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54

Niaea?aeaiea

Aaaaeaiea …………………………………………………………………. 3

Aeaaa I. Iiiai/eaiiua iao?eoeu.

§1. Yeaiaioa?iua i?aia?aciaaiey iiiai/eaiiie iao?eoeu….. 4

§2. Eaiiie/aneee aeae ?-iao?eoeu……………………………….. 5

§3. Iaeaieueoea iauea aeaeeoaee ieii?ia…………………….. 10

§4. Oneiaey yeaeaaeaioiinoe ?-iao?eoe……………………….. 15

§5. Yeaiaioa?iua aeaeeoaee iiiai/eaiiie iao?eoeu………… 19

Aeaaa II. Iao?e/iua iiiai/eaiu.

§1. Aeaeaiea iao?e/iuo iiiai/eaiia. Iaiauaiiay oai?aia Aaco. 23

§2. Neaey?iay yeaeaaeaioiinoue…………………………………. 28

§3. Oa?aeoa?enoe/aneee iiiai/eai iao?eoeu…………………. 29

§4. Ieieiaeueiue iiiai/eai iao?eoeu………………………… 31

§5. E?eoa?ee iiaeiaey iao?eoe………………………………….. 33

§6. Ii?iaeueiay oi?ia AEi?aeaia……………………………….. 36

Aeaaa III. Ooieoeee io iao?eoe.

§1. Iiiai/eai io aei?aeaiiaie iao?eoeu……………………….. 40

§2. Neaey?iua ooieoeee…………………………………………. 42

§3. I?aaenoaaeaiea cia/aiee ooieoeee iiiai/eaiaie………… 46

§4. Yeaiaioa?iua aeaeeoaee ooieoeee…………………………. 48

§5. Noaiaiiua ?yaeu……………………………………………… 49

Eeoa?aoo?a ……………………………………………………………… 53

Aaaaeaiea

Aeeieiiiay ?aaioa ninoieo ec o?ao aeaa.

Ia?aua aeaa ia?aa?aoa I aeaau iinayuaiu eco/aieth naienoa iiiai/eaiiuo
iao?eoe. A §3, yoie aea aeaau, aaiaeyony iiiyoey iaeaieueoeo iaueo
aeaeeoaeae ieii?ia e eiaa?eaioiuo iiiaeeoaeae iiiai/eaiiie iao?eoeu.
Ia iniiaa yoiai a iineaaeothueo aeaoo ia?aa?aoao ?anniao?eaathony
oneiaey yeaeaaeaioiinoe ?-iao?eoe e no?ieony aiaeeoe/aneay oai?ey
yeaiaioa?iuo aeaeeoaeae.

N eaaeaeie eaaae?aoiie iao?eoeae naycaiu aeaa iiiai/eaia:
oa?aeoa?enoe/aneee e ieieiaeueiue. Yoe iiiai/eaiu ea?atho aieueooth
?ieue a ?acee/iuo aii?inao oai?ee iao?eoe. Ai II aeaaa
?anniao?eaathony naienoaa oa?aeoa?enoe/aneiai e ieieiaeueiiai
iiiai/eaia. Yoiio enneaaeiaaieth i?aaeiinueathony iniiaiua naaaeaiey i
iiiai/eaiao n iao?e/iuie eiyooeoeeaioaie e i aeaenoaeyo iaae ieie.
Iineaaeiee ia?aa?ao II aeaau iinayuai ii?iaeueiie oi?ia AEi?aeaia.

A aeaaa III, iinayuaiiie ooieoeeyi io iao?eoeu, ?anniio?aiu aii?inu
iao?e/iiai en/eneaiey, aeey ?aoaiey eioi?uo eniieuecoaony
aiciiaeiinoue i?eaaaeaiey iao?eoe e ii?iaeueiie aei?aeaiiaie oi?ia. A
§5, yoie aea aeaau, ?anniio?ai aii?in i noiaeeiinoe noaiaiiiai ?yaea io
iao?eoeu A.

I?eaaaeaiiue iaoa?eae eeethno?e?oaony a ?aoaieyo ?acee/iuo i?eia?ia.

Aeaaa I. Iiiai/eaiiua iao?eoeu.

§1. Yeaiaioa?iua i?aia?aciaaiey iiiai/eaiiie iao?eoeu.

Iiiai/eaiiie iao?eoeae eee ?-iao?eoeae iacuaaaony i?yiioaieueiay
(a /anoiinoe, eaaae?aoiay) iao?eoea A (?) = ?a? 1/4 (e) ?, aaea
i=1, 2, …, m; j=1, 2, …, n; yeaiaiou eioi?ie yaeythony
iiiai/eaiaie io iaeiiai ia?aiaiiiai ? n /eneiauie eiyooeoeeaioaie ec
iniiaiiai iiey E.

Yeaiaioa?iuie i?aia?aciaaieyie ?-iao?eoeu A(?) iacuaathony
i?aia?aciaaiey neaaeothueo oeiia:

I. Ia?anoaiiaea aeaoo no?ie.

II. Oiiiaeaiea no?iee ia /enei n ? E, n ? 0.

III. I?eaaaeaiea e iaeiie no?iea ae?oaie no?iee, oiiiaeaiiie ia ethaie
iiiai/eai f (e), и aiaeiae/iua i?aia?aciaaiey noieaoeia.

Yeaiaioa?iua i?aia?aciaaiey I, II, III ?aaiineeueiu oiiiaeaieth
iiiai/eaiiie iao?eoeu A(?) neaaa niioaaonoaaiii ia neaaeothuea
eaaae?aoiua iao?eoeu ii?yaeea m:

(i) (j) (i) (j)

1 0 1 0 1
0

S’ = n , S” = 1… b(e) ….(i), S”‘ =
0 1 ,

0 1 0 1 1 0

0 1

o.a. a ?acoeueoaoa i?eiaiaiey i?aia?aciaaiee I, II, III iao?eoea A(?)
i?aia?acoaony niioaaonoaaiii a iao?eoeu S’· A(?), S”· A(?), S”‘· A(?).
Iiyoiio i?aia?aciaaiey oeia I, II, III iacuaathony eaauie
yeaiaioa?iuie iia?aoeeyie.

Niaa?oaiii aiaeiae/ii ii?aaeaeythony i?aaua yeaiaioa?iua iia?aoeee
iaae iiiai/eaiiie iao?eoeae (yoe iia?aoeee i?iecaiaeyony ia iaae
no?ieaie, a iaae noieaoeaie) e niioaaonoaothuea ei iao?eoeu ii?yaeea n:

1 0 1 0 1
0

O’ = n (i), O” = 1………….(i), O”‘ =
0…1……….(i) b(e)……….(j) 1…0……….(j)
.

0 1 0 1 0 1

A ?acoeueoaoa i?eiaiaiey i?aaie yeaiaioa?iie iia?aoeee iao?eoea A(?)
oiiiaeaaony ni?aaa ia niioaaonoaothuoth iao?eoeo O.

