Theorems · Definition · field theory
Polynomial.IsRoot
{R : Type u} → [inst : Semiring R] → Polynomial R → R → PropIsRoot p x implies x is a root of p. The evaluation of p at x is zero
- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 152 results in Mathlib
- Foundations
- Depth 66 from the axioms, rests on 917 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.evalproof · cited by 796
Cited by158
Results whose statement or proof uses this declaration.
- Polynomial.mem_rootsstatement · cited by 30
- Polynomial.IsRoot.defstatement · cited by 30
- Polynomial.dvd_iff_isRootstatement and proof · cited by 15
- Polynomial.isRoot_cyclotomic_iffstatement and proof · cited by 12
- Polynomial.mem_roots'statement and proof · cited by 8
- Polynomial.finite_setOfPred_isRootstatement · cited by 7
- IsAlgClosed.exists_rootstatement · cited by 7
- Polynomial.degree_eq_one_of_irreducible_of_rootstatement and proof · cited by 7
- Polynomial.rootMultiplicity_eq_zerostatement and proof · cited by 6
- Polynomial.mul_divByMonic_eq_iff_isRootstatement · cited by 5
- IsIntegral.coeffproof · cited by 4
- IsSepClosed.exists_rootstatement · cited by 4