Theorems · Theorem · field theory
Polynomial.taylor_eval
∀ {R : Type u_1} [inst : CommSemiring R] (r : R) (f : Polynomial R) (s : R),
Polynomial.eval s ((Polynomial.taylor r) f) = Polynomial.eval (s + r) f- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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 · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_Cproof · cited by 145
- Polynomial.eval_addproof · cited by 84
- Polynomial.taylorstatement · cited by 42
- Polynomial.eval_compproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- IsIntegral.coeffproof · cited by 4
- Polynomial.exists_mul_sq_add_linear_part_eq_eval_addproof · cited by 2
- Polynomial.resultant_taylorproof · cited by 0
- Polynomial.taylor_eval_subproof · cited by 0