evalEval — Mathlib

English

Same as previous: aeval (C x) p = mapAlgHom (aeval x) (swap p).

Русский

То же самое: aeval(C x) p = mapAlgHom(aeval x)(swap p).

LaTeX

$$$\\mathrm{aeval}(\\mathrm{C}\\;x)\\; p = \\mathrm{mapAlgHom}(\\mathrm{aeval}(x))\\Bigl(\\mathrm{swap}(p)\\Bigr).$$$

Lean4

/-- If the evaluation (`evalEval`) of a bivariate polynomial `p : R[X][Y]` at a point (x,y)
is zero, then `Polynomial.evalEval x y` factors through `AdjoinRoot.evalEval`, a ring homomorphism
from `AdjoinRoot p` to `R`. -/
@[simps!]
noncomputable def evalEval : AdjoinRoot p →+* R :=
  lift (evalRingHom x) y <| eval₂_evalRingHom x ▸ h

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