Theorems · Definition · field theory

Polynomial.aevalAeval

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring A] → [inst_2 : Algebra R A] → A → A → Polynomial (Polynomial R) →ₐ[R] A

Given valuations x and y of the variables in an R-algebra A, aevalAeval x y is the unique R-algebra homomorphism from R[X][Y] to A sending X to x and Y to y.

Defined in

Mathlib.Algebra.Polynomial.Bivariate

Cited by

13 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAlgebra