Osnovy teorii Galua.

126

726 ~~~~~Ill.L Papeuwumbte ypa,6enenw

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Taime~ iiejiofl dpHKLutie OT KO34)14)M4LHeHT0B ypaBHeHH51 (3.12). cPyHKU1451
rae A -A, 6ylleT JteIIHTbC5I Ha A. JReftCTBHTeJnbHo, 6y~aem C45HTaTb nepemeHHOR1 BeJi5q4HHY Xe, a OCTaJlbHbie KOPH51 X1 X2i X3,, X4 6yaem Cl51HTTb
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ocraioityocfi, c oJ1Holl CTOPOHbl, HeH3MeHHo1f1 npH HpoHi3BOJ1CTBe TpaHcflO3HiUMH (XOX1.), a C iipyrOOI CTOPO11IA, meH5LOLMy1O OT 3TOft TpaHCn1O31~1LHH
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x0 - x4. lBepR B icaqeCT~e HepemeHHO1f1 BmeCTO X0 jtpyr~e KoA145, mbi
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X0, X1, X2 X$, X4 51 HOTOMY Bb1i3)K3eTC51 KaK iteiasi paUH1OHajibHafl 4)yHK[Uw or K094X4)HiteHTOB ypaBHeHHH (3.12). TaKH1M o6pa3oM mbi Himeem:
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0TKyaa~
i-.ie B H C - iteame pattHo~afibiiie 4)1yHKLLHH OT Ko344(HutieHTOB ypaB~eKHR 5(3.12).
7. HpHmeHHM 3TOT pe3yJUbTaT 1< Bb1414CJ1eHH1O K03(j~j3HLt5eHTOB ypaB(3.16) U6~+ A1U5 + A2U4 + A3U3 ~ A4 U2 + AS5U+AO= 0,
KOTOPOMY yRtOl3.eTBops~eT Ben.TIHqHa U v - VI. Ee (O394MLUPHiu TbI
flBJISIIOTC5I CHMMeTpHt4eCfMim epyHKLJJ4MH OT pa3HOCTefl
(3.17) 1UV-V1, U1=v2-v3, U2=V4-V5, U-=V06-7,
U4=V8 _V9, U-5=V10-V11,
ijte v, 2 VP V6) V8-, V1 Rioaiyqaro0c 513 V) nriH HOMOLUIH nOJCTaHoBoK
3HiaKornepemewliof rpynibni, a v,, v., v., 1)7, 1g)9 VI] -- HI5H HOMOJIH MUOMLT~H10B1K, He BXOARLJIJIX B 3Hai(OnepeMeHHy1O rpynnIy. TatiHm o6pa3om, npOH13 -BOARS HaAl COBOIKYnHOCTbIO BeJ1H414iH (3.17), KaK (d)yHKLift1 OT X0, X1, x2, X3, X4,
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Ho Bee-rniIifu A, SIBJIX1OTCff aJnemeHTapHO-c5MMmeTp51'qecKHMH 4pyHKLLH5IMH OT
BeJnli4HH (3.17). 1H3 HMix A2, A4, A6 5IBJISUfOTCSI OAJHOPO1IHbMH I~YHKiLH1SMH
q e T H bi X C T e ri e H e it 51 HOTOMY He 6yiiyT meH5]TbC9, eCITH MbI H3MeHHiM
3HaK Ka)Kazofl 513 B'~J1H'4HH (3.17), T. e. 0OH1 SIB.7I15IOTCI cIAmmeTpHiiqcCKHmt
4~YHKIIHSMH OT -XO, X1, X2, x3, X4; BeniWHlHbl we Al, A,3, A45 6yAryT MeHHTb
3HaK nHpi- r[POHM3oJCTBe HaAl X0, Xi, X2, X3, X. HeqIe~i-bix.OJiCTa1HOBOK 51
UOTOMY B'~pa3RTCH 'B 4bopme A B, rue B~ ei~~LHHJb~1CMe
Tp51EeCKaS! qYHKUVH19 OT XO, XI) X2, X., x4. B CHJ1y 3T01'O MO)KHO npellCTaBH4Tb ypaBeHeHiie (3.16) B TaKom Btae:

(3.18)

(.18) U6+A2LI'+A4U2+A+A(B U5+BjU3+B5)=0