perm filename CURVES.GF[MF,DEK]1 blob sn#750673 filedate 1984-04-19 generic text, type T, neo UTF8
{`$α&Q*Dλ#∪ie ⊂≠nW 8≥.B_N'β ↔εBp_N'#⊂→f∀_ε␈␈␈␈x␈␈␈⎇`π8␈␈␈␈⊂∧X␈␈␈␈λε&α9HfCiX⊂fDYX∪fe)X⊗&eyX_gε9X~gεyX≤OA9`≥∞α9X≡Lc	`∨KCY` ⊂¬"⊂MPλ2(∪gλ∧(⊂
sD#Fey` ∩BC N⊂	``≤gλ	 N⊂∩Y` %3DK'λ	8N⊂∩y` &∪DL'¬`8 →∪RPεP→`∀∧(¬xN	bD/'∧a8 ↔∪B(P9`∩FH¬PN	βQh∧
∪R_∂ε!S⊂NλD⊃ 	∪B⊂⊃CbbxNλD`@
KSB⊂ ∩EYh⊂P	2`Nλ(∧X⊗'∧∀&
sR ∪¬9`⊂⊂	BXNλλ∧h∃'$∧&
3B ∪¬→`⊂⊂	BHNGh∧`∀g∧∧%J3B ∩e	h∂P	2@Nπh∧X∀'#t$J∪Ax ∩%	h∂P	α8Nπh∧@∪g#t#	sQp ⊃Dy`∂PλB8NGh∧_∪gβt!	sQx ⊂∧yh∂ODyh∂O¬	`⊂∞E	h⊂ME→h⊂Le)h⊃e9h∩
%Yh→¬&→h ≥ST9gHπNP
Yh ~sd3gHε_O⊂yp ⊗St*(λ∧hWM5Q`"⊂`_?␈x␈␈␈␈x␈t ≤␈␈x␈u@∀←␈x␈y↓)@λfBiP
&CiX⊂&d9X∩fe	X∃'¬9X↔&f	`_ff9`~gεiX≤'π)`≥gπT"BSCp∨DsD ∞C	` ⊂&ahN⊂λ3λ⊂g(∧ ⊗	SD#	e)h ⊃d"pNP	⊃`→'H∧P
Sd&CπJ8 "T∧Cghλ(O⊂⊂9p
Ahε0O∧!42'APx _sPX	⊂→h∧EλεO↓Bd0' Q8 ↔sP_
⊂Yh↓εh¬`]⊂Ip ⊗SR∧3aPπsa(	K3aK∪pH∞
o⊂( ⊃¬)`∧⊂λ∩PNB(∧∀g↓3p∀g!3h∀g!3h∀'↓C`∀'!CX∪g↓SP∪g!CP∪g↓SH∪g!S@∪g↓S@∪'↓c8∪'!S8∪'↓c(∪g↓c(∪'!c ∪'↓c ∪'↓c_∪g!S_∪'↓c⊂∪'↓cλ∪g!Sλ∪'↓Sλ∪'↓bx∪'↓bx∪'↓bp∪g!Rp∪'↓Rh∪g↓R`∪g↓R`∪g↓RX∪g↓RP∀'↓RP∪g!BH∀'↓R8∀'↓R0∀g↓b ∀g↓b_∀g↓rλ∃'α↓p∃gα⊃`⊗'α!H⊗gαA(↔'αaλ↔gβ⊂P→gλ¬(N⊂
Ih ∀SD)'λ¬λN⊂
	h ∪SD&gλ∧`NP	)` ∩3T#g(∧(N⊂λ9h ⊂3SxNO∪SPNMsS(O3RpO
Sb(OGsq@PCHD_ε⊂␈␈␈␈x␈␈␈⎇Hπ ␈␈␈}λ∧h␈␈␈}X¬fα9P&CIP⊂&d9X∪&e	X∃fei`↔ff)`→ffi`≠fg→`≥PλXN∂'⊃_N∂FAPN⊂λαx∂gλ∧⊂∃λsD"	%	h ⊃$α`N⊂λqX_'(∧H
M∪D&Cπ)h $sTI'(	⊂N⊂∩)h $STHg(	λN	!∧2'$ h _3QxλP	h∞Eλ¬pNπαd.g#1@ ⊗sQH
