invariants de similitude Exercice 1 : Exercice 2 :

k V k n f
V Vfk[X]
∀P∈k[X],∀v∈V, P.v =P(f)(v)
Vfk[X]
Vfk V
f
Vfs
µi1≤i≤s(i≤j⇒µi|µj)
k[X]φ Vfk[X]/(µ1)×... ×k[X]/(µs)
g V k[X]Vg
Vff g
s s (µ1, ..., µs)
f
f
(u1, ..., us)k[X]/(µ1)×... ×k[X]/(µs)
1≤i≤s wi=φ−1(ui)EiV
(fj(wi), j ∈N)EiV
f diµiµi
f|Eif Ei
f|Ei(wi, f(wi), ..., fdi−1(wi)) Ei
f
f
f
f k V
XI −M M
f V

k⊂L M1M2Mn(k)
M1M2k L
Q6
(X−2)5
Q6
(X−1)3(X−2)2(X−3)
M=
308
3−1 6
−2 0 −5
XI −M
fR3M
(e1, e2, e3)R3R[X]R3
f
f
M=
1 4 −2
0 6 −3
−1 4 0
XI −M
fR3M
(e1, e2, e3)R3R[X]R3
f
f