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R- m mn t -R, as usul
Tua is a mo n s R ln)=a ieu as nd R
+ no n
Sum 1n R
Po ssicies Brn ( r) suu -n -(1+ +
(a) p(7¢) >R, hu p =
R R orduns7 as sd tranas2, 2L% J, a, R, C, Z().
(6) 6) is o i.cse. ku (e)#o. Sia Z isa PLO, a
s s prinde , L (e)= (n) ,no ()> (-n)
Ten
Tu inas 2 in R sa Aie esius moulo n
o, n- =0 inR e : R>72/(a),
7L/n ra um a A, as a R Coadaas e tdhn Z
su u dauisans
A SSu R i AI K= F
P aoe nekm 0 P°n
siu QF no F 2Z , en F as
Fe- P Fp- o, P RA ueidey m P a
Exe F A FL polunomi s tn F, ac (F Cz)) -iSnahard F Rac (F(z1) ads ,), () e (x) Coe de As in F.
tequvaara wladan, (e) f o () #o
-2 Prop 1 1dgra doain R is a sus RAF, tluu
aO mo monpm ac (R) F L xtnds inus n R F
rac R SudhB's u 1
B? Ele menks k oc (R) a pa1s (, ) , f,
abeR B(ab)=Jl) J(L)
xei: )B Sa o momep sn,
2 s R
an
Prope sidos Sans wk ar1ncson
axdsto an neusu. u h Saehons Rrac (R)= 8(R)
F.
Q= rac (Z) tx e F eE cF
TF F åt ains suldl 2
Pi RASs.
FF, sa ta clanacktusic isP ch (F=P
h C)Fo a dhannchiis be of F is O c F, so
Rer xezu ) ?lr loma R
is a s a kll , Re
T Smeu dR Al dains R is isomophie &(R)>Yae (R
b)o cld Anks : eT inakU t.
-3 F-sd, Flx]
Savisan Jlad, Gne polyoil s (a)q(x)e Fl*] und tm oynomi als
&(oc) ()am
Tonsiued q (e),s(x) e dvid (x) (x) m a uwain le
Snsuin on
cz) < g(*) (n ca) don c) ( x)* {(x) (e)=lx)
nm &( a**o,-,"*. a o
9 ( 6."*. *
) = a, ba(b.m x"6z '4 +b). =a,**o, b C + Can inet in F, mtos tta Psa iA, 6en o i cln tnws
-m
, ta, -*" T. «a-(a,c * +a, b5
- a, 6. b., ) 2
)-a8**)¢ (z) as dau n Proco S adlucto
,z) as a
()q, (()+, (*) )=q (x)a*)ar, (x),12) (2) +, (*) qx)q(x) +2(x) (-2)a(e) = , («) -, (*)
wless 2, LtS
Diso pono i d's -1
a ema
o,,2} 2+2 |
8(e)=2x+x2x +* () +22 -1 2= - mos
ensen 2ct
+0x +2x+x S - -
2 + 2xt x
2 -2x- 2* =mals)
2t
2x*x = (*2x) (xx -t) 2oc+
nenie (L ePhiat is 1)Can di g(x) e)u wen oun RC«, R a is monde, rud dop coefhao
htnu thl in R
7l). Can t ila 3(x) 2 **/?
is rod Canr t 2t
or uaon , uset do a kld F and polroials tn Flx
Tm F) is prndi pl idorl doan PTb), a k T P Ta an la Te PC*] T=(o),* is prnpal T=(o)
T (o), clasvt a poly n m )eL 0u ma re.
m() CL SSu Pr t P6e) eT\(la)
d senna m (e)
a ma in lL
= q (z)m (x)+ (x) Ja r(x)é da m(z) 9 (x)
(a)eC si e >f(x)-q(* )m (oe )
m (x). (art In)
Colla In F(3) has bim (n() lo), a
= *ta,, x^** amone daA.
m( m (x) ioaals (m(T)), (z) au dshine
Divisb seR S dvdss s cls 3'e
seCr) -Priniga ad attd .
