Theorems · Theorem · field theory
Polynomial.iterate_derivative_X_sub_pow_self
∀ {R : Type u} [inst : CommRing R] (n : ℕ) (c : R),
(⇑Polynomial.derivative)^[n] ((Polynomial.X - Polynomial.C c) ^ n) = ↑n.factorial- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.
Cites16
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
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- 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
- Nat.iteratestatement · cited by 740
- Nat.factorialstatement and proof · cited by 616
- Polynomial.derivativestatement · cited by 331
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.eval_iterate_derivative_rootMultiplicityproof · cited by 1