Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.U_eval_zero
∀ (R : Type u_1) [inst : CommRing R] (n : ℤ), Polynomial.eval 0 (Polynomial.Chebyshev.U R n) = ↑(if Even n then ↑(n / 2).negOnePow else 0)
- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 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.
Cites33
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
- mul_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valstatement and proof · cited by 1,966
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
- Polynomial.evalstatement and proof · cited by 796
- mul_negproof · cited by 590
- Evenstatement and proof · cited by 444
- Int.cast_oneproof · cited by 371
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.U_eval_zero_of_evenproof · cited by 1
- Polynomial.Chebyshev.U_eval_zero_of_oddproof · cited by 0