IP 8.5.17 [8]

Levine : In S ,T=R .

"

,151

,ltkb

,

8%; ( s +

Itt) ) = courts ) + ccaectl

.

Deus : IEI : In 7,20 ( ses ),

-21=1,-

Ms ,ein ( sestet ) gih

[31 ' ( s t.EM.it)= Ears + FEET Asysit

⇒and "12 Estel 't

70

÷ue ( T )

"z":_ Seen Asao ( SES ),

-22=1,

µ7 octet )

" In . Seen As 20 ( SES ),

-22=1,

M€70( tet )

• She M ÷ 1 + Eta E IN ' to } und

E := At, yz

= he 70 ( tet )

go := I - Epic 70TET

[ kouueuauuhmeu : OIET ]

• To := Tv { 04

. Daun gilt :

signs's +IETET = fats 's t⇐EpIE

ExelIs E. bye ( st E)

getISIAH

E can (S + AYCH ),

• EsE⇐otsf = (Efiskfethknin

Benes In Sak 2.6-

• Kor.

2.2 ⇒ Pnz"

= It AT ( y )wr I ,yez

"

, 1×4,151 < is und

k( FUF ) polynomial besdm.lt in kltibl,

cane (F) = char ( P )

. Lemma 2. T ⇒ P±= our (E) + came (5)

. Es gin also DEQPM,

d c- QP wl :

End- Cour ( E) + comet ) = P< ( DM )

.I

- Tells P±*0 ,Iclear ( P± ) = cone ( y ) = darcp )

- k ( D ,d) polynomial be ] date in

KIEL ,also in kltibl .

A

Exhnvsisekuooupolgedrudefiuh.atCine Talmage FEPER

"

ewes

Polgudrs P is ein Sile ( face ) von P,

falls F=0 ist odr a e R"

PERetistiven wl

• ( a ,× ) H qiehj for P

. F= 1 × EP : ( air ) 71a it

%HP/±¥-⇐⇐I. :"

Dewknyense. P = car ( X ) + candy ) =P

'CA

, b)ml X

,Y e R

"

,1×1,41<0 ,

AERM"

,bfRYse . F line fih von P

.

.F Polydor ,

Sita oou F find fekuoou P

. F = car ( Xn F) + cane ( Yn dear (F) )

• Mit EQC F) := { iced : ( A ;, ,x)=b ;

txet )

("

equation set"

von F bye . Air )ist F= { XEP : Aeg # , ,*i×=b¥⇐ , }Halls Ft0 )

.

• In alle I c- [m] :

the P : At,*

. ×=b± } fih won P

• P hat um eadlih nil fetus

• F"

minimal Seiki-

we P,

leu F

iuhlntiouwinwal unh den wilt - later

Sita von P it.

( job uiht - leen Set euthelt ein

win. male fete )

• lineal ( P ) := { ZER"

: xt At EP txep,

# }

a✓ C P )

= keru ( A)

÷ ( A. 0 )

•

Inhalefik von P :

- the Et : F= Ft lineup )

- F= { xe Di: Aeqt, ,*ix= begets )

• P"

spit"

,van Pto und lineal ( M=l a)

↳ Minimal film rid enpuuhlg:

"

Eaten"

( Bsp .: Polytope = besdiehhh Polgab

find spih ,beuu we will leer hid )

• ve P is Coke a P ⇐

vet can ( P , H ) ⇐

v it will kouuthoulineton cos zwiAndrea Puahkn Aes P

.