Theorems · Theorem · commutative algebra
MvPolynomial.transcendental_supported_polynomial_aeval_X_iff
∀ {σ : Type u_1} (R : Type u_2) [inst : CommRing R] [Nontrivial R] {i : σ} {s : Set σ} {f : Polynomial R},
Transcendental (↥(MvPolynomial.supported R s)) ((Polynomial.aeval (MvPolynomial.X i)) f) ↔ i ∉ s ∧ Transcendental R f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Nontrivialstatement and proof · cited by 2,416
- MvPolynomialstatement and proof · cited by 2,140
- Subalgebrastatement · cited by 1,353
- Polynomial.aevalstatement and proof · cited by 615
- MvPolynomial.Xstatement and proof · cited by 552
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.transcendental_supported_X_iffproof · cited by 0