Theorems · Theorem · field theory
Polynomial.eval_intCast_map
∀ {R : Type u_1} {S : Type u_2} [inst : Ring R] [inst_1 : Ring S] (f : R →+* S) (p : Polynomial R) (i : ℤ),
Polynomial.eval (↑i) (Polynomial.map f p) = f (Polynomial.eval (↑i) p)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- map_mulproof · cited by 1,137
- map_addproof · cited by 964
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.evalstatement and proof · cited by 796
- map_powproof · cited by 503
- Polynomial.eval_addproof · cited by 84
- Polynomial.induction_on'proof · cited by 50
- Polynomial.map_addproof · cited by 50
Cited by2
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3
- Polynomial.eval_one_cyclotomic_not_prime_powproof · cited by 1