Theorems · Theorem · field theory
Polynomial.eval_map
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] (f : R →+* S) (x : S),
Polynomial.eval x (Polynomial.map f p) = Polynomial.eval₂ f x p- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.evalstatement · cited by 796
- Polynomial.eval₂statement · cited by 267
- Polynomial.eval₂_eq_eval_mapproof · cited by 29
Cited by37
Results whose statement or proof uses this declaration.
- Polynomial.eval_map_algebraMapproof · cited by 49
- Polynomial.hom_eval₂proof · cited by 16
- Polynomial.map_aeval_eq_aeval_mapproof · cited by 14
- Algebra.IsInvariant.isIntegralproof · cited by 6
- Matrix.aeval_self_charpolyproof · cited by 6
- ascPochhammer_eval_castproof · cited by 4
- Polynomial.mem_roots_mapproof · cited by 2
- Polynomial.mem_roots_map_of_injectiveproof · cited by 2
- IsIntegral.map_of_comp_eqproof · cited by 2
- Polynomial.X_sub_C_mul_removeFactorproof · cited by 2
- Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomialproof · cited by 2
- Polynomial.cyclotomic.eval_applyproof · cited by 2