Algèbre Polynômes

K=R C K[X]
KP, Q ∈
K[X]
Pdeg P
P
P+Q P Q
P(Q(X))
P Q
P Q
P Q
P
P
P Q
P=Q
k(x1, . . . , xk),(y1,...yk)∈
Kkxj
L k −1j1k
L(xj) = yj
a b ab = 12 a+b= 5√2
P P 0
n P (n)n∈N

K=R
(P+Q)0(P Q)0
(P+Q)(n)(P Q)(n)
P0
P
P
P Q
PGCD PPCM P Q
PGCD(X3−1, X3−3X2+ 3X−1)
X3−1X3−3X2+ 3X−1
C[X]R[X]
C[X]R[X]
K[X]
R[X]K[X]