Theorems · Theorem · field theory
Polynomial.degree_lt_iff_coeff_zero
∀ {R : Type u} [inst : Semiring R] (f : Polynomial R) (n : ℕ), f.degree < ↑n ↔ ∀ (m : ℕ), n ≤ m → f.coeff m = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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.
Cites12
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
- Finsetproof · cited by 13,712
- LinearOrderproof · cited by 8,572
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreestatement · cited by 643
- WithBot.someproof · cited by 541
- not_leproof · cited by 328
- Polynomial.supportproof · cited by 237
- WithBot.bot_lt_coeproof · cited by 37
- Finset.sup_lt_iffproof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.mem_degreeLTproof · cited by 14
- Polynomial.degree_map_leproof · cited by 7
- Polynomial.degree_smul_leproof · cited by 5
- Polynomial.degree_smul_of_smul_regularproof · cited by 2
- Polynomial.exists_approx_polynomial_auxproof · cited by 1