Theorems · Theorem · dynamical systems

Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotent

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {P : Polynomial R}
  {x : S}, IsNilpotent ((Polynomial.aeval x) P) → ∀ (n : ℕ), IsNilpotent (P.newtonMap^[n] x - x)

Defined in

Mathlib.Dynamics.Newton

Cited by

2 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra