algEquivOfAssociated — Mathlib

English

If f and g are equal, algEquivOfEq f g hfg is the identity via algHomOfDvd.

Русский

Если f = g, то эллиптично через algEquivOfEq получается тождественный переход через algHomOfDvd.

LaTeX

$$algEquivOfEq f g hfg = identity via algHomOfDvd$$

Lean4

/-- The canonical algebraic equivalence between `AdjoinRoot p` and `AdjoinRoot g`,
where the two polynomials `f g : R[X]` are associated. -/
noncomputable def algEquivOfAssociated (f g : R[X]) (hfg : Associated f g) : AdjoinRoot f ≃ₐ[R] AdjoinRoot g :=
  .ofAlgHom (algHomOfDvd f g hfg.symm.dvd) (algHomOfDvd g f hfg.dvd) (by ext; simp) (by ext; simp)

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