⊂9hπλ¬HNεβQp∧L3Q8∂F!bxNED⊃ 	K3Q0⊃βbr`N¬DP@∞
sQ0 ∩%)h
P	∩PNE(∧H∀g"T$
3A0 ⊃e→h
P	α@NE(∧8∀'"T#	sA0 ⊃$yh
PλR8NE(∧ ∪g"T!IsA( ⊂dih
Pλ"0NE(∧λ∪'"Sx∪gαSx∪'"Sp∪'"Sh∪'"SX∪'αSX∪'"SH∪'"S@∪'"S0∪gαS0∪'"S ∪g"S⊂∪g"Sλ∪'αS∪g"Rp∪g"R`∀'"RP∀'αRH∀'"R8∀g"R ∃'"R⊂∃'αax∃g"qX⊗g#↓8↔'#⊃_↔gβPX→'(¬@NP
ih ∃∪T)'λ¬λNP	yh ∪∪T%'(∧@NPλih ⊂sT gGYh≥'Fih→gEyp∃gDix⊂'c~λπQλ0?x␈␈␈␈x␈␈{ ∞?x␈␈⎇0	?x␈␈␈0pKF∪⊃xLI3"HM3#λMLs#8∪C33H⊃¬S3`∞G∪3pHS4 ¬DiX ⊂BB@MPλAλ⊗'λ∧(πKS4#Cε)X ∩!# N⊂	 @≠&h∧XβN∪D&↓')X ∪@3`N⊂	`⊂∨&hλxN⊂∩	` $34I'λ	_N⊂∩9` %∪4Jgλ	0N
↓$,'ε↓⊂ ∃3Bp⊂
9`⊗εH¬λN
cQλ¬
3BP∂C"β⊂N
$⊂P
∪B@⊃AcαpN
∧@(
3R0∪cBhN	D`⊂∂∪B( ∩¬9`∩P	αXNIλ∧H∃'∧4%J3B_ ∩e→h⊃⊂	B@NλH∧`∀'∧$&
∪Rλ ∪$y`⊂P	R8NHλ∧h∪g∧∀&	SR ∪∧ih∂P	B0Nλλ∧X∪'#t%ISQx ∩DYh∂P	α0Nπh∧@∪'#t#I3Qx ⊃$ih∂PλB0NGh∧⊂∪'#t ISQx∨ISR≡ISR≥ISR≤Isb≠	sRλ→J∪R⊂_
∪R_⊗J∪b_∀J3R(∩
sb0∂K∪RHSbhπ3d4gHε0NPIp _3d.gh¬HO⊂
ip ∀St''h∧HOPλIx∨gg~→(%*λ⊂hbD !@2?␈␈x␈␈␈␈xm9␈␈␈xu@%␈␈␈x⎇CRq@LGs∩(M
3"hM33_M
dphMN$!0MOβQ`MOC∩⊂MPλ↓0∪&h∧⊂

∪4"∧%I` ⊃!rpMPλp`→&h∧H¬
∪D%αεiX ∩`s@N⊂	@(≥&h∧p↓O∪D'GiX #sDH'λ	λMP∩)` $sDIgλ	 MP∩Y` %SC ¬⊂	`_∧H¬(NBd)g¬AP ∀3BX∞D!#(N
CphλSBH⊂BBCN
∧08SB@∩↓#"hNID`_∞3B0∪Cb`N	(∧@∃g∧T$
sR  ∩%)`⊃P	2HNλh∧X∀g$$&
∪B⊂ ∪¬	`⊃⊂	B@NH(∧h∪g∧∀&IsR ∪$y`⊂P	B0NHλ∧`∪'#t&	SB ∩dih∂P	20NGh∧P∩g#t$	SAx ∩∧ih∂Pλr(NGh∧(∪'#t"	SQx ⊂Dih∂Pλ∩0NGgr0NHπR0NHπ20NHπ∩8Oλεb8NH&2@NHFα@NHeR@Oλe∩HNI$BXO	Cr`NJ#αpO!cλO⊂
→p →ST2'HελO⊂Yx ⊗3d+'H¬⊂OP	ix ∩3t"'gyx≤hε*λ∃($~_
