Theorems · Theorem · field theory
Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zero
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} (a : R),
p ≠ 0 → Polynomial.eval a (p /ₘ (Polynomial.X - Polynomial.C a) ^ Polynomial.rootMultiplicity a p) ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Nontrivialproof · cited by 2,416
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreeproof · cited by 643
- pow_succproof · cited by 374
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.eval_divByMonic_eq_trailingCoeff_compproof · cited by 1