Theorems · Theorem · field theory
Polynomial.trailingCoeff_nonzero_iff_nonzero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.trailingCoeff ≠ 0 ↔ p ≠ 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 90 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.
Cites4
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.trailingCoeffstatement · cited by 20
- Polynomial.trailingCoeff_eq_zeroproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.nilRank_le_natTrailingDegree_charpolyproof · cited by 3
- LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRankproof · cited by 2
- LinearMap.polyCharpoly_coeff_nilRankAux_ne_zeroproof · cited by 2
- Polynomial.rootMultiplicity_eq_natTrailingDegree'proof · cited by 1
- Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegreeproof · cited by 1
- Polynomial.natTrailingDegree_mem_support_of_nonzeroproof · cited by 1