Theorems · Theorem · field theory
Polynomial.smeval_monomial
∀ {R : Type u_1} [inst : Semiring R] (r : R) {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ]
[inst_3 : MulActionWithZero R S] (x : S) (n : ℕ), ((Polynomial.monomial n) r).smeval x = r • x ^ n- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- zero_smulproof · cited by 716
- Polynomial.monomialstatement and proof · cited by 256
- MulActionWithZerostatement and proof · cited by 79
- Polynomial.smevalstatement · cited by 65
- Polynomial.smul_powproof · cited by 9
- Polynomial.smeval_eq_sumproof · cited by 9
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.smeval_mulproof · cited by 9
- Polynomial.smeval_compproof · cited by 5
- Polynomial.smeval_C_mulproof · cited by 3
- Polynomial.smeval_mul_Xproof · cited by 2
- Polynomial.smeval_X_mulproof · cited by 1
- Polynomial.smeval_at_natCastproof · cited by 1
- Polynomial.smeval_commuteproof · cited by 1
- Polynomial.smeval_commute_leftproof · cited by 1
- Polynomial.smeval_monomial_mulproof · cited by 1
- Polynomial.smeval_smulproof · cited by 0
- Polynomial.smeval_X_pow_assocproof · cited by 0
- Polynomial.smeval_assoc_X_powproof · cited by 0