commAlgEquiv_C — Mathlib

English

The commAlgEquiv is the algebraic equivalence that enumerates the symmetry between S1 and S2 in the two-variable mv-polynomial setting.

Русский

Комм-эквивалентность описывает симметрию между S1 и S2 в двухтипных mv-многочленах.

LaTeX

$$$\text{commAlgEquiv}\; R\; S_1\; S_2 : MvPolynomial S_1 (MvPolynomial S_2 R) \simeq_{R} MvPolynomial S_2 (MvPolynomial S_1 R)$$$

Lean4

@[simp]
theorem commAlgEquiv_C (p) : commAlgEquiv R S₁ S₂ (.C p) = .map C p :=
  by
  suffices
    (commAlgEquiv R S₁ S₂).toAlgHom.comp (IsScalarTower.toAlgHom R (MvPolynomial S₂ R) _) = mapAlgHom (Algebra.ofId _ _)
    by exact DFunLike.congr_fun this p
  ext x : 1
  simp [commAlgEquiv]

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