#(J
   >> |$@$H$3$m$,!"$I$&$d$C$F$_$F$b>ZL@$G$-$=$&$b$"$j$^$;$s!#(J
   >> |$@$3$&$$$&>l9g!">ZL@$G$-$J$$;v$r>ZL@$7$J$1$l$P$J$j$^$;$s!#(J
   >> |$@$5$i$K!"(J($@;d$O(J)$@$I$NDxEY>ZL@$7$K(J$@$/$$$N$+!)(J
   >> |
   >> | A or not(A) $@$/$i$$$+!)(J not(A) or not(not(A)) $@$/$i$$$+!)(J
   >> |$@$O$?$^$?(J not(not(A)) -> A $@$/$i$$$+!)(J $@$=$N$$$E$l$G$b$J$$$+!)(J
   >>
   >>$@$3$l$b$^$?!"8xM}%9%-!<%^$NOC$@$H$9$l$P!"!V(JA or not(A) $@$/$i$$!W(J
   >>$@$H!V(Jnot(not(A)) -> A $@$/$i$$!W$OF1$8$K$J$C$F$7$^$$$^$9$M!#(J

$@$"$C!"$9$_$^$;$s(J$@!#$=$N$H$&$j$G$9!#(J
$@$$$D$b!"(JA$@$KF~$k%U%)!<%`%i$N7A$r@)8B$7$F;H$C$F$$$k$b$N$G$9$+$i!"$D$$!#(J

--
$@@P86(J  $@:H(J : $@KLN&@hC<2J3X5;=QBg3X1!Bg3X(J $@>pJs2J3X8&5f2J!J>pJsO@M}3X!K(J
From: satoshi@whale.ryukoku.ac.jp (Satoshi Kobayashi)
Newsgroups: fj.sci.math
Subject: Re: Q in intutionistic math.
Date: 7 Nov 92 01:13:51 GMT
	<NAO.92Oct11151547@mimo.jaist-east.ac.jp>
	<1992Oct28.042628.19061@kudpc.kyoto-u.ac.jp>
	<RYU.92Nov2125034@sysipk.sys.titech.ac.jp>
Organization: Ryukoku Univ., Seta, Japan
In-reply-to: ryu@sys.titech.ac.jp's message of 2 Nov 92 03:50:34 GMT


$@>.NSAo(J@$@N6C+Bg3X$G$9!#(J
$@CY$$%U%)%m!<$G0-$$$N$G$9$,!D!#(J

In article <RYU.92Nov2125034@sysipk.sys.titech.ac.jp> ryu@sys.titech.ac.jp (ryu) writes:

 | |  $@;d$b<+L@$@$H;W$$$^$9!#K\$N#4(J$@#3$+$i#4#5%Z!<%8$rFI$`$H!"#Q$+$i:n$C$?(J
 | |$@#Q!0(J\check$@$O<+A3$J$b$N$G$9$+$i!#(J
 |
 |$@$=$&$J$s$G$9$1$I$M!#(J
 |$@$=$N#4#3$+$i#4#5%Z!<%8$N8e$N!"#5#2%Z!<%8$G=g=xBP$rDj5A$7$F$$$k$h$&$K=q(J
 |$@$$$F$$$^$9$M!#(J
 |$@$=$l$G!"(J$@!V2?$d$=$l!)!W$H;W$C$F$7$^$C$?$s$G$9$h!#(J
 |
 |$@$G$b!"<B:]$O#4#0%Z!<%8$G=g=xBP$N8xM}$,@.$jN)$D$3$H$,$9$G(J$@$K<($5$l$F$$$k(J
 |$@$s$G$9$h!#%^%C%?%/!#(J
 |
 |$@!t>/$7$O=gHV$r9M$($m!"$C$F$s$@!#(J

40$@%Z!<%8$GB8:_$,<($5$l$F(J$@$$$k$N$O!"=g=xBP$G$O$J$/!"=g=x$N$J$$(J
$@BP(J {a,b} $@$G$9!#$=$7$F!"$=$l$rMQ$$$F(J52$@%Z!<%8$G=g=xBP$rDj5A$7(J
$@$F$$(J$@$k$o$1$G$9!#$H$$$&$o$1$G!"(J40$@%Z!<%8$G!V=g=xBP$N8xM}!W$H=q(J
$@$$$F$$$k$N$O!"K\Ev$O$^$:$$$G$9!#(JAxiom of pairing $@$NF|K\8lLu(J
$@$O!VBP$N8xM}!W$H$7$?$[$&$,$h$$$G$7$g$&!#4dGH?t3X<-E5$G$O$=$&(J
$@$J$C$F$$$^$7$?!#(J
--
			$@N6(J$@C+Bg3XM}9)3XIt?tM}>pJs3X2J(J    $@>.NS(J  $@Ao(J
			satoshi@whale.ryukoku.ac.jp
			0775-43-7523($@3X2J;vL3<<(J) 0775-43-7528($@8&5f<<(J)
			0775-43-7524(FAX)
From: shige@tlab.yaskawa.co.jp (Masaru Shigesada)
Newsgroups: fj.sci.math
Subject: Re: 4ji-Houtei-Shiki
Date: 6 Nov 92 02:22:42 GMT
	<OKABE.92Nov4223444@sole.kutsuda.kuis.kyoto-u.ac.jp>
Distribution: fj
Organization: Yaskawa Electric Corporation
In-reply-to: okabe@kutsuda.kuis.kyoto-u.ac.jp's message of 4 Nov 92 13:34:44 GMT


