Theorems · Theorem · field theory
Polynomial.taylor_coeff_one
∀ {R : Type u_1} [inst : Semiring R] (r : R) (f : Polynomial R),
((Polynomial.taylor r) f).coeff 1 = Polynomial.eval r (Polynomial.derivative f)- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 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.
Cites11
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.taylorstatement · cited by 42
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.hasseDeriv_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.exists_mul_sq_add_linear_part_eq_eval_addproof · cited by 2