Theorems · Theorem · field theory
Polynomial.derivative_map
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (p : Polynomial R) (f : R →+* S),
Polynomial.derivative (Polynomial.map f p) = Polynomial.map f (Polynomial.derivative p)- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- Finset.rangeproof · cited by 1,341
Cited by17
Results whose statement or proof uses this declaration.
- Polynomial.Separable.mapproof · cited by 14
- Polynomial.separable_mapproof · cited by 6
- hasDerivAt_bernoulliFunproof · cited by 5
- Algebra.FormallyUnramified.of_isSeparableproof · cited by 5
- Polynomial.iterate_derivative_mapproof · cited by 4
- Algebra.FormallyEtale.of_isSeparable_auxproof · cited by 1
- Polynomial.aeval_add_of_sq_eq_zeroproof · cited by 1
- Algebra.discr_powerBasis_eq_normproof · cited by 1
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zeroproof · cited by 1
- Polynomial.hasStrictDerivAt_aevalproof · cited by 1
- eval_minpolyDiv_selfproof · cited by 1