Theorems · Theorem · field theory
Polynomial.eval_monomial
∀ {R : Type u} [inst : Semiring R] {x : R} {n : ℕ} {a : R}, Polynomial.eval x ((Polynomial.monomial n) a) = a * x ^ n- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 99 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.
Cites8
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- Polynomial.evalstatement · cited by 796
- Polynomial.monomialstatement · cited by 256
- Polynomial.eval₂_monomialproof · cited by 19
Cited by21
Results whose statement or proof uses this declaration.
- Polynomial.eval_compproof · cited by 29
- Polynomial.eval₂_eq_eval_mapproof · cited by 29
- Polynomial.eval_C_mulproof · cited by 4
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.hasStrictDerivAtproof · cited by 3
- Polynomial.eval_one_mapproof · cited by 3
- Polynomial.aeval_continuousMap_applyproof · cited by 2
- Polynomial.eval_intCast_mapproof · cited by 2
- Polynomial.bernoulli_eval_oneproof · cited by 2
- PolynomialModule.eval_smulproof · cited by 2
- Polynomial.bernoulli_three_eval_one_quarterproof · cited by 1
- Asymptotics.SuperpolynomialDecay.polynomial_mulproof · cited by 1