Theorems · Theorem · field theory
Polynomial.coeff_X_pow
∀ {R : Type u} [inst : Semiring R] (k n : ℕ), (Polynomial.X ^ k).coeff n = if n = k then 1 else 0- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement · cited by 5,681
- one_mulproof · cited by 2,841
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- map_oneproof · cited by 861
Cited by50
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.coeff_derivativeproof · cited by 14
- Polynomial.coeff_mul_X_powproof · cited by 9
- Polynomial.coeff_X_pow_selfproof · cited by 7
- Polynomial.coeff_freeMonicproof · cited by 6
- Polynomial.coeff_mul_X_pow'proof · cited by 5
- Polynomial.degreeLT.basis_valproof · cited by 4
- IsIntegral.coeffproof · cited by 4
- Polynomial.taylor_coeffproof · cited by 4
- spectralNorm_zero_ltproof · cited by 3
- FiniteField.orderOf_frobeniusAlgHomproof · cited by 3
- Polynomial.support_trinomialproof · cited by 3