Theorems · Theorem · field theory
Polynomial.Splits.nextCoeff_eq_neg_sum_roots_mul_leadingCoeff
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} [inst_1 : IsDomain R],
f.Splits → f.nextCoeff = -f.leadingCoeff * f.roots.sum- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Multiset.mapproof · cited by 876
- Polynomial.evalproof · cited by 796
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- Multiset.prodproof · cited by 528
- Polynomial.leadingCoeffstatement and proof · cited by 498
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Splits.nextCoeff_eq_neg_sum_roots_of_monicproof · cited by 2