Theorems · Theorem · field theory
Polynomial.coeff_ne_zero_of_eq_degree
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.degree = ↑n → p.coeff n ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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
- WithBotstatement · cited by 1,498
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.mem_support_iffproof · cited by 30
- Finset.mem_of_maxproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.integralNormalization_coeffproof · cited by 6
- Polynomial.roots_degree_eq_oneproof · cited by 1
- Polynomial.logMahlerMeasure_of_degree_eq_oneproof · cited by 0
- Polynomial.mahlerMeasure_of_degree_eq_oneproof · cited by 0