Theorems · Theorem · field theory
Polynomial.eq_zero_of_hasseDeriv_eq_zero
∀ {R : Type u_1} [inst : Semiring R] (f : Polynomial R) (r : R),
(∀ (k : ℕ), Polynomial.eval r ((Polynomial.hasseDeriv k) f) = 0) → f = 0- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites12
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
- Polynomial.coeffproof · cited by 1,045
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.extproof · cited by 118
- Polynomial.hasseDerivstatement and proof · cited by 19
- Polynomial.coeff_zeroproof · cited by 12
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.taylor_eq_zeroproof · cited by 3
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