  $@HKDj!w0B@nEE5!$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
Newsgroups: fj.sci.math
From: ishihara@is15e0s10.jaist-east.ac.jp (Hajime Ishihara)
Subject: Re: intuitionism & constructivism (Re: Q in int. math.)
Organization: Japan Advanced Institute of Science and Technology Hokuriku,
	Ishikawa, Japan
Distribution: fj
Date: Fri, 13 Nov 1992 00:35:07 GMT


$@@P86!wKLN&@h(J$@C<Bg$G$9!#(J

In article <525@keu02.rtri.or.jp> shingo@ipc02.rtri.or.jp (Shingo MATSUMOTO) writes:

   >>$@!V9-$$0UL#$G$N9=@.<g5A!W$H(J
   >>$@!V69$$0UL#$G$N9=@.<g5A!W$N0c$$$H$$$&$N$O(J
   >>$@7?!J=89g!K$rDj5A$9$k$H(J$@$-$K(J
   >>impredicative$@$G$b$h$$$N$+(J
   >>predicative$@$G$J$1$l$P$$$1$J$$$N$+(J
   >>$@$H$$$&$3$H$G$9$+!)(J
   >>
   >>$@$3$3$G(Jpredicative$@$J7?Dj5A$H$O!"$9$G$K$"$k7?$N$_$rMQ$$$F?7$?$J7?$rDj5A$9$k$3$H!#(J
   >>impredicative$@$J7?Dj5A$O!"7?$rF0$/JQ?t$rMQ$$$k$+$i!"(Jpredicative$@$J$b$N$h$j6/NO!#(J

$@!V9-$$!W$H$$$&$N$O;d$,>!<j$K(J$@;H$C$?8@MU$G!"?t3XE*$JDj5A$K$OBP1~$7$F$$$^$;$s!#(J

--
$@@P86(J  $@:H(J : $@KLN&@hC<2J3X5;=QBg3X1!Bg3X(J $@>pJs2J3X8&(J$@5f2J!J>pJsO@M}3X!K(J
From: f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi)
Subject: Re: Extension of Monmole's problem ( Re: Two questions )
Organization: Osaka Prefectural College of Technology
Distribution: fj
Date: Mon, 9 Nov 1992 03:23:26 GMT

  $@0f>e!wBg:eI\N)9b@l$G$9!#(J

In article <868@shako.sk.tsukuba.junet> koji@aries.sk.tsukuba.ac.jp (Koji Yamada) writes:
>>$@LdBj!##N8D$NM9JXJ*$HF1?t$NIuE{$,$"$k!#1n$,>!<j$KM9JXJ*$rIuE{$K$D$a$F$$(J
>>$@$/;~!"@5$7$$08@h$KFO$/M9JXJ*$N4|BTCM$O2?DL$+!#!J3FIuE{$KM9JXJ*$O$R$H$D(J
>>$@F~$k!#1n$K$O08L>$OFI$a$J$$!#!K(J
>>
>
>$@KM$OEz$rCN$i$J$$$N$G$9$,!"(J
>$@$3$l$O%b%s%b!<%k$NLdBj$N3HD%$G$9$M!#$9$J$o$A(J
>$@@5$7$/FO$/M9JXJ*$,#0DL$G$"$k3NN($,(J
>
>            k
>    N   (-1)
>   $@&2(J  ------
>   k=0   k!
>
>
>$@$G!"(JN $@"*(J $@!g$H$7$?;~!">e$N3NN($O(J 1/e $@$G$9$h$M!#(J
>$@$G$9$+$i!";d$O<!$N$h$&$J?dB,$rN)$F$?$N$G$9$,!"(J
>
>   N $@"*(J $@!g(J $@$H$7$?;~!"@5$7$$08@h$KFO$/M9JXJ*$N?t$O(J
>   $@J?6Q$,(J 1 $@$N%]%"%=%sJ,I[$K=>$&!#(J
>
>$@$3$l$O@5$7$$$N$G$7$g$&$+!)(J

  $@6K8B$K$*$$$F$O$=$&$J$C$F$$$k$O$:$G$9!#!JMW>ZL@!)!K(J

>$@87L)$J2rEz!"Kt$O>e<j$J2r<a$r$4B8CN$NJ}$O$I$&$>65$($F2<$5$$!#(J
>$@59$7$/$*4j$$$7$^$9!#(J

  $@<j;f$NLdBj$OM-8B$N>l9g$G$9!#L58B$@$H1n$b$D$+$l$k$G$7$g$&$+$i!#(J

-- 
================================== $@0f>e9@0l!wBg:eI\N)9b@l(J=====================
                   Phone : (0720) 21-6401 ($@Fb@~(J304)  Fax : (0720) 21-0134
                   E-mail: f51323@sakura.kudpc.kyoto-u.ac.jp
=========================================$@;d$O(Jmohta$@;a$K5wN%$r$*$$$F$$$^$9!#(J====
From: koshi@okds1.osaka-kyoiku.ac.jp (Kunio Koshigiri)
Newsgroups: fj.sci.math
Subject: Re: about Mathematica
Date: 10 Nov 92 13:40:39 GMT
Distribution: fj
Organization: Information Processing Center, Osaka Kyoiku Universiy

$B1[6M!wBg:e650iBg$G$9!#(J

In article <JOE.92Nov9123609@hoihoi.kocb.astem.or.jp> joe@kocb.astem.or.jp (Kazuki Joe) writes:
> $B$=$l$,!"#2#1!v#2#1$N5U$r5a$a$k$?$a$K!"(JInverse[A]$B$r$d$C$F$bMn$A$F$7$^$&(J
> $B$s$G$9$h!#:G=i$OC1$K%a%b%j$,B-$j$J$$$@$1$@$m$&$H7Z$/;W$C$F$$$F!"!J#M#a(J
> $B#c$N!K2>A[5-21%*%s$K$7$F!"%Z!<%8!&%U%!%$%k$r$A$g$C$HIU$1B-$7$F!"!"!"!"(J
> $B$G$b$@$a$@$C$?$s$G$9!#$G!"7k6I!"%a%b%j#8#M#B!"%Z!<%8!&%U%!%$%k#6#0#M#B(J
> $B$G<B9T$7$?=j!"#1#0F|4V7W;;$7$F!"7k6IMn$A$F$7$^$$$^$7$?!##1#0!v#1#0$J$i(J
> $B?t==J,$G:Q$`$N$K!"%7%9%F%`A4BN$,Mn$A$F$7$^$&$H$3$+$i!"$I$&$b%P%0=-$$$J(J

$B>k$5$s$N7W;;$5$l$F$$$k$N$O!"?tCM$G$O$J$/$F%7%s%\%k$G$9$h$M!)(J
$B?tCM7W;;$G$O!"5U9TNs$N7W;;$K$+$+$k;~4V$O9b!9(JO(N^3)$BDxEY$G$9$,(J
$B?t<0$N>l9g$O!"$b$78=$l$k9`$,$^$H$^$i$J$$>l9g!"<0(J($B9`?t(J)$B$,(J
$B;X?t4X?tE*$KA}$($d$7$J$$$G$7$g$&$+!)=>$C$F;~4V$bF1MM$K!)(J

$B!Z<XB-JT![(J
$B<!$N$h$&$JC1=c$JNc$G$A$g$C$H$@$1;n$7$F$_$^$7$?!#(J
n$B8D$N%7%s%\%k$+$i$J$k%j%9%H$r=g$K2sE>$7$F:n$C$?9TNs$N5U$G$9!#(J

In[1]:= L[0][n_]:=RotateRight[Array[a,n]]
In[2]:= M[n_]:=Table[L[k][n]=RotateLeft[L[k-1][n]],{k,1,n}]
In[3]:= T[n_]:=Timing[Inverse[M[n]];]
In[4]:= Do[Print[k,T[k],{k,4,8}]
        4{0.25 Second, Null}
        5{1.28333 Second, Null}
        6{6.95 Second, Null}
        7{44.4833 Second, Null}
        8{273.467 Second, Null}
$B$3$l$+$i30A^$9$k$H(J($B$$$$$N$+$J!<!)(J *_*;;)
$B!!!!!!!!(Jt[n] $B!A(J Exp[1.75(n-1)]/900 Sec
$B!!!!!!!!(Jn=21 -> $B?tK|G/$K$J$j$^$9!#(J

$B<!$K!"%7%s%\%k$r0l<oN`$K8:$i$7$F$_$^$9!#3F9TNsMWAG$O(Jx$B$N$Y$->h$G$9!#(J
In[5]:= Do[a[k]=x^(k-1),{k,1,n}]
In[6]:= Do[Print[k,T[k],{k,4,8}]
        4{0.0833333 Second, Null}
        5{0.316667 Second, Null}
        6{0.75 Second, Null}
        7{1.61667 Second, Null}
        8{3.21667 Second, Null}
$B$3$l$+$i30A^$9$k$H(J($B$^$:$$$+$J!<!)(J ^_^;;)
$B!!!!!!!!(Jt[n] $B!A(J 2^(n-1)]/40 Sec
$B!!!!!!!!(Jn=21 -> $B?t;~4V$K$J$j$^$9!#(J

$B$"$l!"(Jn$B!f(J12$B$N>l9g2?J,$?$C$F$b=*$o$i$J$$!&!&!&$d$O$j%P%0$+!)(J
[Mathematica Ver2.0.4; NeXTstation System2.1J RAM20MB]
--
K. Koshigiri
koshi@cc.osaka-kyoiku.ac.jp