Theorems · Theorem · field theory
Polynomial.expand_eval
∀ {R : Type u} [inst : CommSemiring R] (p : ℕ) (P : Polynomial R) (r : R),
Polynomial.eval r ((Polynomial.expand R p) P) = Polynomial.eval (r ^ p) P- Defined in
- Mathlib.Algebra.Polynomial.Expand
- Cited by
- 2 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.
Cites19
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
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- map_addproof · cited by 964
- Polynomial.evalstatement and proof · cited by 796
- map_powproof · cited by 503
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_Cproof · cited by 145
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2