Theorems · Theorem · field theory

Polynomial.aeval_add_of_sq_eq_zero

∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Polynomial R)
  (x y : S),
  y ^ 2 = 0 → (Polynomial.aeval (x + y)) p = (Polynomial.aeval x) p + (Polynomial.aeval x) (Polynomial.derivative p) * y

Defined in

Mathlib.Algebra.Polynomial.Taylor

Cited by

1 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommRingAlgebra