Theorems · Theorem · field theory
Polynomial.pow_rootMultiplicity_dvd
∀ {R : Type u} [inst : Ring R] (p : Polynomial R) (a : R),
(Polynomial.X - Polynomial.C a) ^ Polynomial.rootMultiplicity a p ∣ p- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- pow_zeroproof · cited by 1,094
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- Polynomial.rootMultiplicity_zeroproof · cited by 11
- Polynomial.rootMultiplicity_eq_multiplicityproof · cited by 8
- pow_multiplicity_dvdproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicityproof · cited by 3
- Polynomial.rootMultiplicity_mul_X_sub_C_powproof · cited by 3
- Polynomial.pow_mul_divByMonic_rootMultiplicity_eqproof · cited by 3
- Polynomial.eq_rootMultiplicity_mapproof · cited by 1
- Polynomial.le_rootMultiplicity_mapproof · cited by 1
- Polynomial.le_rootMultiplicity_mulproof · cited by 1
- Polynomial.rootMultiplicity_addproof · cited by 0