⊃λ0←x␈␈␈␈x␈␈{ ∞/x␈␈⎇0	Ox␈␈␈`pKF3αLIS"PMS#⊂∩β3#(∂E33@
π∪#XH∪3h
	∪3xλJ∪4 Ce9X ⊂aRhMPλPX_&h∧0¬S4$αεI` ∩ s(MP	 0≠gλ∧Xα∞34&↓π)` ∪ #`MP	`⊂≡'λλhMP⊃y` #sDH&h	⊂N⊂∩)` $sDIfh	 N⊂∩Y`→Bλ¬PN↓t+'¬a_ ∃3B`P
9`∃F"PP→g¬!`λ∧ε→`∀GAQ ↔g¬αλ∧F¬Y`∀λ@qP⊗'$b αG¬9`∪	 1p∃g∧R8H¬)`∩P	αPN	(∧H∀g$4%J∪B_ ∩e	`⊃P	B8NHH∧`∪g∧$&	sRλ ∪$i`⊂P	R0NH(∧`∪'∧∀&	SR ∪∧ih⊂⊂	2(Nλλ∧X∩g$∧%	3Qx ∩DYh∂P	α0Nπh∧@∩g#t#I3Qx ⊃$ih∂PλB0NGh∧⊂∪'#t ISQx∨ISR≡ISR≥ISR≤Isb≠	sRλ→J∪R⊂_
∪b⊂⊗J3R_∀JSR(∩
sb0∂K3b@sRhπSd5'Hε8O⊂Ip _3d/'H¬PO⊂
yx ∀sd'gh∧POPλYx ⊂∀βPPtα`Qλ41 "⊂`→←␈x␈␈␈␈x␈v@≤←␈x␈z`∩␈␈x␈⎇@y@ε&AyP	&BYP&c9P∂&d	X⊃fdYX∀&e9X↔'¬yX→&fT'@SC@ ∩@YX≥PλPHN∂H∧ε&h∧⊂≥∧∪D"LbIX ∩E1HN⊂	r⊂∂'λ¬0	IS4Hgλ	⊂N⊂∩)` $s4J'λ	 N⊂∩Y`→↓λ¬xNd/g¬`@ _∪B`¬Py`∃Cλ¬xN
AT0'¬⊂p _∪B@πMR8NIas⊂∧I3B0λ↓B N	BαpπI∪B(λKα"_NIα∩X
λSB λJ"b⊂Nλb"8H3R⊂		#2λNλB"_∞H3Rλ	λCrNλ""⊂H∪R	πD2Nλα!`∩H∪Qx	εdbNλα⊃H∀λ∪QxλEe∩λNGB⊃(∃H∪Ax묬BNGB↓⊂⊗H3QpπD¬rλNG!px↔HSApπβ&∩λNG!`X→λSQhπαε2_NG!P0~λsQhε@fR NG(∧_∩g#T I3Qh∨	sQp≥IsQp≤
3ap~
SQx_∪R⊗3Rλ∪L∪b⊂⊂LSR(

∪b@πNST7gHε`O⊂
→p →ST2'HελO⊂ix ⊗3d+'H¬_OP	ix ∩3t"'gyx≥(ε:⊗($* 
⊃λ0␈x␈␈␈␈x␈␈{@
Ox␈␈}@	?x␈␈␈0⊂MA30@Mβ∪0xMDS!0MF3!hMH∪2_M	s2PMK3#λMM∪38 ⊃9P≥Na)X∨B)X ⊂%⊃HM⊂λR⊂&h∧@Is$&βEiX ∪`S(N⊂⊃→h "3TD'(λ8N⊂⊂yh !STBg(λ N $+'%0( ∃∪RH∧⊂
)h∪βλ¬N	!t''$!_ ∪∪R⊂	)h∂ε(∧HNπβR↓I∪QP⊂¬a" NEd@p	λsQ(∪A#∩_NEλ∧(⊃gαT"λsQ( ⊂d9h
Pλ" NEλ∧⊂∩'αT!λsQ( ⊂$9h
Pλα_NEλ∧⊃gαSx⊃g"Sp∩'"Sh∩'"S`∩'αSh⊃g"S`⊃g"SX⊃g"SP⊃gαSP∩'"SH∩'"S@∩'"S@⊃gαS@⊃g"S8⊃g"S0⊃g"S ∩gαRh⊗'"R0→'"Qx≤'"Q@≡gαaλ≡g"PP≡g"P_≡g(∧pN⊂		h ⊂3SPNLsR`N	SQpNEsQNαSP_"⊂`~∨␈x␈␈␈␈x␈v`≥←␈x␈{∩␈␈x␈⎇↓9@	&ByP
