Theorems · Definition · field theory
Polynomial.nextCoeff
{R : Type u} → [inst : Semiring R] → Polynomial R → RThe second-highest coefficient, or 0 for constants
- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 60 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.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
Cited by46
Results whose statement or proof uses this declaration.
- Polynomial.nextCoeff_of_natDegree_posstatement · cited by 6
- Polynomial.leadingCoeff_eraseLead_eq_nextCoeffstatement and proof · cited by 5
- Polynomial.natDegree_pos_of_nextCoeff_ne_zerostatement and proof · cited by 5
- Polynomial.nextCoeff_eq_zero_of_eraseLead_eq_zerostatement and proof · cited by 5
- Polynomial.Monic.nextCoeff_mulstatement and proof · cited by 3
- Polynomial.Monic.nextCoeff_multiset_prodstatement and proof · cited by 3
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3
- Polynomial.natDegree_eraseLead_add_onestatement and proof · cited by 3
- Polynomial.coeff_one_reversestatement and proof · cited by 2
- PowerBasis.trace_gen_eq_nextCoeff_minpolystatement and proof · cited by 2
- PowerBasis.trace_gen_eq_sum_rootsproof · cited by 2
- Polynomial.Splits.nextCoeff_eq_neg_sum_roots_of_monicstatement · cited by 2