Caiaoei, /oi iao?eoea O’ niaiaaeaao n iao?eoeae S’, a iao?eoeu O”, O”‘
niaiaaeatho n iao?eoeaie S”, S”‘, anee a iineaaeieo iiiaiyoue ianoaie
eiaeaenu i e j. Iao?eoeu oeia S’, S”, S”‘ (eee, /oi oi aea, oeia O’, O”,
O”‘) iacuaathony yeaiaioa?iuie.

Aeaa e-мao?eoeu A(?) e B(e) оaeeiaeiauo ?acia?ia m x n iacuaathony
yeaeaaeaioiuie, A(?) ~ B(e), anee io iao?eoeu A(?) e B(e) iiaeii ia?aeoe
i?e iiiiue oeaii/ee ec eiia/iiai /enea yeaiaioa?iuo i?aia?aciaaiee.
Ioiioaiea yeaeaaeaioiinoe iaeaaeaao o?aiy iniiaiuie naienoaaie:

1) ?aoeaeneaiinoue: eaaeaeay iao?eoea yeaeaaeaioia naia naaa A(?) ~
B(e);

2) neiiao?ey: anee A(?) ~ B(e), тi B(e) ~ А(e);

3) o?aiceoeaiinoue: anee A(?) ~ B(e), e B(e) ~ С(e), тi A(?) ~ N(e).

§2. Eaiiie/aneee aeae ?-iao?eoeu

Auoa auei iieacaii, /oi ioiioaiea yeaeaaeaioiinoe o?aiceoeaii,
neiiao?e/ii e ?aoeaeneaii. Ionthaea neaaeoao, /oi niaieoiiinoue anao
?-iao?eoe aeaiiuo ?acia?ia m x n ?acaeaaaony ia iaia?anaeathueany
eeannu yeaeaaeaioiuo iao?eoe, o.a. ia oaeea eeannu, /oi ethaua aeaa
iao?eoeu ec iaeiiai eeanna yeaeaaeaioiu, a ec ?aciuo eeannia – ia
yeaeaaeaioiu iaaeaeo niaie. Aicieeaao aii?in i eaiiie/aneie oi?ia
?-iao?eoeu, oa?aeoa?ecothuae aeaiiue eeann yeaeaaeaioiuo ?-iao?eoe.

Eaiiie/aneie aeeaaiiaeueiie ?-iao?eoeae ?acia?ia m x n iacuaaaony
e-мao?eoea, o eioi?ie ia aeaaiie aeeaaiiaee noiyo iiiai/eaiu A1(e),
Е2(e), …, Е?(?), aaea ? – iaiueoaa ec /enae m e n, i?e/ai ia ?aaiua
ioeth n?aaee yoeo iiiai/eaiia eiatho noa?oea eiyooeoeeaiou, ?aaiua
aaeeieoea, e eaaeaeue neaaeothuee iiiai/eai aeaeeony ia i?aaeuaeouee,
ana aea yeaiaiou aia aeaaiie aeeaaiiaee ?aaiu ioeth.

O a i ? a i a 1. Anyeay ?-iao?eoea eiia/iui /eneii yeaiaioa?iuo
i?aia?aciaaiee iiaeao auoue i?eaaaeaia e eaiiie/aneie aeeaaiiaeueiie
oi?ia.

Aeieacaoaeuenoai. Ionoue A(?) – i?yiioaieueiay iiiai/eaiiay iao?eoea.
I?eiaiyy e A(?) eae eaaua, oae e i?aaua yeaiaioa?iua iia?aoeee i?eaaaeai
e eaiiie/aneie aeeaaiiaeueiie oi?ia.

N?aaee anao ia ?aaiuo ioeth yeaiaioia a?1/4(e) мao?eoeu A(?) aicueiai
oio yeaiaio, eioi?ue eiaao iaeiaiueooth noaiaiue ioiineoaeueii ?, e
iooai niioaaonoaothuae ia?anoaiiaee no?ie e noieaoeia naeaeaai aai
yeaiaioii a11(e). Пinea yoiai iaeaeai /anoiua e inoaoee io aeaeaiey
iiiai/eaiia a?1(e) e a11/4(e) нa a11(e):

a?1(e) = a11(e) q?1(e) + r?1 (e), a11/4(e) = a11(e) q11/4(e) + r11/4(e)

(i = 2, 3, …, m; j = 2, 3, …, n).

Anee oioy au iaeei ec inoaoeia r?1(e), r11/4(e) (i = 2, …, m; j = 2, …,
n), iai?eia? r11/4 (e), нa ?aaai oiaeaeanoaaiii ioeth, oi, au/eoay ec
j-ai noieaoea ia?aue noieaaoe, i?aaeaa?eoaeueii iiiiiaeaiiue ia
q11/4(e), мu caiaiei yeaiaio a11/4(e) оnoaoeii r11/4(e), кioi?ue eiaao
iaiueooth noaiaiue, iaaeaee a11(e). Тiaaea iu eiaai aiciiaeiinoue
niiaa oiaiueoeoue noaiaiue yeaiaioa, noiyuaai a eaaii aa?oiai oaeo
iao?eoeu, iiianoea ia yoi ianoi yeaiaio n iaeiaiueoae noaiaiueth
ioiineoaeueii ?.

Anee aea ana inoaoee r21(e), … rm1(e); r12(e), …, r1n(e) рaaiu
oiaeaeanoaaiii ioeth, oi, au/eoay ec i-ie no?iee ia?aoth, iiiiiaeaiioth
i?aaeaa?eoaeueii ia q?1(e) (i = 2, …, m), a ec j-ai noieaoea – ia?aue,
i?aaeaa?eoaeueii iiiiiaeaiiue ia q11/4(e) (j = 2, …, n), iu i?eaaaeai
iaoo iao?eoeo e aeaeo

a11(e) 0 … 0

0 a22(e) … a2n(e)

….…………………… .

0 am2(e) … amn(e)

Anee i?e yoii oioy au iaeei ec yeaiaioia a?1/4(e) (i = 2, …, m; j = 2,
…, n) ia aeaeeony aac inoaoea ia a11(e), тi, i?eaaaeyy e ia?aiio
noieaoeo oio noieaaoe, eioi?ue niaea?aeeo yoio yeaiaio, iu i?eaeai e
i?aaeuaeouaio neo/ath e, neaaeiaaoaeueii, niiaa niiaeai caiaieoue
yeaiaio a11(e) мiiai/eaiii iaiueoae noaiaie.

