Theorems · Theorem · field theory
Polynomial.iterate_derivative_map
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (p : Polynomial R) (f : R →+* S) (k : ℕ),
(⇑Polynomial.derivative)^[k] (Polynomial.map f p) = Polynomial.map f ((⇑Polynomial.derivative)^[k] p)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement and proof · cited by 806
- Nat.iteratestatement and proof · cited by 740
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.derivative_mapproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.aeval_iterate_derivative_of_ltproof · cited by 2
- Polynomial.sumIDeriv_mapproof · cited by 1
- Polynomial.aeval_iterate_derivative_selfproof · cited by 1
- Polynomial.derivativeFinsupp_mapproof · cited by 0