Theorems · Definition · field theory
Polynomial.Bivariate.swap
{R : Type u_1} → [inst : CommSemiring R] → Polynomial (Polynomial R) ≃ₐ[R] Polynomial (Polynomial R)The R-algebra automorphism given by X ↦ Y and Y ↦ X.
- Defined in
- Mathlib.Algebra.Polynomial.Bivariate
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 116 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.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- AlgEquivstatement · cited by 1,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- AlgEquiv.ofAlgHomproof · cited by 13
- Polynomial.aevalAevalproof · cited by 13
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.Bivariate.aveal_eq_map_swapstatement and proof · cited by 1
- RatFunc.irreducible_minpolyX'proof · cited by 1
- IsAlgebraic.adjoin_singletonproof · cited by 1
- Polynomial.Bivariate.swap_C_Cstatement · cited by 1
- Polynomial.Bivariate.swap_Ystatement · cited by 1
- Polynomial.Bivariate.Transcendental.algEquivAdjoin_swap_eq_aevalstatement and proof · cited by 1
- Polynomial.Bivariate.aevalAeval_swapstatement and proof · cited by 0
- Polynomial.Bivariate.swap_Cstatement · cited by 0
- Polynomial.Bivariate.swap_Xstatement · cited by 0
- Polynomial.Bivariate.swap_applystatement · cited by 0
- Polynomial.Bivariate.swap_map_Cstatement and proof · cited by 0
- Polynomial.Bivariate.swap_monomialstatement and proof · cited by 0