Theorems · Theorem · field theory
Polynomial.coeff_X_pow_mul
∀ {R : Type u} [inst : Semiring R] (p : Polynomial R) (n d : ℕ), (Polynomial.X ^ n * p).coeff (d + n) = p.coeff d- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 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 and proof · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.coeffstatement and proof · cited by 1,045
- Commute.eqproof · cited by 91
- Polynomial.coeff_mul_X_powproof · cited by 9
- Polynomial.commute_X_powproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.isRegular_X_powproof · cited by 3
- Polynomial.X_pow_dvd_iffproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1