Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.S_comp_two_mul_X
∀ (R : Type u_1) [inst : CommRing R] (n : ℤ), (Polynomial.Chebyshev.S R n).comp (2 * Polynomial.X) = Polynomial.Chebyshev.U R n
- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.compstatement and proof · cited by 193
- Polynomial.Chebyshev.Ustatement and proof · cited by 71
- Polynomial.Chebyshev.Sstatement and proof · cited by 38
- Polynomial.Chebyshev.inductproof · cited by 30
- Polynomial.X_compproof · cited by 29
- Polynomial.mul_compproof · cited by 24
- Polynomial.one_compproof · cited by 18
- Polynomial.Chebyshev.U_zeroproof · cited by 17
- Polynomial.Chebyshev.U_add_twoproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.S_eq_U_comp_half_mul_Xproof · cited by 3
- Polynomial.chebyshev_U_eq_dickson_two_oneproof · cited by 0