Iineieueeo ia?aiia/aeueiue yeaiaio a11(e) иiae ii?aaeaeaiioth noaiaiue e
i?ioeann oiaiueoaiey yoie noaiaie ia iiaeao iaia?aie/aiii
i?iaeieaeaoueny, oi iinea eiia/iiai /enea yeaiaioa?iuo iia?aoeee iu
aeieaeiu iieo/eoue iao?eoeo aeaea

a1(e) 0 … 0

(*) 0 b22(e) … b 2n(e)

….…………………… ,

0 bm2 (e) …bmn (e)

a eioi?ie ana yeaiaiou b?1/4(e) дaeyony aac inoaoea ia a1(e). Еnee
n?aaee yoeo yeaiaioia b?1/4(e) иiathony ia ?aaiua oiaeaeanoaaiii ioeth,
oi i?iaeieaeay oio aea i?ioeann i?eaaaeaiey aeey no?ie n iiia?aie 2,
…, m e noieaoeia n iiia?aie 2, …, n, iu iao?eoeo (*) i?eaaaeai e aeaeo

a1 (e) 0 0 … 0

0 a2(e) 0 … 0

0 0 n33(e) … n3n(e) ,

…………………………

0 0 nm3(e) … сmn(e)

aaea a2(e) aeaeeony aac inoaoea ia a1(e), а ana iiiai/eaiu n?1/4(e)
дaeyony aac inoaoea ia a2(e). П?iaeieaeay yoio i?ioeann aeaeaa, iu a
eiioea eiioeia i?eaeai e iao?eoea aeaea

a1(e) 0 … 0 0 … 0

0 a2(e)… 0 0 … 0

…….…………………..

0 0 …as(e) 0 … 0 ,

0 0 … 0 0 … 0

………………………..

0 0 … 0 0 … 0

aaea iiiai/eaiu a1(e), a2(e), …, as(e) (s ? m, n) ia ?aaiu
oiaeaeanoaaiii ioeth e eaaeaeue ec ieo aeaeeony ia i?aaeuaeouee aac
inoaoea.

Iiiiiaeay ia?aua s no?ie ia niioaaonoaothuea ioee/iua io ioey /eneiaua
iiiaeeoaee, iu niiaeai aeiaeoueny oiai, /oiau noa?oea eiyooeoeeaiou
iiiai/eaiia a1(e), a2(e), …, as(e) бuee ?aaiu aaeeieoea.

Oaeei ia?acii iu aeieacaee, /oi i?iecaieueiay i?yiioaieueiay
iiiai/eaiiay iao?eoea A(?) yeaeaaeaioia iaeioi?ie eaiiie/aneie
aeeaaiiaeueiie.

Aeaiiay oai?aia ooaa?aeaeaao, /oi eaaeaeue eeann yeaeaaeaioiuo iao?eoe
niaea?aeeo, ii iaiueoae ia?a, iaeio iao?eoeo, eiathuoth eaiiie/aneoth
aeeaaiiaeueioth oi?io.

I?eia?

Iaeoe eaiiie/aneoth oi?io e eiaa?eaioiua iiiaeeoaee -iao?eoeu

-1 -1 -2

3+ -1 3+-1

A() = +1 3++2 +1 3+2+3

-1 -3 -3 -6

O?aoee noieaaoe au/eoaai ec inoaeueiuo:

1 0 -1 -1

1 3+1 -1 3

A() 0 3+1 +1 3++2

2 0 -3 –3

(ec aoi?ie e /aoaa?oie no?ie au/eoaai ia?aoth, oiiiaeaiioth
niioaaonoaaiii ia 1 e 2)

1 0 -1 -1

0 3+1 0 3+1

0 3+1 +1 3++2

0 0 –1 –1

(ec III e IV noieaoeia au/eoaai I, oiiiaeaiiue niioaaonoaaiii ia -1 e
-1)

1 0 0 0

0 3+1 0 3+1

0 3+1 +1 3++2

0 0 –1 –1

(II e III noieaoeu au/eoaai ec IV)

1 0 0 0

0 3+1 0 0

0 3+1 +1 0

0 0 –1 0

(ec III no?iee au/eoaai II e iieo/aiioth no?ieo i?eaaaeyai e IV)

1 0 0 0

0 3+1 0 0

0 0 +1 0

0 0 0 0

(ia?anoaaeyai II e III no?iee, a oaeaea aoi?ie e o?aoee noieaoeu)

1 0 0 0

0 +1 0 0

0 0 3+1 0 .

0 0 0 0

Yoi eaiiie/aneay iao?eoea; cia/eo iao?eoea A() eiaao eiaa?eaioiua
iiiaeeoaee: A1()=1, A2()=+1, A3()=3+1, A4()=0.

§3. Iaeaieueoea iauea aeaeeoaee ieii?ia

Ionoue F – eaeay-ieaoaeue ?-iao?eoea ii?yaeea n. Ninoaaei aa
anaaiciiaeiua ieii?u ii?yaeea e (e = 1, 2, …, n). Yoe ieii?u yaeythony
iiiai/eaiaie io ?. Iaicia/ei eo iaeaieueoee iauee aeaeeoaeue /a?ac
De(e) (нaeaieueoei iauei aeaeeoaeai iu oneiaeiny iacuaaoue iauee
aeaeeoaeue iaeaunoae noaiaie ni noa?oei eiyooeoeeaioii 1. Iiyoiio ana
ia ?aaiua ioeth iiiai/eaiu De(e) иiatho noa?oee eiyooeoeeaio 1). Anee
ieaaeaony, /oi ana ieii?u e-ai ii?yaeea ?aaiu ioeth, oi ii
ii?aaeaeaieth aoaeai n/eoaoue De(e)=0. В /anoiinoe, D1(e) еnoue
iaeaieueoee iauee aeaeeoaeue yeaiaioia iao?eoeu F, a Dn(e) рaaai
ii?aaeaeeoaeth F, aeaeaiiiio ia naie noa?oee eiyooeoeeaio.

O a i ? a i a 2. Yeaeaaeaioiua ?-iao?eoeu eiatho iaeei e oio aea
iaeaieueoee iauee aeaeeoaeue ieii?ia e-ai ii?yaeea (e = 1, 2, …, n).

