Theorems · Theorem · field theory
Polynomial.nextCoeff_of_natDegree_pos
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, 0 < p.natDegree → p.nextCoeff = p.coeff (p.natDegree - 1)- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 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.
Cites5
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.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.nextCoeffstatement · cited by 46
Cited by6
Results whose statement or proof uses this declaration.
- PowerBasis.trace_gen_eq_nextCoeff_minpolyproof · cited by 2
- Polynomial.natDegree_eraseLeadproof · cited by 2
- Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zeroproof · cited by 1
- Polynomial.nextCoeff_C_mul_X_add_Cproof · cited by 1
- Polynomial.nextCoeff_X_add_Cproof · cited by 1
- Polynomial.signVariations_eraseLead_mul_X_sub_Cproof · cited by 0