Theorems · Theorem · field theory
Polynomial.taylor_eq_zero
∀ {R : Type u_1} [inst : Semiring R] (r : R) (f : Polynomial R), (Polynomial.taylor r) f = 0 ↔ f = 0- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.leadingCoeffproof · cited by 498
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.taylorstatement and proof · cited by 42
- Polynomial.leadingCoeff_taylorproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.degree_taylorproof · cited by 2
- Polynomial.taylor_injectiveproof · cited by 2
- Polynomial.eq_zero_of_hasseDeriv_eq_zeroproof · cited by 0