Theorems · Theorem · field theory
Polynomial.taylor_monomial
∀ {R : Type u_1} [inst : Semiring R] (r : R) (i : ℕ) (k : R),
(Polynomial.taylor r) ((Polynomial.monomial i) k) = Polynomial.C k * (Polynomial.X + Polynomial.C r) ^ i- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.monomialstatement · cited by 256
- Polynomial.taylorstatement · cited by 42
- Polynomial.monomial_compproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_taylorproof · cited by 4