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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.

MvPolynomial.finSuccEquiv · cited by 22MvPolynomial.finSuccEquivMvPolynomial.optionEquivLeft_apply · cited by 7MvPolynomial.optionEquivL…MvPolynomial.optionEquivLeft_coeff_some_coeff_none · cited by 7MvPolynomial.optionEquivL…AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin · cited by 7AlgebraicIndependent.mvPo…MvPolynomial.toPolynomialAdjoinImageCompl · cited by 5MvPolynomial.toPolynomial…MvPolynomial.transcendental_supported_polynomial_aeval_X · cited by 4MvPolynomial.transcendent…MvPolynomial.optionEquivLeft_X_none · cited by 3MvPolynomial.optionEquivL…MvPolynomial.isUnit_iff · cited by 2MvPolynomial.isUnit_iffMvPolynomial.degreeOf_mul_eq · cited by 2MvPolynomial.degreeOf_mul…MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero · cited by 2MvPolynomial.aeval_toPoly…MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zero · cited by 2MvPolynomial.coeff_toPoly…MvPolynomial.natDegree_optionEquivLeft · cited by 2MvPolynomial.natDegree_op…MvPolynomial.optionEquivLeft_C · cited by 2MvPolynomial.optionEquivL…MvPolynomial.optionEquivLeft_X_some · cited by 2MvPolynomial.optionEquivL…MvPolynomial.optionEquivLeft_symm_C_X · cited by 2MvPolynomial.optionEquivL…DFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringPolynomial · cited by 5681PolynomialFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialAlgEquiv · cited by 1681AlgEquivPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CMvPolynomial.X · cited by 552MvPolynomial.XMvPolynomial.aeval · cited by 298MvPolynomial.aevalMvPolynomial.rename · cited by 168MvPolynomial.renamePolynomial.aevalTower · cited by 14Polynomial.aevalTowerAlgEquiv.ofAlgHom · cited by 13AlgEquiv.ofAlgHomMvPolynomial.optionEquivLeftCITED BYCITES

Cites13

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Cited by39

Results whose statement or proof uses this declaration.