Theorems · Theorem · field theory
Polynomial.eval_eq_sum
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {x : R}, Polynomial.eval x p = p.sum fun e a => a * x ^ e- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 67 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.evalstatement · cited by 796
- Polynomial.sumstatement and proof · cited by 67
- Polynomial.eval₂_eq_sumproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.coeff_zero_eq_eval_zeroproof · cited by 20
- Polynomial.eval₂_at_applyproof · cited by 13
- Polynomial.eval_eq_sum_rangeproof · cited by 8
- Polynomial.eval_eq_smevalproof · cited by 4
- Polynomial.eval_eq_sum_range'proof · cited by 2
- Polynomial.eval_eq_sum_degreeLTEquivproof · cited by 1
- Polynomial.mahlerMeasure_le_sum_norm_coeffproof · cited by 1
- SModEq.evalproof · cited by 0