Theorems · Theorem · field theory
Polynomial.exists_iterate_derivative_eq_factorial_smul
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R) (k : ℕ),
∃ gp, gp.natDegree ≤ p.natDegree - k ∧ (⇑Polynomial.derivative)^[k] p = k.factorial • gp- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Nat.iteratestatement and proof · cited by 740
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.aeval_iterate_derivative_of_geproof · cited by 2