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π
n−1
( ) P Q π
n−1
[P Q] π
n−1
: [P Q]∩π
n−1
= ∅
P Q
π
n−1
π
n−1
⊂ A
n
f : A
n
→ R f(M) = b
1
x
1
M
+ . . . + b
n
x
n
M
+ b
n+1
P Q π
n−1
sgn(f(P )) = sgn(f(Q))
f(M)
π
m
π
0
k
A
n
π
m
∩ π
0
k
6= ∅
π
m
= {M
0
, L
m
} π
0
k
= {M
0
0
, L
0
k
}
A
n
π
m
∩ π
0
k
3 A
π
m
∩ π
0
k
= {A, L
m
∩ L
0
k
}
B ∈ π
m
∩ π
0
k
⇐⇒
−→
AB ∈ L
m
, L
0
k
⇐⇒
−→
AB ∈ L
m
∩ L
0
k
π
m
= {M
0
, L
m
} π
0
k
= {M
0
0
, L
0
k
}
r = r
0
+ t
α
a
α
α = 1, . . . , m r =
r
0
0
+ u
a
b
a
a = 1, . . . , k M ∈ π
m
∩π
0
k
{t
α
} {u
a
} r
0
+ t
α
a
α
= r
0
0
+ u
a
b
a
M
t
α
a
α
− u
a
b
a
= r
0
0
− r
0
Á-3:26A BAB-D87/8 751* 151 0 B /62)5* 50,,AC .3-/735/7B :5 6AC 35E:*3,-/7* /:< Ȉ / < º< VWXYZY[Y\]Y^ }hi njbj xaemfeoghvghi π Ä}nmd xgkgfaiw sig nkm (fjloasbcm) igsva P a Q omyji eg gnb} higfgb} n−1 gi πn−1 w mhoa gip fmlgv [P Q] bm hgnmfyai igsmvw efabjnomyjqar πn−1 : [P Q]∩πn−1 = ∅ ¹ efgiakbgd ho}sjm xgkgfadw sig igsva P a Q omyji eg fjlbcm higfgbc gi πn−1 ªZ« ^ 2/7> 90.*3.6-/1-/7> π ⊂ A 0:**7 235B,*,0* º< .3* D*60: 2,1½0 f : An → R -3:26- f (M ) = b1x1M + . . . + bnxnM + bn+1 < n−1 n -15E57> )7- 7-)10 P 0 Q 6*57 .- -D,2 /7-3-,2 -7 πn−1 7-9D5 0 7-6>1- 7-9D5 1-9D5 sgn(f (P )) = sgn(f (Q)) < 510: -+35E-: 2 90.*3.6-/1-/70 B 50,,-: .3-/735,/7B* 0:**7/8 DB* /7-3-,A~ .- -D,2 /7-3-,2 90.*3.6-/ 1-/70 2,1½08 f (M ) .30,0:5*7 .-6-07*6>,A* E,5)*,08 5 .- D3292 F -730½57*6>,A* < ^µ Ť]\Y XW[¡Y\]Y W[Y° ]\\ WXX\Y^ 2/7> E5D5,A DB* .6-/1-/70 πm 0 πk0 B 50,,-/ .3-/735,/7B* An < 5/ /:-730: B-E:-,A* /62)50 0C BE50:,-9- 35/.-6-*,08 < ^ π ∩ π0 6= ∅ < XYZ[¡Y\]Y^ Æhoa eoghvghia πm = {M0, Lm} a πk0 = {M00 , L0k } k efgp m k hifjbhikm An adm{i bme}higm emfmhmsmbamw ig gba emfmhmvj{iht eg eoghvghia _ admbbgw mhoa πm ∩ πk0 3 A w ig πm ∩ πk0 = {A, Lm ∩ L0k } £¤Y[¥^ */7B07*6>,- B ∈ π ∩ π0 ⇐⇒ − → AB ∈ Lm , L0k ⇐⇒ m k AB ∈ Lm ∩ L0k < −→ 2/7> .6-/1-/70 πm = {M0, Lm} 0 πk0 = {M00 , L0k } E5D5,A /--7B*7/7B*, ,- .535:*730)*/10:0 235B,*,08:0 r = r0 + tαaα α = 1, . . . , m 0 r = ) r00 + ua ba a = 1, . . . , k < 5D02/ B*17-3 B/81- 7- 10 M ∈ πm ∩ πk0 0:**7 DB5 ,5+-35 B,273*,,0C 1--3D0,57 {tα} 0 {ua} < 30 ¨7-: r0 + tαaα = r00 + uaba < 7/D5 /6*D2*7 )7- B,273*,,0* 1--3D0,57A 7-)10 M 2D-B6*7B-387 B*1 7-3,-:2 235B,*,0 α tα a − ua b = r0 − r a 0 0 G Ç
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