eval₂AddMonoidHom — Mathlib

English

Evaluation commutes with finite sums of polynomials: ev(p.sum g) equals the sum of ev(p) evaluated at each g(i).

Русский

Оценка commute с конечной суммой полиномов: eval(p.sum g) даёт сумму eval(p) для каждого g(i).

LaTeX

$$$\operatorname{ev}_{f,x}\bigl(p.sum g\bigr) = \sum_i \operatorname{ev}_{f,x}\bigl(g(i)\bigr)$$$

Lean4

/-- `eval₂AddMonoidHom (f : R →+* S) (x : S)` is the `AddMonoidHom` from
`R[X]` to `S` obtained by evaluating the pushforward of `p` along `f` at `x`. -/
@[simps]
def eval₂AddMonoidHom : R[X] →+ S where
  toFun := eval₂ f x
  map_zero' := eval₂_zero _ _
  map_add' _ _ := eval₂_add _ _

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