clo re, nLe $Lu)
u H clu Ofr (
D
ta,g ispoyoniol Ac). al, alg C) el, clg - cl -(,3) 3) Smo
San at , d Ia dve Pra
8,8 cds
A'8'1&,Fl)is&n d,d' drktt a a un See saa ho
F-3 P
exists
P
Ju s penpal (F6) is a PId) , T- ( )
(R),lass -()- &F()o V Can dao
cl,ey > cc',ecc" X=alrba acc. bc c'= clactbc')
maEuu) FheAeS, p(x)e F) oa pret -7
no ainds of ma n dscre
T) I2). .. q (a)
n22
Sln P) () - I~
1 a (ne P«}+ G(x) q(«) S a.
al) fc)k (a b(x)g (e) k(x )
ahr egk,la, k halht be = (a kt be)f
en
P ()
To s8 d2moe geneca
Su icuals fa, g ) = (?())+ (g(*o)
Evec T,S 1Is In R I+Tiirjl iel,jeJa dls ToS
tn R
Pncpa Sum a{
(),y) 6), gPM) (R-goe) (A() T
aX ra. = a,\c+ a,-0, z* tQ,0
/o.eF . c sca oc prena ds Ponaal s
0 opude qc&8,3) , kd dauis To
A&2s 3 , 3)
is ph e man ln now
(3 2 + ) )
Exe (P,g) ad (,)ha
u sa
remasne
(,3) - nea+t
( o neAnailn
ramp F=7/^= 5 -f (2e) 2e 2 x2z+, 1(«)z-**l.
Rd (¢a),z(z?)) emann en
(xt2A 2x tl, x'-x+1)
-z +l, T* -+x 3=0 3+X*
cdf(x)g () = *+l onc V
-2x
2) F F lo, 1) f(x)= *'t*°, (z)= 24X+|
emaan (z, x'2)
(z, z*)
(z ) T
&,au uladres pri
2C
- 10
Cplor vs M u mandn)
F3 Ten Le sist udea polns omials 9r eFLx), m r o Su at o oan
d O -
+
ola osef+ (f) 2ve
has a w etndese
Yemahd
Pco + Wck -q e (4) 3e )
CeQ (E) o set
Such C Vwa
-2e(t) , ht sdf +le)= +e)
Coyess () : uqeseed O a «ll (o miols { Jkra n
(-b2x+ b,x«b. 6,#0 E- 2
6us F:>/e)
4uaduic atx t+(f\
A padns (a,a,)a¬F o,1
telx a or all Rnea 6mh don
&n 3 ic
Cos F
sis 2,z Cocs adad ,4) a;e F
-it n
tus ? 4+4,r elAs s asre sìdus o ulo P
a ossibu F/( )
EKA F F=Q (= *+x*|. daaks as paromids o{ Ja at mogt
at,
o ul n K, mulkpas polno mus ,u sals a
2
rvi fon
(24)( -3z) = 2-S -3x -2-Sx -3 (-r-)-2-5�x) = +S
o 2 +*t(f)
-3t 1f(x\)
(24x)C-3)=4S 1n x+t). Xx = x-- x -l I R/r -
-3-S*t2
3*3* t 3 2) F F to,} o-2z+S
=z+**l As.
R: 7 Ix*xri) c(x)= xt*
= -I = (wd 2)
T s a kIS uMBr naAs
IFCxl/x*zed
-12 Rmean yo ro c-a
remain lA, a
x -a) C
eaF(x) F
(x )+c (a-a) gla)+c =
=0gla) +C =C &la) =C
lx)- (z-a)g (*) * Pla) isla)
(z) is avi des (x-a) ,0 remaln
is la)
e F Consfe pono is FLax3-e oses ane
he)t(x -a) k(a) jkn, n, (spo sweh
t(aa
R/z-) S sa IR 2 2
3
Com Son -13
FLx a Bo au PTDs
Invti Fl-)-F
ae
Sa Conste
(n) (-a) posi unn
ie Pornmial
n m k a)=q(z )h(x)
P° e ite u cGe polynd
23,,7,1,1) P) at.
eFa no e duiGle lnamdy
(uille's la aeks ) (i&L elan.s)
WM C
z1- p.(x).. P«() PiPa i radobn
o C Ju po s
=(-) p P
T =a a P P(z)
T moade esu,
ced ed,q) ecm ,) ec ,3)
opi , an+bm Som a, So a(« ),
alx){r\r b(x)g)
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