AlgebraicIndepOn — Mathlib

English

Definition of the isomorphism between mvPolynomial (Option ι) and Polynomial over the algebra generated by the x-family.

Русский

Определение изоморфизма между mvPolynomial(Option ι) и Polynomial над порожденной алгеброй семейством x.

LaTeX

$$Definition: mvPolynomialOptionEquivPolynomialAdjoin (hx) : MvPolynomial (Option ι) R ≃+* Polynomial (adjoin R (Set.range x))$$

Lean4

/-- `AlgebraicIndepOn R v s` states that the elements in the family `v` that are indexed by the
elements of `s` are algebraically independent over `R`. -/
abbrev AlgebraicIndepOn (s : Set ι) : Prop :=
  AlgebraicIndependent R fun i : s ↦ x i

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