Theorems · Definition · commutative algebra
MvPolynomial.supported
{σ : Type u_1} → (R : Type u) → [inst : CommSemiring R] → Set σ → Subalgebra R (MvPolynomial σ R)The set of polynomials whose variables are contained in s as a Subalgebra over R.
- Defined in
- Mathlib.Algebra.MvPolynomial.Supported
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 84 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Set.imageproof · cited by 5,609
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Subalgebrastatement · cited by 1,353
- MvPolynomial.Xproof · cited by 552
- Algebra.adjoinproof · cited by 535
Cited by24
Results whose statement or proof uses this declaration.
- MvPolynomial.supported_eq_range_renamestatement · cited by 5
- MvPolynomial.mem_supportedstatement · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xstatement and proof · cited by 4
- MvPolynomial.supportedEquivMvPolynomialstatement and proof · cited by 3
- algebraicIndependent_comp_subtypestatement · cited by 2
- MvPolynomial.mem_supported_varsstatement · cited by 2
- MvPolynomial.transcendental_polynomial_aeval_Xproof · cited by 2
- MvPolynomial.transcendental_supported_polynomial_aeval_X_iffstatement and proof · cited by 1
- MvPolynomial.supported_le_supported_iffstatement and proof · cited by 1
- MvPolynomial.supported_monostatement · cited by 1
- algebraicIndependent_of_finiteproof · cited by 1
- algebraicIndependent_subtypestatement · cited by 1