Theorems · Definition · commutative algebra
MvPolynomial.optionEquivRight
(R : Type u) → (S₁ : Type v) → [inst : CommSemiring R] → MvPolynomial (Option S₁) R ≃ₐ[R] MvPolynomial S₁ (Polynomial R)
The algebra isomorphism between multivariable polynomials in Option S₁ and
multivariable polynomials with coefficients in polynomials.
- Defined in
- Mathlib.Algebra.MvPolynomial.Equiv
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- AlgEquivstatement · cited by 1,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.aevalproof · cited by 615
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.Cproof · cited by 400
- MvPolynomial.aevalproof · cited by 298
- AlgEquiv.ofAlgHomproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.optionEquivRight_applystatement and proof · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- MvPolynomial.optionEquivRight_symm_applystatement and proof · cited by 2
- RingHom.FinitePresentation.polynomial_inductionproof · cited by 1
- MvPolynomial.optionEquivRight_Cstatement · cited by 0
- MvPolynomial.optionEquivRight_X_nonestatement · cited by 0
- MvPolynomial.optionEquivRight_X_somestatement · cited by 0