Aeieacaoaeuenoai. Ionoue F1, F2 – aeaa yeaeaaeaioiua ?-iao?eoeu.
Iaicia/ei iaeaieueoea iauea aeaeeoaee eo ieii?ia e-ai ii?yaeea
niioaaonoaaiii /a?ac De1(e) и De2(e). Т?aaoaony iieacaoue, /oi
De1(e) = De2(e). Нai ecaanoii, /oi F2 iiaeii iieo/eoue ec F1
oeaii/eie yeaiaioa?iuo i?aia?aciaaiee. I?aaeiieiaeei nia/aea, /oi yoa
oeaii/ea ninoieo oieueei ec iaeiiai yeaiaioa?iiai i?aia?aciaaiey.
Ionoue, iai?eia?, F2 iieo/aaony ec F1 oiiiaeaieai anao yeaiaioia i-e
no?iee iao?eoeu F1 ia /enei ??0. Niioaaonoaaiiua ieii?u F1 e F2 oiaaea
eeai nianai ia ioee/athony ae?oa io ae?oaa, eeai ioee/athony eeoue
iinoiyiiui iiiaeeoaeai ?. Iaeiaei iinoiyiiue iiiaeeoaeue ia aeeyao ia
au/eneaiea iaeaieueoaai iauaai aeaeeoaey iiiai/eaiia, iiyoiio De1 = De2.
Oi aea naiia aoaeao e a neo/aa, eiaaea F2 iieo/aaony ec F1
oiiiaeaieai ia ? yeaiaioia eaeiai-eeai noieaoea iao?eoeu F1. Ionoue
oaia?ue F2 iieo/aaony ec F1 iaeiei ec yeaiaioa?iuo i?aia?aciaaiee;
iai?eia?, ionoue F2 aicieeaao a ?acoeueoaoa i?eaaaeaiey e i-e no?iea
iao?eoeu F1 yeaiaioia j-e no?iee, oiiiaeaiiuo ia f(e). Пieaaeai, /oi
De2 aeaeeony ia De1.

A naiii aeaea, ieii?u e-ai ii?yaeea iao?eoe F1, F2 iiaeii ?acaeoue
ia o?e eeanna. E ia?aiio iu ioianai oa ec ieo, eioi?ua ia niaea?aeao
yeaiaioia i-e no?iee. Niioaaonoaaiiua ieii?u iao?eoe F1, F2 a yoii
neo/aa, i/aaeaeii, ?aaiu ae?oa ae?oao. Ei aoi?iio eeanno ioianai oa
ieii?u, eioi?ua niaea?aeao yeaiaiou e i-e e j-e no?ie. Yoe ieii?u o
iao?eoe F1, F2 aoaeoo niiaa ?aaiuie, oae eae aaee/eia ii?aaeaeeoaey ia
iaiyaony, anee e yeaiaioai iaeiie ec aai no?ie i?eaaaeythony aaee/eiu
i?iii?oeeiiaeueiua yeaiaioai eaeie-eeai ae?oaie no?iee. Iaeiiaoe, e
o?aoueaio eeanno iu ioianai ieii?u, niaea?aeauea yeaiaiou i-e no?iee e
ia niaea?aeauea yeaiaioia j-e no?iee. Niioaaonoaaiiua ieii?u yoiai
eeanna eiatho aeae:

…………. …………………………………

i1 = f io1 … f iok , i2 = f io1 + f jo1
? f(e) … f iok + f jok ? f(e) ,

…………. …………………………………

aaea iaauienaiiua no?iee o iaieo ieii?ia iaeeiaeiau. Ia iniiaaiee
oai?aiu neiaeaiey ii?aaeaeeoaeae

…………… ………………

i2 = f io1 … f iok + f(e) f jo1 ……… f jok
= i1 ± f(e)N1 ,

…………… ……………….

aaea N1 – iaeioi?ue ieii? iao?eoeu F1. Ana ieii?u e-ai ii?yaeea
iao?eoeu F1 aeaeyony e ia De1. Ec iaoeo ?annoaeaeaiee aeaeii, /oi ia
De1 aeaeyony e ana ieii?u e-ai ii?yaeea iao?eoeu F2, oae eae iie eeai
niaiaaeatho n niioaaonoaaiiuie ieii?aie iao?eoeu F1, eeai
au?aaeathony /a?ac ieo eeiaeii. Ii a oaeii neo/aa De1 aieaeao
iiiaeeoaeai a iaeaieueoee iauee aeaeeoaeue ieii?ia e-ai ii?yaeea
iao?eoeu F2, o.a. aieaeao iiiaeeoaeai a De2. Eoae, anee F2
iieo/aaony ec F1 iaeiei yeaiaioa?iui i?aia?aciaaieai, oi De2 aeaeeony
ia De1. Niaa?oay iaae F2 ia?aoiia yeaiaioa?iia i?aia?aciaaiea, iu
iieo/ei F1. Iiyoiio, De1 oaeaea aeieaeai aeaeeoueny ia De2. Ii anee
noa?oea eiyooeoeeaiou aeaoo iiiai/eaiia ?aaiu e yoe iiiai/eaiu aeaeyony
aac inoaoea ae?oa ia ae?oaa, oi iie niaiaaeatho. Oaeei ia?acii, De1 =
De2. Iiea aeieacaii ?aaainoai iaeaieueoeo iaueo aeaeeoaeae a
i?aaeiieiaeaiee, /oi F2 iieo/aaony ec F1 iaeiei yeaiaioa?iui
i?aia?aciaaieai. Iaeiaei anee De(e) нa iaiyaony i?e eaaeaeii
ioaeaeueiii yeaiaioa?iii i?aia?aciaaiee, oi, i/aaeaeii, De(e) нa
eciaieony e i?e ianeieueeeo iineaaeiaaoaeueiuo i?aia?aciaaieyo. Iioiio
oai?aia aeieacaia a iauai aeaea.

Au/eneei iiiai/eaiu D1(e), …, Dn(e) дey iao?eoeu, eiathuae eaiiie/aneee
aeeaaiiaeueiue aeae .

d1(e)

d2(e)

.

D = . .

.

dn(e)

*oiau iieo/eoue eaeie-ieaoaeue ieii? e-ai ii?yaeea, iu aeieaeiu ec D
au/a?eiooue n-k no?ie e n-k noieaoeia. Anee ec D au/a?eiooue i-th
no?ieo, oi a i-i noieaoea inoaioony oieueei ioee. Iiyoiio, /oiau
iieo/eoue ieii?, ioee/iue io ioey, iu aeieaeiu au/a?eiooue ana
noieaoeu iao?eoeu D, iiia?a eioi?uo ?aaiu iiia?ai au/a?eioouo no?ie.
Oaeei ia?acii, ioee/iua io ioey ieii?u e-e noaiaie aeieaeiu eiaoue aeae

do1(e)

do2 (e)

. = do1 (e) do2 (e) … dok(e). (1)

.

.

dok(e)

Iaeaieueoei iauei aeaeeoaeai yoeo ieii?ia aoaeao De(e). Иc ia?aaainoa
1 ? ?1 ? o2 ? … ? ok ? n neaaeoao, /oi 1 ? ?1, 2 ? o2, … , k ? ok.
Iiyoiio doi(e) дaeeony ia di(e), а cia/eo, do1(e) … dok(e) дaeeony ia
d1(e) … dk(e). Мu aeaeei, neaaeiaaoaeueii, /oi ana ieii?u e-ai ii?yaeea
iao?eoeu D aeaeyony ia ieii?

d1(e)

.