fCyX⊃&DiX∀&e9X⊗ff	X→'ε9X≠&gβh¬gπ∪8	fgC⊂gπRp∂&h∧∀HSD!	∧yX ⊃#rXN⊂λqP↔gλ∧P
s4'Bg→` %∪DJ'λ	(N⊂∩iX %sDL'λ	@N⊂∪→`_↓hε⊂N!T/g¬1λ ↔SBP
⊂I`∀EH¬XN
β∀,g∧qX ⊗3B8∞π!β_NI#q@εL3B(⊂¬α"xN	∧0xSB ∪αβ2hN	λ∧P⊗'$$&
sB⊂ ∪¬9`⊃⊂	RPNH(∧h∃'∧∀&JSR ∪E→`⊂⊂	b@NGh∧p∀'∧∧&J∪Qx ∪%	`∂P	R8NGh∧`∪g#d&	sAx ∩dih∂⊂	"8NGH∧H∪g#d$	SAp ⊃dyh∂⊂λb0NGH∧ ∪g#d!ISQp ⊂$yh∂⊂λα0NGGb0NGg28NGg∩8NHεb8OπfB@NHε∩@NH%RHOλEαPNHdBXO	βr`NIcαpO
acλNP
	p →3d0gH¬pO⊂)p ∃sd)gh∧xOP	)p ⊃St (π*→h¬:λ⊃)α4 !@4␈␈␈x␈␈␈␈xn7?␈␈xx@%␈␈␈x⎇↓3⊂XM∧∪1_M¬s!XMG3"λMI∪"8MJS2hMKs#_MMS3@≡Bs3X~Ds3p↔ε34 
#iX ⊂d"_MPλa`∀'λ∧@∪4%Dε→` ∪!∪0MP⊃Y` #SDG'λλpN⊂⊃y` #sDGg(λpN T,g¬pH ∃sRhε⊂
Y`∃Dλ¬_NJ"$)'∧q0 ∀∪B0P	yh∩εc`8∀g∧1pC%	h⊂H"⊃⊂∪g#r ¬EDy`∂	`QX∪'#T#ISAh ⊃dih∞⊂λr8NFh∧@∪'βD#ISQX ⊃dih
⊂λr0Nεh∧0∪'#$#I3QP ⊃DYh
⊂λR(NεH∧(∩g#$"	3QP ⊂dYhPλ2(NεH∧⊂∩g#$ I3QP ⊂∧Yh
∂dYhOdYhODY`
∂$Yh
∂∧Ih
∞DYh
∞$Yh

dih

$ih
E	h
E9h
J%Yh
I%yh∞π&Ih∂DG)h ~∪T2g(ε⊂O⊂ih ⊗sT+g(¬_O⊂	ih ∩3d!'G9p~'e~_⊃λ0
/x␈␈␈␈x␈␈{0∞?x␈␈⎇P	?x␈␈}pHLCs⊃(Mε3!hMλ32_MIS"HMK∪2pML33_MMS3@≡αsCH≠DS3`_F∪3p⊗G34 Id)` ⊂d"0MPλah∃'λ∧@SD%∧F9X ∪A38N⊂∩→` $S4Igλ	 N⊂∩I` %3DJgλ	(N t/'¬pX ↔∪BhπP)`∃Dh¬HN
BT,'%↓@ ∃SB8
⊂
Y`∪π#P8↔g∧Qxβ%ih∩λ"!⊂⊗g∧2 εEEI`⊃IA↓P∃g$∀$JsBλ ∩E)h⊂⊂	"PNλλ∧X∀g#t%J3Ax ∩e→h∂⊂	B@Nπh∧X∀'#d%J∪Qh ∩e	`∂⊂	"8NG(∧P∪g#T$IsAh ∩$yh∞P	α8NG(∧8∪'#T#	SAh ⊃$yh∞PλB8NG(∧_∪'#T!	SQh ⊂∧ih∞Odih∞O$ih∞O∧ih∂∞$ih∂
