` 4 # affixh ßfizs ±fflfl 4 οffyr %-as&8v bχ 4 ± F ffi±a D & M? F &Q U ν ff@ + 6Ψ N F L 4f9 &Q &U &ν &ff ff ffij μ%& A F u B F ffi9 fi! bχ 42 ± V ffi94ame F ffi9 > A V &?»HS*5hM! @ ZRQ2ΞC]ffi :ρh92b ; V L 4f9?» α, β, A V L+:fl&9?» γ =νp7 ffi α = β & l, Offi γ = α + β A > F =ME V &?»HSG*5hM@ ZR fi~[e, T fi[c ]ffi ; > F L 4 k = V L 49?» α, A V L+:fl& 9?» δ =νp7 ffi k = α & gν2 Offi δ = kα?q2d g ν2lp# >B tm V ffi > P Π& οffyr α + β = β + α; 2 α + β+γ = α +β + γ; :9g ffijg Offi, + α = α; 4 o9g:97g Offi α, ff% α + α =; 5 α = α; 6 klα = klα; 7 k + lα = kα + lα; 8 kα + β =kα + kβ 2 %-as_c } > F Πμ: n χgqμ&me Offi F n, ;g&q2d gν 2 <μ > F Π&9%-aS } 2 fl»@ &Ω" /'fi/'fi&q2dω =/'fihs& gν2 <μ9ω >Π&%-aS } Ω >Π 2 2 ^D&}ßQμ&ME Offi R 2 2, ^D&Q2DΩ =^DHS& gν2 <μω >Π&9%-aS } 4 *5AΩ S [a, b] Π&μ:eB Qμ&ME Offi C[a, b], ; B &Q2DΩ =B & gν2 <μω >Π&9%-aS %-as&t"-k j?»ffifl&ξ 2 o9?»&7?»ffifl&ξ
α =, α = α, k =; 4? k α =,B k =I α = 4 J=χ bχ 4 ± V ffi > F Π&9%-aS? V L& n 9g α,α 2,,α n lp α,α 2,,α n %-!=Ξ 2 V L 4g+`9 α,α 2,,α n %-flfl B α,α 2,,α n ffi%-as V &QJ n ffi V &χ Offi dimv = n ffl V ffi > F Π& n χ οffyr I±Ajg&%-aSn:J xχ >*ffi?a%-aslχa 4/9%-!=&g B CM%-aSffi»ν οffyr %-as F [x] bχ 44 ± α,α 2,,α n ffi n χ%-as V &QJ B V L& 4 g α, χa x,x 2,,x n ff% α = x α + x 2 α 2 + + x n α n B x,x 2,,x n ffi α AJ α,α 2,,α n #& +U, OR x,x 2,,x n T } A[Ω^D<μ&Ω >Π%-aS R 2 2 L #r^dffiqj E =,E 2 =,E 2 =,E 22 = o9 A = a a 2 a 2 a 22 R 2 2 A = a E + a 2 E 2 + a 2 E 2 + a 22 E 22 } 2 A > F Π&fl»@ n &/'fiqμ&%-as F [x] n L,x,x 2,,x n ffiqj 5 JffH=SfiffH ± α,α 2,,α n D β,β 2,,β n ffi n χ%-as V &fqj y I8^D+fi*ρ ntmjψ β = p α + p 2 α 2 + + p n α n, β 2 = p 2 α + p 22 α 2 + + p n2 α n, β n = p n α + p 2n α 2 + + p nn α n β,β 2,,β n =α,α 2,,α n P 2
xl p p 2 p n p 2 p 22 p 2n P = p n p n2 p nn P ffi9j α,α 2,,α n $J β,β 2,,β n & kdw$ Λ α V, I*ffi α = x α + x 2 α 2 + + x n α n = y β + y 2 β 2 + + y n β n α =α,α 2,,α n B&7& +UTm ;fiffi x x 2 x n x x 2 x n =β,β 2,,β n = P y y 2 y n y y 2 y n, 6 %-OaS bχ 45 ± V ffi > F Π&9%-aS V &94aOM W ffi V &9OaS? W ; V &Q2D gν2<μ%-as A%-aS V L 99j?»Qμ&OME {} ffi V &9OaS ffi V &joasξ%-as V Φ ffi V &9OaS Cf9OaSff ffi V & Πf*yr x<&oas ffi gπf*yr bχ 46 ± α,α 2,,α s ffi%-as V & s 9g B4aME Lα,α 2,,α s ={k α + k 2 α 2 + + k s α s k i F, i =, 2,,s} =;g&q2d gν2ffi6ψ& 6fiνffi V &9OaS ffi9 α,α 2,,α s Φ Z^*yr b 4 ± α,α 2,,α s D β,β 2,,β s ffi%-as V &fqg B Lα,α 2,,α s Lβ,β 2,,β s #y # α,α 2,,α s `9 β,β 2,,β s %-flfl 2 Lα,α 2,,α s =Lβ,β 2,,β s #y #gq α,α 2,,α s D β,β 2,,β s 'R α,α 2,,α s &Lψ!=QffiOaS Lα,α 2,,α s &J χ '; gq α,α 2,,α s &J
