Theorems · Theorem · field theory
Polynomial.coeffList_eq_cons_leadingCoeff
∀ {R : Type u_1} [inst : Semiring R] {P : Polynomial R}, P ≠ 0 → ∃ ls, P.coeffList = P.leadingCoeff :: ls- Defined in
- Mathlib.Algebra.Polynomial.CoeffList
- 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.
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
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.coeffListstatement · cited by 22
- Polynomial.withBotSucc_degree_eq_natDegree_add_oneproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.coeffList_eraseLeadproof · cited by 4
- Polynomial.signVariations_eq_eraseLead_add_iteproof · cited by 1
- Polynomial.head?_coeffListproof · cited by 1
- Polynomial.coeffList_monomialproof · cited by 1
- Polynomial.signVariations_eraseLeadproof · cited by 0
- Polynomial.head_coeffListproof · cited by 0