Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : Invertible 2] (n : ℤ), Polynomial.Chebyshev.C R n = 2 * (Polynomial.Chebyshev.T R n).comp (Polynomial.C ⅟2 * Polynomial.X)
- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- map_oneproof · cited by 861
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement and proof · cited by 268
- Polynomial.compstatement and proof · cited by 193
- Polynomial.Chebyshev.Tstatement and proof · cited by 108
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.dickson_one_one_eq_chebyshev_Tproof · cited by 1
- Polynomial.Chebyshev.C_two_mul_complex_cosproof · cited by 1
- Polynomial.Chebyshev.C_two_mul_complex_coshproof · cited by 1