Osnovy teorii Galua.

116

M.. Pagpewumbie ypa6uenuq

IlocTyna% TaKHiM O6pa3OM CO BceMH CKO6KaMH B BbIpaH~eHHH (2.12), Mbi
Bb~pa3HM 1~ jB BIJite OA~HoOPu-OfH JII4HeR1HOA 4yHKIjUIi OT nep~oqIoti
qth ~ID 12 ce- C ejbiwMH paLUIOI-HaJIbHbIMHi Ko34X(PH[LeHTamHi. HIycTI
*j=a10. 'r + a11* - + ** + v
0, - + all 1 + + a,,a1 -
OTcMoxa MU! 13BeCTHum npiiemom (cm. rnaiaBy II, ~ 3.9) HffOAqHM AARi
ceAepyouee ypaBl-eHHe e -A CTerleHH:
aoo-i~, a0,1, a..,ea 0'ae '~* a1 T
BepR cHaqan'a B Kaqecripe e npocrofl XLeJHTeJb J)- 1, mu! n7oJyu4HM
ypaSneH~e rnpocoT0 CTeneHH.;jiaiiee 6epeM, B Ka4CCTBe e HoBbif JaenJiweJb el,,
JAeABi1LHftC5I Ha e. Tori~a KBaKAbIf neptioi pam6beTC51 Ha -L! HoBbix nee
pHOAIOB, 11p~qe.,Y MOKHQ, nOCyryna% alaj~iolHx4Ho, rIOCTPOHTb ypaB~eHne
C~teH ' KOTOPOM y ~JBJIeTBOP510T HOBbie nep~o~.bi, a KOS44rnHLHeHTamt4
RESxIoTC51 4)YHK~U1H CTapb1x rnepioJ~oB. TaKHiM HT~yeM WINJ nHtHBeJem ero peweH~e K peineHwio ypaB~eii1it~ npoCTb1X Crenleteft. B STOM Cjiyqae yzio6Hee
He IIOJb3OBaTLCg npHemom rviarbl II, ~ 3.9, a COCTaBJ15BTb, HOJlb3y$1Cb rayccoBIM- npiiemom, 3JaemeHTapHO-CHimme ipwieCK~e 4!YHKILHH OT coHn51ix{HHUK
nepHoXAoB. Jlyt~uie BceIro npocnea1M~b o6pa3oBa!*ie TaKHKX ypaBHeHHfl Ha nphiBoJ1Hmbix Hiiwe lpHimepax.
9. Hnp 11 M e p 1: p = 17. AAR5 9Toro npocTroo qiicn~a 6 51B13.'ieTCBa nepBoo6pa3HbIM KopHem. Onpe~aejuniM Bbtii'emi ero CUereHefl:
6, 2,12, 4, 7,8,14, 16, 11,15, 5, 13, 10, 9, 3,1 1.
Ibepu 9TH BbitieTbi qepe3 OJL'4i, CTPOUM cJIeXIIoflHe 8-,qjnenHue nepHo~ubi:
ps + a-2 ~ e- + a-8 + a-16 + a15 + s13 + S9,
P- a + P-12 ~ a7 + aU4 + 61 + a5+ a10 + as.
0
)Ia% nlofyqeHH41 np~0I3BeJaeHm% -q-q npH~aBJAlem no 1 K nOKa3aTenJImM 'UeHOB
Bbipa)effi4H nepiioita -q CMOTPHM,, B KaKOM 143 nepm1iOitO HaIxoJITC% nolly-,qaembie HOKa3aTJiiH, B Hom~enaem STH HepHOJabl B KaqeCTBe caa~raeMbLx:
' + %~ + ql + ri+ 8 + i~+ 1h+ m
8 q —j - 4, -5,q4m1.
TaKHM We o6pa3oM nonyqaeM H 'q.
= m +" + + + + ql + q + 4r,= +,l