Theorems · Theorem · commutative algebra
MvPolynomial.uniqueAlgEquiv_symm_apply
∀ (R : Type u) [inst : CommSemiring R] (σ : Type u_2) [inst_1 : Unique σ] (p : Polynomial R), (MvPolynomial.uniqueAlgEquiv R σ).symm p = Polynomial.eval₂ MvPolynomial.C (MvPolynomial.X default) p
- Defined in
- Mathlib.Algebra.MvPolynomial.Equiv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringUnique
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- AlgEquivstatement · cited by 1,681
- AlgEquiv.symmstatement and proof · cited by 615
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.Cstatement · cited by 400
- Uniquestatement and proof · cited by 400
- Polynomial.eval₂statement · cited by 267
- MvPolynomial.uniqueAlgEquivstatement and proof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.toMvPolynomial_eq_rename_compproof · cited by 1
- IsTranscendenceBasis.polynomialproof · cited by 1
- MvPolynomial.uniqueAlgEquiv_symm_monomialproof · cited by 1
- AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmptyproof · cited by 0