aevalDifferential_single — Mathlib

English

Invariants of HasCoeffs are preserved under the quotient by the relation ideal.

Русский

И invariants HasCoeffs сохраняются при проходе к частному по образу отношения.

LaTeX

$$$\\mathrm{Quotient} \\ (\\mathrm{Ideal.span} \\mathrm{(range}(P.\\mathrmrelationOfHasCoeffs)))$ preserves invariants$$

Lean4

@[simp]
theorem aevalDifferential_single [DecidableEq σ] (i j : σ) :
    P.aevalDifferential (Pi.single i 1) j = aeval P.val (pderiv (P.map j) (P.relation i)) :=
  by
  dsimp only [aevalDifferential]
  rw [← Pi.basisFun_apply, Basis.constr_basis]

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