Theorems · Theorem · field theory
Polynomial.aeval_iterate_derivative_of_ge
∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_3) [inst_1 : CommRing A] [inst_2 : Algebra R A] (p : Polynomial R)
(q : ℕ) {k : ℕ},
q ≤ k →
∃ gp,
gp.natDegree ≤ p.natDegree - k ∧
∀ (r : A), (Polynomial.aeval r) ((⇑Polynomial.derivative)^[k] p) = q.factorial • (Polynomial.aeval r) gp- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommRingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- LE.le.transproof · cited by 3,151
- map_mulproof · cited by 1,137
- Polynomial.natDegreestatement and proof · cited by 1,105
- Nat.iteratestatement and proof · cited by 740
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.aeval_sumIDerivproof · cited by 1
- Polynomial.aeval_sumIDeriv_of_posproof · cited by 1