Osnovy teorii Galua.

102

102 ~~~~Ill. Paspewwumue ypadeneuiw

nepenluluem 3TH 4)OpMyfibI TaK:
(1.7) ~x1+x,s. + xn e =-a,-,
X1+X2e-+...+ f
x 2+x 2C~~... + xl, 2u-1) p
]lla~ee o6paTHM BHMimHHl~ua, TO, IqTO ypalneutie
-1+ Xn-2 ______X t I
umeeT iOPHuRMH S, 62. C Ie a nIOTOM)y, cKmraxbwBasi paBeHCTsa (1.7) i-i co6Mpa~i Ko34xIMHtweH~bl FPH Xl1 X2**, Xn) mb! nOJnyqIM:
OC-ra~rbHbie KOPHtH Mb! mo1Kem 11fylOJHTb, yMHowa3H 4)opmyJm (1.7) Ha
HeKCOTOpIPIe CTeI1eHl C H cKma.Eb!Ba~i HX. Ho MO)KHO IIOJIyqI4Tb Te }Ke BbIpa)KeHHI AJIJI OCTaJIbHbIX KopHeil, flOXLCTaBJsiH B Bbipa)KeHHe (1.8) Ha meCTO
OAHIO H3 fl 3HaqeHHfl KOPHR n-PI cUerime, coo6paano C BnivameHHIMH (.)
Eaxe pa3 noaLqepK~em, 'ITO UYHKJIH'IeCKOe nonie K (xlX2,.. -,,X.) He co~-,
AIep)KI4T KCop~eRl n-a C~eneHH 143 e.ImiHbitb B TO Bpemg 1aK Mbl, BBOAR$
paAHFKaJlbHbie Bbipa)KeHHR, Tem camb1m BBOAIHM KOPHH 113 e.uH1tumbi. BbapaweHHlI(x11Cv_) HOCSIT Hma3Bae pe3OqbBeHT A a r pa r4.:
4. Ky6H'*eciuie ypaeHeuHli. IIHpJIOiuH 3TOT Crioco6 K pe[weivio iKy6HqIecKHx ypaBHeHHI4.
[1yC~b ypaa~eH~e
(1.9) - ~~XS + px + r=O
2,ti
HMCCz~T KOPIIH X,, X., x3. Bb!4HiCrnM B;)awerir.f' (xl, u~e ae -e
1 +j /1 3 1m
(IS & 2 (X, + S X2+e P2-X)3-x3 +-X23 4- X83+
+ 3 e,-1(XI' X2+x22 x-3+x3x)+ (XI X2- -9 x2 x +xx )+ Xx2 XSHi -I ymma o~otix rbwpaiwcuilfl j3 ct~oftax pariia 3q, a pa3HocrL(x191)3=9q + -s- a(3q~ i/+ v —a.7}D