. = d1(e) … d k(e) (2)

.

dk(e)

Anee yoio ieii? ?aaai ioeth, oi e ana ieii?u e-ai ii?yaeea iao?eoeu D
oaeaea ?aaiu ioeth. Niaeanii ii?aaeaeaieth a yoii neo/aa De(e)=0. Еnee
ieii? (2) ioee/ai io ioey, oi iiiai/eaiu d1(e), …, d k(e) оoee/iu io
ioey e eiatho noa?oee eiyooeoeeaio 1. Ii oiaaea e ieii? (2) eiaao
noa?oee eiyooeoeeaio 1. Iineieueeo ana ieii?u (1) aeaeyony ia (2), oi
De(e) сiaiaaeaao n (2). Neaaeiaaoaeueii, a iaieo neo/ayo eiaai

De(e) = d1(e)d2(e)… d k(e) (к = 1, 2, …, n) (3)

Oaeiau iiiai/eaiu De(e) кaiiie/aneie aeeaaiiaeueiie iao?eoeu n
aeeaaiiaeueiuie yeaiaioaie d1(e), … , d n(e).

?anniio?ei oaia?ue i?iecaieueioth ?-iao?eoeo F. Iaicia/ei /a?ac De(e)
нaeaieueoee iauee aeaeeoaeue ieii?ia noaiaie e yoie iao?eoeu.
Niaeanii oai?aia 1. iao?eoeo F yeaiaioa?iuie i?aia?aciaaieyie iiaeii
i?eaanoe e eaiiie/aneie aeeaaiiaeueiie oi?ia

d1(e)

.

D = . .

.

dn(e)

Niaeanii oai?aia 1. iiiai/eaiu De(e), вu/eneaiiua aeey iao?eoeu D,
niaiaaeatho n niioaaonoaaiiuie iiiai/eaiaie De(e), вu/eneaiiuie aeey F.
Oaeei ia?acii, iiiai/eaiu De(e) мao?eoeu F e aeeaaiiaeueiua yeaiaiou
eaiiie/aneie aeeaaiiaeueiie iao?eoeu D, e eioi?ie iiaeii i?eaanoe F
naycaiu niioiioaieyie (3).

Ionoue D1(e), … , Dr(e) оoee/iu io ioey, a inoaeueiua iiiai/eaiu
Dr+1(e), … , Dn(e), еnee iie anoue, ?aaiu ioeth. Oiaaea ec (3) eiaai

D1(e) = d1(e), d1(e) = D1(e),

D2(e) = d1(e)d2(e), d2(e) = D2(e) : D1(e),

…………………. …………………….

Dr(e) = d1(e)d2(e) … dr(e), dr(e) = Dr(e) : Dr-1(e),

Dr+1(e) = d1(e)d2(e) … dr(e)dr+1(e), dr+1(e) = Dr+1(e) : Dr(e).

Iineieueeo dr+1(e)=0, oi dr+2(e), … , dn(e) тaeaea aeieaeiu auoue ?aaiu
ioeth, e iu eiaai ieii/aoaeueii

d1(e) = D1(e), d2(e) = D2(e) : D1(e), … , dr(e) = Dr(e) : Dr-1(e),

dr+1(e) = … = dn(e) = 0 (4)

Oai naiui iu iieo/eee neaaeothuoth oai?aio:

O a i ? a i a 3. Anee iaeaieueoea iauea aeaeeoaee De(e) мeii?ia
ii?yaeea e ?-iao?eoeu F i?e e=1, 2, … r ioee/iu io ioey, a Dr+1(e)=0,
тi aeeaaiiaeueiua yeaiaiou de(e) кaiiie/aneie aeeaaiiaeueiie iao?eoeu,
e eioi?ie F i?eaiaeeony yeaiaioa?iuie i?aia?aciaaieyie, au?aaeathony
/a?ac De(e) пi oi?ioeai (4) e ii?aaeaeythony, oaeei ia?acii, iao?eoeae
F iaeiicia/ii.

Iiiai/eaiu d1(e), … , dn(e) iacuaathony eiaa?eaioiuie iiiaeeoaeyie
iao?eoeu F. *enei r, a ?aaainoaao (4) yoi – ?aia iao?eoeu F.
Aeaenoaeoaeueii, ?aia iao?eoeu F anoue ii?yaeie iaeaunoaai ieii?a
F,ioee/iiai io ioey. Anee yoio ii?yaeie ?aaai r, oi, neaaeiaaoaeueii,
Dr(e)?0, a Dr+1(e)=0. Оa?aoii, oneiaey Dr(e)?0, Dr+1(e)=0 оcia/atho, /oi
iaeioi?ue ieii? ii?yaeea r ioee/ai io ioey, a ana ieii?u ii?yaeea r+1
?aaiu ioeth. Neaaeiaaoaeueii, ?aia F ?aaai r.

§4. Oneiaey yeaeaaeaioiinoe ?-iao?eoe.

Ia?aia oneiaea yeaeaaeaioiinoe. Aeey oiai /oiau iiiai/eaiiua iao?eoeu
ii?yaeea n auee yeaeaaeaioiu , iaiaoiaeeii e aeinoaoi/ii, /oiau
iaeaieueoea iauea aeaeeoaee eo ieii?ia e-ai ii?yaeea niaiaaeaee i?e
e=1, 2, … , n.

Iineieueeo niaiaaeaiea iaeaieueoeo iaueo aeaeeoaeae ieii?ia
?aaiineeueii niaiaaeaieth niioaaonoaothueo eiaa?eaioiuo iiiaeeoaeae,
oi ia?aia oneiaea yeaeaaeaioiinoe iiaeii noi?ioee?iaaoue e a
neaaeothuai aeaea: aeey yeaeaaeaioiinoe ?-iao?eoe iaiaoiaeeii e
aeinoaoi/ii, /oiau eo niioaaonoaothuea eiaa?eaioiua iiiaeeoaee auee
?aaiu.

Aeieacaoaeuenoai i/aaeaeii. A naiii aeaea, anee aeaa ?-iao?eoeu F, G
yeaeaaeaioiu, oi eo iaeaieueoea iauea aeaeeoaee De(e) оaeeiaeiau
(oai?aia 2). Ia?aoii, anee iiiai/eaiu De(e) у F e G ?aaiu, oi F e G
yeaiaioa?iuie i?aia?aciaaieyie i?eaiaeyony e iaeiie e oie aea
eaiiie/aneie aeeaaiiaeueiie iao?eoea (oai?aia 3). Ii aeaa iao?eoeu,
yeaeaaeaioiua o?aoueae yeaeaaeaioiu iaaeaeo niaie; neaaeiaaoaeueii, F
yeaeaaeaioia G, /oi e o?aaiaaeinue.

Aoi?ia oneiaea yeaeaaeaioiinoe. Aeey oiai /oiau iiiai/eaiiua iao?eoeu F
e G ii?yaeea n auee yeaeaaeaioiu, iaiaoiaeeii e aeinoaoi/ii, /oiau iie
oaeiaeaoai?yee niioiioaieth

G = PFQ,

aaea P, Q – iaeioi?ua iiiai/eaiiua iao?eoeu n iinoiyiiuie ioee/iuie io
ioey ii?aaeaeeoaeyie.