Ξp ] Euclid yr &*5 bχ 42 42 Ξp ] Euclid yr ± V ffiω >Π&%-aS A V Π*59 α = β?ωb OR α, β, ν:#&-kλ α, β =β,α; 2 kα, β =kα, β; α + β,γ =α, γ+β,γ; 4 α, α, y α, α =#y # α = xl α, β, γ ffi V L& 4g k ffi 4Ω B α, β ffig α = β & o *5huK&Ω%-aSaS V ffi Ξp ]yr, T Ξffyr 2 ρ~^yclqu bχ 422 ± V ffiwfflas 4g α V, 47Ω α, α ffi α & Yc I, Offi α, N α = α, α $,';j&gi:jg,'; &g ffi"ψg 494jg α `"ψfλ β = α α b 42 x - WΛxiflnV_Ψ wfflas V L 4g α, β, : α, β α β, xl'ci:a α = β &'Ψμd uv_ψ α + β α + β bχ 42 ± V ffiwfflas 44jg α, β, *5 α = β &PY θ 9# fi~*λ α, β cosθ = α β θ π οffi # α, β =Ψ α = β %t I ', Offi α β U%tn bχ 424 wfflas V L&Q4jg?νpffiffEX B Hffi 9EXgQ b 422 wfflas&qexgq α,α 2,,α n Ω*%-!= 4
bχ 425 A n χwfflas V L 9 n 9gQμ&EXgQ ffi V & QEXJΞ9"ψgQμ&EXJ ffifinexj b 42 ± ε,ε 2,,ε n ffi n χwfflas&qfinexj ; α, β V, 8 x,x 2,,x n T D y,y 2,,y n T 5ffiflfl α, β ACQJ&Sfi B α, β =x y + x 2 y 2 + + x n y n 8Φqο Schmidt EXF2WQ%-!=&gQFμ=ν'R&f fex&gq ± α,α 2,,α n ffiwfflas V &QJ } W R &QJ FffifiNEXJ v k β = α =, β = α, β 2 = α 2 α 2,β β,β β,, β n = α n αn,β β,β β αn,β 2 β 2,β 2 β 2 αn,β n β n,β n β n α = β 2 = α 2 α 2,β β,β β =,α 2 = 2 β = α α,β β,β β α,β 2 β 2,β 2 β 2 = =,α = 2, 6 2 = 2 W β,β 2,β "ψf % γ = β β = γ 2 = β 2 β 2 = 6 γ = β β = 2 2,, 5
γ,γ 2,γ Nffiμz&fiNEXJ 4 %tw$ψu%tn&r^kdw$ bχ 426 ± A ffi n [^D? A T A = AA T = I, B A ffiex^d } ± θ ffi9y, [Ω ^D cosθ -sinθ A = sinθ cosθ ffiex^d } 2 Ξ[^D A = 2 6 6 2 6 2 ffi9ex^d %tw$^ff: Λ A ffiex^d B A T = A ffiex^d 2 EX^D&KffiEX^D Λ A ffiex^d B A = ± 4 Ω^DffiEX^D&ß/ρVffi A &i, gqffi R n &finexj b 424 finexjhs&@-^dffiex^d %-ffh&*5 4 οfftm *5 4 ± V ffi > F Π&9%-aS σ ffi V Π&9ffH? ; V L 4f9g α, β D > F L& 4 k, +: B σ ffi V Π&9 οfftm σα + β =σα+σβ, σkα =kσα 6
2 %-ffh&-k -K %-ffhπjgffμjg -K 2 %-ffh ο%-="qed%-="fi ff -K %-ffhπ%-&=&gqffμ%-&=&gq %-ffh&^d b 4 ± σ ffi n χ%-as V &9%-ffH α,α 2,,α n ffi V & QJ B%-ffH σ 9J& σα,σα 2,,σα n fi}~* bχ 42 ± σ ffi n χ%-as V &9%-ffH α,α 2,,α n ffi V & QJ W σα,σα 2,,σα n flflffi α,α 2,,α n &%-QEΛ σα =a α + a 2 α 2 + a n α n, σα 2 =a 2 α + a 22 α 2 + a n2 α n,, σα n =a n α + a 2n α 2 + a nn α n O BΠfiμffi xl n [^D σα,α 2,,α n =σα,σα 2,,σα n σα,α 2,,α n =α,α 2,,α n A a a 2 a n a 2 a 22 a 2n a n a n2 a nn ffi οfftm σ "n α,α 2,,α n μ^w$ 4 wfflas&exffh bχ 4 ± σ ffi n χwfflas V &9%-ffH, ffi V &uk? ; 4& α, β V, : σα,σβ = α, β, B σ ffi V &9 %ttm b 42 %-ffh σ ffiwfflas V &9EXffH #y ##iρvh μdλ σ οg&, ff N 4 α V, : σα = α ; 2? ɛ,ɛ 2,,ɛ n ffi V &QfiNEXJ tm σɛ,σɛ 2,,σɛ n ffi V &QfiNEXJΞ σ AsQfiNEXJ#&^DffiEX^D 7
44 οfftm"v nμ^w$ b 44? α,α 2,,α n D β,β 2,,β n ffi V &fqj V &%-ffh ACfQJ&^D5ffiffi A D B?ffi α,α 2,,α n $ β,β 2,,β n &@-^ Dffi C, B: B = C AC 5 } ψffiω } A R L± α =,,,,β =,, 2,,γ =,,,, zg ξ = γ + k α + k 2 β, ff% ξ = α, β +EX ffiωλaf;xe AM5/` } 2 2G R L&f9g α =, 2,,β =, 4, z= α, β +EX& g ffiωλjv7td x,y,z, YM8TDaF;XE A5/`< } ±D A lp A 2 4A +E =, y A T = A, F A 2E ffiex^d ffiωλ]?uknyh_^b[2;xqb[ } 4 ± α ffi n χig y α T α = F A = E 2αα T ffi EX^D ffiωλoi } 5 ± A =a ij n n ffiex^d A ij ffi,ifi A L?» a ij &! <O fi F A ij = ±a ij ffiωλ =B[2_^B[<PN2G[ ZWG[Y,LB[29R } 6 ±5b^D P R A = Q [D F P, Q +ffiex^d y R = ffiex^d xl P ffi m [D Q ffi n ffiωλ =B[2_^<PN2G[ W6CB[24 ->B[S < @: 8