Theorems · Definition · commutative algebra
MvPolynomial.optionEquivLeft
(R : Type u) → (S₁ : Type v) → [inst : CommSemiring R] → MvPolynomial (Option S₁) R ≃ₐ[R] Polynomial (MvPolynomial S₁ R)
The algebra isomorphism between multivariable polynomials in Option S₁ and
polynomials with coefficients in MvPolynomial S₁ R.
- Defined in
- Mathlib.Algebra.MvPolynomial.Equiv
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 109 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.Cproof · cited by 1,598
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.aevalproof · cited by 298
- MvPolynomial.renameproof · cited by 168
- Polynomial.aevalTowerproof · cited by 14
Cited by39
Results whose statement or proof uses this declaration.
- MvPolynomial.finSuccEquivproof · cited by 22
- MvPolynomial.optionEquivLeft_applystatement and proof · cited by 7
- MvPolynomial.optionEquivLeft_coeff_some_coeff_nonestatement and proof · cited by 7
- AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoinproof · cited by 7
- MvPolynomial.toPolynomialAdjoinImageComplproof · cited by 5
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- MvPolynomial.optionEquivLeft_X_nonestatement · cited by 3
- MvPolynomial.isUnit_iffproof · cited by 2
- MvPolynomial.degreeOf_mul_eqproof · cited by 2
- MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zeroproof · cited by 2
- MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zeroproof · cited by 2
- MvPolynomial.natDegree_optionEquivLeftstatement and proof · cited by 2