dyh∂
$yh∂LDyp∂e→h∂Je)h⊂IE9h⊃H%Ip∩εEyh∀∧ε9h ~3d3'(ε_O⊂	p ↔∪T-'H¬0O⊂
)x ∪3d$gh∧_OO3s8Pt∩(R¬(D_εX␈␈␈␈x␈␈␈⎇`ε`␈␈␈␈ ∧X␈␈␈␈X↓&`YX∧&AIXπfb)P&c→P∞fd	X⊃fDyX∃&eYP_ffIX≠Pλ0 M∞g XMOF⊃_MPλ∩@
&H∧(∂H34$¬E	P ∪↓bpMP	p(~gλλHNP⊃→h "∪TCgλλ8NP⊂ih !3TB'¬P⊂ ∃SRXαP
Ih∀Bλ¬⊂NIAD('∧Px ∪SR⊂	P	Ih⊂¬H∧PNGC∀$gβAh∂A∧Ih
λα`X∩'"r εDd9`	`QH⊃g"T"HsQ( ⊃∧9h
Pλ2_N¬H∧⊂∩'"T!	∪Q( ⊂D9h
Pλ∩_N¬H∧⊃g"T λsQ(∨HsQ(∨	∪A(∨	∪Q(≡I∪Q(≡HsQ(≡λsA(≡λsQ(≥HsQ(≥	∪Q(≤I∪A(≤I∪Q(≤HsQ(≤λsQ(≠HsA(≠HsQ(~I3Q(↔
sQ(∪SA(⊂∞∪Q(O3Q(	∂3Q ¬OSA(α∂3T'g(∧@N⊂λ)h≥g&Ih⊗g∧yh⊂'#	hλg↓9hα⊃λ0
Ox␈␈␈␈x␈␈{@⊂/x␈␈⎇P	ox␈␈⎇0HM∧∪!(Mε31hMH∪2_MISB8MJSBXMKSBxML3C_N
∪C(MN∪CHN∞gaN∂π↓PN∂F"⊂N⊂λαh∀&h∧_∀3D#λF)` ∩C#8N⊂
x∨'λ	pN⊂∪y` (∪DPgλ
⊂N⊂∀)` (sBP∧⊂∞)`∀β(εxN	b∧7'∧a_ ≠∪B0
P
)`∩EhεPN	#∀4'∧QP →sB(
Pi`∩πC`P≡'∧B∧G	h⊃HB18≠'∧20¬G&I`⊃P	s_Nλh¬_g∧4(L∪B_ ∀Ey`⊃P
"pNHH¬_⊗g∧$)K3B⊂ ∀eI`⊃⊂
2`NH(¬_∃g∧∀)JSB⊂ ∀%9h⊂P
∩PNλ(¬∃'$∧(
3Bλ ∪E)h⊂⊂	bHNλ(∧`∀g$∧%J3Bλ ∩%→h⊂⊂	αHNHλ∧0∀g∧∀"
3Rλ ⊂%)h⊂Oe→h⊃∞e)h⊃∞%)h⊃M%)h∩E)p∩E)h∪
E)h∀	%)p∀H¬9p∃εe9h⊗E¬Yp_αeyp →st1'H¬pOP→p ∃St(gh∧`P⊂λix ⊂4βXOM4αpPIT⊃hQD(D_εh␈␈␈␈x␈␈␈⎇`π ␈␈␈}x∧X␈␈␈␈P¬&α)H&#YP⊂fDYP∀fEYX_&f)P≠&g	X≥fgYX∨fh∧⊂N⊂λ3xβfh∧(≥C∪D#MB→X ∩&!(N⊂	"pgλ∧`∃π∪4'	Cy` ∀∧∩_N⊂
!X∪gλ¬ 
K∪D+C&→` %SDK'λ	0NP∩i` %SCλβPi`↔β(¬XNJb∀,g¬⊃( ⊗∪B8⊂
yh∩Fh¬(N	βT*'∧2 ∀SRλ⊃π`BpNλ$1X∧K∪Qx∪¬aBXNπdq_λ
SAx∀βb2PNGE0@
3Ap ∩e→h∞P	2HNπH∧X∀'#T%J∪Ah ∩e	h∞P	"8NGλ∧P∪gβD%	sQ` ∩$y`∞⊂	∩8NGλ∧@∪g#4$	SA` ⊃dih∞⊂λR8NFh∧(∪g#4"	SA` ⊂dih∞⊂λ"0