Theorems · Theorem · field theory
Polynomial.smeval_eq_sum
∀ {R : Type u_1} [inst : Semiring R] (p : Polynomial R) {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ]
[inst_3 : MulActionWithZero R S] (x : S), p.smeval x = p.sum (Polynomial.smul_pow x)- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Polynomialstatement and proof · cited by 5,681
- MulActionWithZerostatement and proof · cited by 79
- Polynomial.sumstatement and proof · cited by 67
- Polynomial.smevalstatement · cited by 65
- Polynomial.smul_powstatement and proof · cited by 9
- Polynomial.smeval_defproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.smeval_addproof · cited by 22
- Polynomial.smeval_monomialproof · cited by 13
- Polynomial.smeval_Xproof · cited by 11
- Polynomial.smeval_Cproof · cited by 8
- Polynomial.eval_eq_smevalproof · cited by 4
- Polynomial.smeval_zeroproof · cited by 2
- Polynomial.smeval_neg_natproof · cited by 1
- Polynomial.eval₂_smulOneHom_eq_smevalproof · cited by 0
- Polynomial.smeval_X_powproof · cited by 0