Theorems · Theorem · field theory
Polynomial.eval_geom_sum
∀ {R : Type u_1} [inst : CommSemiring R] {n : ℕ} {x : R},
Polynomial.eval x (∑ i ∈ Finset.range n, Polynomial.X ^ i) = ∑ i ∈ Finset.range n, x ^ i- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xstatement and proof · cited by 1,639
- Finset.rangestatement and proof · cited by 1,341
- Polynomial.evalstatement · cited by 796
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_powproof · cited by 75
- Polynomial.eval_finsetSumproof · cited by 25
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.eval_one_cyclotomic_not_prime_powproof · cited by 1
- Polynomial.cyclotomic_posproof · cited by 1
- IsPrimitiveRoot.prod_one_sub_pow_eq_orderproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- IsPrimitiveRoot.isRoot_geom_sumproof · cited by 0