Osnovy teorii Galua.

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75

rae u (x) Ht v (x) tieKOTOpbie noJmiHombi. HOJACTaBJ01H ciojta x 0 6yaem
13 cimy f (6) = 0 HmeTb:
~~~~g ~ ~ 0 (0
OTKYAaB ~ P)= (0). v (0). TaKHM o6pa3o~l Mbl Bceria mo}Kem npea,CTaBHTb KaWKJ~L1O BeJIH'HHY noji5I B BHae n ron Hii oIAia OrT0
20. H y C rb ~ y(0/ raie y (X) - UIOJHHOM. Ecarn ero Crerlel-b BbIU1
n -ITO pa3aenJItm ero Ha f (x). EIoJy4Him y/(x)=f (x) q(x) + t(x), rae
r (X) -1ORH4HOM CentmH Hie BblHin fl - 1. HlOA~CTaBJ15ffI x =, rnOiy'qHM
7(0) ~ r ('4. 14 T. JI.
30. LTJOKa1Kem, qTO KawK~aag Be~i1H4HHa noJi5 mo)KT 6blTb npeAlCTaB~neHa,B epopme (3.6) OJLHO3HaqHO. qLOUIyCTH4M IHpOTHBHoe, T. e. nyCTb HmeeT meCTO
a( + a1 ~.. + a ~0n-I = 0 + b 6 +..+ b;;j'1 -rue He Bce a,= I)( =,1 2,., i 1). Toraa HoJIMHOM
(a - -i x'.1- + (2-2-b;2), xn2 + +(a, - b1) x-J (ao -bo=,11o.TIeHf HmeTb C f1(X) o6ULHfii 1opnb m nOTO M B CHJI Teopemwb 44 aeaHITCH
Ha f (x), 'ITO HeBO3MO)KHo, TaK KaK ero CTeI1eHb HfDme, 'leM CTerieHb f x).
9. EcaiH BeJ1H flaH ~ HOhIH 3aaUHa B HopmaJTbHOM Buiae (3.6), TO
H3J1o)ellfblil B H. 5 nptHem HOCTPOeHi4Hf ypaBHeHL1q, KOTOPOMY yatoBIeTBopfieT
~,mowe(T 6blTb 3ameHeH 6onee yuto6HbxM TnpaKTH'Ieci(H npuemom. HlyCm
=a0 + a10 +..+ a n10 1. Byaem YMHO)KaTb o6e 'iaCru 9T0F0 paBeH-,CTBa riocJiej~OBaTeJlbH() Ha 1, 0,02,.. 0n-1 H HoHH)(ub C~eerfienonHOly'IIoUlHXCA1 HOJJHHOMOB npH HomomIH oI1HcaHI-OFO B H. 8, 20 pHpIema. fHyCrb MUI
~=ao + a16. + au22
(3.7) ~ 0 a 0,1+ al,16 +.. + a 106'1
= — a,,1. + a1ni +..+ a.~
nepenmwlem 3TY CHiCre~y Taic:
(ao + al.0 +. + a ~ 0,

a0 1+ a1 0 +., + (a,~, - 6~ =0