I?aaeaea /ai ia?aeoe e aeieacaoaeuenoao yoiai ooaa?aeaeaiey, naeaeaai
ianeieueei caia/aiee. Ionoue

1

.

.

.

1

A = ? i-y no?iea,

1

.

.

.

1

aaea ?- iaeioi?ia /enei, ioee/iia io ioey. Oiiiaeay i?iecaieueioth
iao?eoeo F ia A neaaa, iu oaeaeei, /oi ana yeaiaiou iao?eoeu F inoaioony
aac eciaiaiey, e?iia yeaiaioia i-e no?iee eioi?ua oiiiaeathony ia ?.
Oaeei ia?acii, eaaeaeia yeaiaioa?iia i?aia?aciaaiea oeia II,
niaa?oaaiia iaae iao?eoeae F, ?aaiineeueii oiiiaeaieth F ia
iiaeoiaeyuoth iao?eoeo A neaaa. Aiaeiae/ii, anee oiiiaeeoue iao?eoeo F
neaaa ia iao?eoeo

1… 0 … 0 … 0

0 …1… f(e)…0 i-y no?iea

A =

0… 0 … 1 … 0 j-y no?iea,

0 … 0 … 0 … 1

aaea ana aeeaaiiaeueiua yeaiaiou ?aaiu aaeeieoea, yeaiaio, noiyuee a
i-e no?iea e j-i noieaoea, ?aaai f(e), а inoaeueiua yeaiaiou ?aaiu
ioeth, oi a ?acoeueoaoa e yeaiaioai i-e no?iee F i?eaaayony yeaiaiou aa
j-e no?iee, oiiiaeaiiua ia f(e). Сeaaeiaaoaeueii, eaaeaeia yeaiaioa?iia
i?aia?aciaaiea oeia III ?aaiineeueii oiiiaeaieth F neaaa ia
niioaaonoaaiioth iao?eoeo A.

Iaeiiaoe, oai aea niiniaii eaaei oaaaeeoueny, /oi yeaiaioa?iua
i?aia?aciaaiey iao?eoeu F oeia II, III noieaoeia ?aaiineeueiu
oiiiaeaieth F ia niioaaonoaaiiua iao?eoeu A, A ni?aaa.

Ia?aeaeai oaia?ue e aeieacaoaeuenoao aoi?iai oneiaey yeaeaaeaioiinoe.

Iaiaoiaeeiinoue. Ionoue iao?eoea G yeaeaaeaioia iao?eoea F. Yoi
icia/aao, /oi G iiaeao auoue iieo/aia ec F oeaii/eie iineaaeiaaoaeueiuo
yeaiaioa?iuo i?aia?aciaaiee. Eaaeaeia yeaiaioa?iia i?aia?aciaaiea iu
iiaeai caiaieoue oiiiaeaieai ia iao?eoeo aeaea A eee A niioaaonoaaiii
neaaa eee ni?aaa. A ?acoeueoaoa iieo/ei ?aaainoai

G = P1P2 … Pp FQ1Q2 … Qq, (5)

aaea eaaeaeay ec iao?eoe Pi , Qj eiaao aeae A eee A (i, j = 1, 2, …).

Iieiaeei ? = P1P2 … Pp , Q = Q1Q2 … Qq.

Iineieueeo ii?aaeaeeoaee iao?eoe A ?aaiu aaeeieoea, a ii?aaeaeeoaee
iao?eoe A yaeythony iinoiyiiuie, ioee/iuie io ioey /eneaie oi
ii?aaeaeeoaee iao?eoe P e Q aoaeoo oaeaea iinoiyiiuie, ioee/iuie io ioey
/eneaie. Niioiioaiea (5) aeaao

G = PFQ,

e iaiaoiaeeiinoue aeieacaia.

Aeinoaoi/iinoue. Aeiionoei ia?aoii, /oi

G = PFQ, (6)

aaea P e Q – iiiai/eaiiua iao?eoeu n iinoiyiiuie, ioee/iuie io ioey
ii?aaeaeeoaeyie. Iaeaieueoee iauee aeaeeoaeue Dn(e) вnao ieii?ia
ii?yaeea n iao?eoeu ? ?aaai ii?aaeaeeoaeth ?, aeaeaiiiio ia aai noa?oee
eiyooeoeeaio. Oae eae yoio ii?aaeaeeoaeue anoue iinoiyiiia /enei, oi
Dn(e)=1. Иc niioiioaiey (3) ia?aa?aoa 3 i?e e=n iieo/aai

Dn(e) = d1(e)d2(e) … dn(e) = 1,

ioeoaea d1(e) = d2(e) = … = dn(e) = 1,

aaea d1(e), … dn(e) – иiaa?eaioiua iiiaeeoaee iao?eoeu ?. Ii
eiaa?eaioiua iiiaeeoaee aaeeie/iie iao?eoeu E oaeaea ana ?aaiu
aaeeieoea, eai A eiaao eaiiie/aneee aeeaaiiaeueiue aeae. Niaeanii
ia?aiio i?eciaeo yeaeaaeaioiinoe ionthaea neaaeoao, /oi iao?eoea ?
yeaeaaeaioia A e, cia/eo, iiaeao auoue iieo/aia ec A oeaii/eie
yeaiaioa?iuo i?aia?aciaaiee. Eaaeaeia yeaiaioa?iia i?aia?aciaaiea
iiaeii caiaieoue oiiiaeaieai ia iao?eoeo oeia A eee A. A ?acoeueoaoa ?
aoaeao i?aaenoaaeaia neaaeothuei ia?acii:

? = P1 … Pe A Q1 … Q? = P1 … Pe Q1 … Q?

aaea Pi, Qj – iao?eoeu oeiia A, A.

I?eiaiyy oa aea naiua ?annoaeaeaiey e iao?eoea Q, iieo/ei aiaeiae/iia
?aceiaeaiea

Q = M1 … MsN1 …Nt.

Iiaenoaaeyy yoe ?aceiaeaiey a (6) i?eaeai e ?aaainoao

G = P1 … Pe Q1 … Q?FM1 … MsN1 …Nt, (7)

Ec eioi?iai aeaeii, /oi G iieo/aaony iineaaeiaaoaeueiui oiiiaeaieai
iao?eoeu F ia iao?eoeu Pi, Qi , Mi, Ni oeia A eee A. Ii eaaeaeia
oaeia oiiiaeaiea ?aaiineeueii iaeioi?iio yeaiaioa?iiio
i?aia?aciaaieth. Neaaeiaaoaeueii, G yeaeaaeaioia F, e aeieacaoaeuenoai
caeii/aii.

§5. Yeaiaioa?iua aeaeeoaee iiiai/eaiiie iao?eoeu.

