Theorems · Theorem · field theory
Polynomial.pow_mul_divByMonic_rootMultiplicity_eq
∀ {R : Type u} [inst : Ring R] (p : Polynomial R) (a : R),
(Polynomial.X - Polynomial.C a) ^ Polynomial.rootMultiplicity a p *
(p /ₘ (Polynomial.X - Polynomial.C a) ^ Polynomial.rootMultiplicity a p) =
p- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 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.
Cites15
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
- zero_addproof · cited by 2,366
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.Monicproof · cited by 461
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- Polynomial.divByMonicstatement and proof · cited by 77
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.modByMonic_add_divproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zeroproof · cited by 2
- Polynomial.eval_iterate_derivative_rootMultiplicityproof · cited by 1
- Polynomial.eval_divByMonic_eq_trailingCoeff_compproof · cited by 1