?anniio?ei i?iecaieueioth ?-iao?eoeo F, yeaiaioaie eioi?ie yaeythony
iiiai/eaiu io ? n eiyooeoeeaioaie ec iniiaiiai iiey E. Iaicia/ei /a?ac
d1(e), d2(e), … , dn(e) иiaa?eaioiua iiiaeeoaee iao?eoeu F. *anoue yoeo
iiiaeeoaeae iiaeao ?aaiyoueny ioeth, iiyoiio i?aaeiieiaeei aeey
ii?aaeaeaiiinoe, /oi d1(e), …, dr(e) нoeth ia ?aaiu, a dr+1(e)= …=dn(e)=
0. Чenei r, anoue ?aia iao?eoeu F. ?aceiaeei eaaeaeue ec iiiai/eaiia
d1(e), …, dr(e) нa iiiaeeoaee, iai?eaiaeeiua a iiea E.
Ionoue, iai?eia?, di(e) = [a1(e)]?? [?2(e)]?? … [ak(e)]?k , aaea a1(e),
…, ak(e) -?acee/iua iai?eaiaeeiua iiiai/eaiu ni noa?oei eiyooeoeeaioii
1. Au?aaeaiey [a1(e)]??, …, [?k(e)]?k ,iacuaathony yeaiaioa?iuie
aeaeeoaeyie eiaa?eaioiiai iiiaeeoaey di(e). Эeaiaioa?iua aeaeeoaee anao
iaiinoiyiiuo eiaa?eaioiuo iiiaeeoaeae iao?eoeu F iacuaathony aa
yeaiaioa?iuie aeaeeoaeyie. Iai?eia?, anee eiaa?eaioiua iiiaeeoaee
iao?eoeu F ?aaiu niioaaonoaaiii 1, ?, e?(e+1), e?(e+1)?, тi yeaiaioa?iua
aeaeeoaee aoaeoo ?, e?, e?, e+1, (e+1)?. Эeaiaioa?iue aeaeeoaeue aeaea
[a(e)]k, aaea ?(e) нai?eaiaeeiue iiiai/eai, iacuaatho i?eiaaeeaaeauei
iiiai/eaio a(e). В ?anniio?aiiii i?eia?a yeaiaioa?iua aeaeeoaee ??, e?,
e?п?eiaaeeaaeao ?, a ?+1 e (?+1)? п?eiaaeeaaeao ?+1.

O a i ? a i a 4. Ii?yaeie, ?aia e nenoaia yeaiaioa?iuo aeaeeoaeae
?-iao?eoeu F aiieia ii?aaeaeytho aa eiaa?eaioiua iiiaeeoaee e,
neaaeiaaoaeueii, ii?aaeaeytho F n oi/iinoueth aei yeaeaaeaioiinoe.

Aeieacaoaeuenoai eaaei oyniyaony ec neaaeothuaai i?eia?a. Ionoue
ii?yaeie F ?aaai 6, ?aia 4, yeaiaioa?iua aeaeeoaee ?, e?, e?, e+1,
(e+1)?, e-1, e-1. Пineieueeo ii?yaeie F anoue 6, oi F eiaao oanoue
eiaa?eaioiuo iiiaeeoaeae d1(e), …, d6(e). Иc ieo d5(e) = d6(e) = 0,
тae eae ?aia F aeieaeai auoue 4. Anee ?aceiaeeoue d1(e), …, d4(e) нa
iiiaeeoaee, oi aeieaeiu iieo/eoueny oeacaiiua naiue yeaiaioa?iuo
aeaeeoaeae. Iineieueeo, iaeiaei, d4(e) дaeeony ia d3(e), d2(e) и d1(e),
oi a d4(e) вoiaeyo yeaiaioa?iua aeaeeoaee, i?eiaaeeaaeauea ei anai
iai?eaiaeeiui iiiai/eaiai, e i?eoii a aunoeo noaiaiyo. Iiyoiio d4(e) =
e?(e+1)?(e-1). С?aaee inoaaoeony yeaiaioa?iuo aeaeeoaeae ?, e?, e+1,
e-1 вunoea aeieaeiu aieoe a d3(e); сeaaeiaaoaeueii, d3(e) =
e?(e+1)(e-1). В naith i/a?aaeue aunoea ec inoaaoeony aeieaeiu
ninoaaeoue d2(e), т.a. d2(e)=e. Пineieueeo ana yeaiaioa?iua aeaeeoaee
oaea ?ani?aaeaeaiu, oi d1(e)=1. Яnii, /oi yoio niinia i?eiaiei a
ethaii neo/aa, /oi e aeieacuaaao oai?aio.

Yeaiaioa?iua aeaeeoaee caaenyo io iniiaiiai iiey E. Iai?eia?, ionoue
eiaa?eaioiua iiiaeeoaee iaeioi?ie ?-iao?eoeu F ?aaiu ??+1, (e?+1)?. Еnee
iniiaiia iiea anoue iiea aauanoaaiiuo /enae, oi iiiai/eai ??+1
нai?eaiaeei e yeaiaioa?iuie aeaeeoaeyie iao?eoeu F yaeythony ??+1 e
(??+1)?. Оaeiaei, anee iniiaiia iiea – iiea anao eiiieaeniuo /enae, oi
??+1= (e – i)(e + i) e yeaiaioa?iuie aeaeeoaeyie F aoaeoo e+i, (e+i)?,
e-i, (e-i)?.

*oiau iieo/eoue yeaiaioa?iua aeaeeoaee ?-iao?eoeu, eiathuae
eaiiie/aneoth aeeaaiiaeueioth oi?io, aeinoaoi/ii acyoue, niaeanii
ii?aaeaeaieth, ana yeaiaioa?iua aeaeeoaee aa aeeaaiiaeueiuo yeaiaioia.
Yoi aea i?aaeei eiaao ianoi e aeey i?iecaieueiie aeeaaiiaeueiie
?-iao?eoeu.

Eaiia. Nenoaia yeaiaioa?iuo aeaeeoaeae i?iecaieueiie aeeaaiiaeueiie
?-iao?eoeu F anoue iauaaeeiaiea yeaiaioa?iuo aeaeeoaeae aa
aeeaaiiaeueiuo yeaiaioia.

I?eia?u:

1) Iaeaeai yeaiaioa?iua aeaeeoaee -iao?eoeu

1 0 0 0

0 2+2 0 0

A() = 0 0 (4-4)2 0

0 0 0 0

iaae iieyie ?aoeeiiaeueiuo, aeaenoaeoaeueiuo e eiiieaeniuo /enae.
Iao?eoea A() eiaao eaiiie/aneoth oi?io. Iiyoiio ia aa aeaaiie
aeeaaiiaee noiyo eiaa?eaioiua iiiaeeoaee A1()=1, A2()=2+2, A3()=(4-4)2,
A4()=0.

?aceaaay A2() e A3() ia iai?eaiaeeiua iiiaeeoaee iaae eaaeaeui ec
oeacaiiuo iieae, iieo/ei nenoaiu yeaiaioa?iuo aeaeeoaeae:

1. iaae iieai ?aoeeiiaeueiuo /enae:

a1()=2+2, a2()=(2+2)2, a3()=(2-2)2 ;

2. iaae iieai aeaenoaeoaeueiuo /enae:

a1()=2+2, a2()=(2+2)2, a3()=(+2)2, a4()=(-2)2 ;

3. iaae iieai eiiieaeniuo /enae

a1()=+2i, a2()=-2i, a3()=(+2i)2, a4()=(-2i)2,

a5()=(+2)2, a6()=(-2)2 .

2) Iaeoe eiaa?eaioiua iiiaeeoaee -iao?eoeu A() ?acia?ia 6o8 e ?aiaa 5,
anee aeaiu aa yeaiaioa?iua aeaeeoaee +1, +1, (+1)3, (-1)2, (-1)2.

Oae eae /enei anao eiaa?eaioiuo iiiaeeoaeae ?aaii iaiueoaio ec
?acia?ia iao?eoeu, o.a. 6, a /enei eiaa?eaioiuo iiiaeeoaeae, ioee/iuo io
ioey, ?aaii ?aiao, o.a. 5, oi A6()=0. Aeaeaa A5()= (+1)3(-1)2,
A4()=(+1)(-1)2, A3 ()=+1.

Oae eae iu oaea eniieueciaaee ana yeaiaioa?iua aeaeeoaee, oi ae?oaeo
eiaa?eaioiuo iiiaeeoaeae iieiaeeoaeueiie noaiaie ia iiaeao auoue.
Iiyoiio A2()= A1()=1.

3) Iaeoe eaiiie/aneoth oi?io aeeaaiiaeueiie -iao?eoeu
A()=2, 0, 2+, 2-1, 4-2. Caeanue ii?yaeie iao?eoeu ?aaai 5, a
?aia ?aaai 4. Iiyoiio A5() =0. Yeaiaioa?iua aeaeeoaee aeeaaiiaeueiuo
yeaiaioia:

2, , +1, +1, -1, 2, +1, -1.

Cia/eo,

A4()= 2(+1)( -1)= 4-2, A3()= 2(+1)( -1)= 4-2,

A2()= (+1)= 2+, A1()=1.

Eaiiie/aneay oi?ia eiaao aeae 1, 2+, 4-2, 4-2, 0.

Aeaaa II. Iao?e/iua iiiai/eaiu.

§1. Aeaeaiea iao?e/iuo iiiai/eaiia. Iaiauaiiay oai?aia Aaco.

Iao?e/iui iiiai/eaiii io ia?aiaiiie iacuaaaony au?aaeaiea aeaea

F(e) = Аi em + A1 em-1 + A2 em-2 + … + Am , (1)

aaea Ai, …, Am – eaaae?aoiua iao?eoeu iaeiiai e oiai aea ii?yaeea n
yeaiaioaie ec iniiaiiai iiey E. *enei m iacuaaaony noaiaiueth
iiiai/eaia, anee Ai?0. Aeaa iiiai/eaia iacuaathony ?aaiuie, anee ?aaiu
iao?eoeu, noiyuea a yoeo iiiai/eaiao i?e iaeeiaeiauo noaiaiyo
ia?aiaiiie ?. Neeaaeuaathony e ia?aiiiaeathony iao?e/iua ?-iiiai/eaiu
ii iau/iui i?aaeeai. ssnii, /oi eaaeaeue ?-iiiai/eai iiaeii caienaoue a
aeaea iaeiie iao?eoeu, yeaiaioaie eioi?ie yaeythony iaueiiaaiiua
iiiai/eaiu io ??, e ia?aoii. Iai?eia?,

1 2 + 5 6 e + 1 0 e? = e? +5e + 1 6+ 2

0 3 7 -2 0 1 7e e?-2e + 3 .

Iiyoiio iao?e/iua ?-iiiai/eaiu yaeythony eeoue iniaui aeaeii caiene
?-iao?eoe .

Iiiai/eai F(e) нacuaaaony ?aaoey?iui, anee iao?eoea Ai ia?aoeia.

Noiia (?aciinoue) aeaoo iao?e/iuo iiiai/eaiia iaeiiai e oiai aea
ii?yaeea iiaeao auoue i?aaenoaaeaia a aeaea iiiai/eaia, noaiaiue
eioi?iai ia i?aainoiaeeo iaeaieueoae ec noaiaiae aeaiiuo iiiai/eaiia.

I?iecaaaeaiea aeaoo iao?e/iuo iiiai/eaiia ?aaii iiiai/eaio, noaiaiue
eioi?iai iaiueoa eee ?aaia noiia noaiaiae niiiiaeeoaeae. Anee oioy
au iaeei eo aeaoo niiiiaeeoaeae ?aaoey?iue iiiai/eai, oi a yoii neo/aa
noaiaiue i?iecaaaeaiey anaaaea ?aaia noiia noaiaiae niiiiaeeoaeae.

Ionoue aeaiu aeaa iao?e/iuo iiiai/eaia A(e) и A(e) iaeiiai e oiai aea
ii?yaeea n, i?e/ai A(e) – рaaoey?iue iiiai/eai:

A(e) = Аiem + A1em-1 + … + Am (Ai?0),

A(e) = Вie? + A1e?-1 + … + A? (|Ai|?0).

Aoaeai aiai?eoue, /oi iao?e/iua iiiai/eaiu Q(e) e R(e) яaeythony
niioaaonoaaiii i?aaui /anoiui e i?aaui inoaoeii i?e aeaeaiee A(e) нa
A(e), еnee

A(e) = Q(e)В(e) + R(e) (2)

e noaiaiue R(e) мaiueoa noaiaie A(e).

Niaa?oaiii aiaeiae/ii aoaeai iacuaaoue iiiai/eaiu ^Q(e) и ^R(e)
niioaaonoaaiii eaaui /anoiui e eaaui inoaoeii i?e aeaeaiee A(e) нa
A(e), еnee

A(e) = A(e) ^Q(e) + ^R(e) (3)

e noaiaiue ^R(e) мaiueoa noaiaie A(e).

A iauai neo/aa iiiai/eaiu Q(e) e R(e) нa niaiaaeatho n ^Q(e) e ^R(e).

Iieaaeai, /oi eae i?aaia, oae e eaaia aeaeaiea iao?e/iuo iiiai/eaiia
iaeiiai e oiai aea ii?yaeea anaaaea auiieieii e iaeiicia/ii, anee
aeaeeoaeue – ?aaoey?iue iiiai/eai.

?anniio?ei i?aaia aeaeaiea A(e) ia A(e). Еnee m

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