Theorems · Theorem · field theory
Polynomial.map_map
∀ {R : Type u} {S : Type v} {T : Type w} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) [inst_2 : Semiring T]
(g : S →+* T) (p : Polynomial R), Polynomial.map g (Polynomial.map f p) = Polynomial.map (g.comp f) p- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 75 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- RingHom.compstatement and proof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.extproof · cited by 118
- Polynomial.coeff_mapproof · cited by 114
Cited by75
Results whose statement or proof uses this declaration.
- Polynomial.eval₂_mapproof · cited by 20
- IsGalois.card_aut_eq_finrankproof · cited by 16
- Polynomial.map_cyclotomicproof · cited by 15
- Polynomial.map_aeval_eq_aeval_mapproof · cited by 14
- IsAlgebraic.restrictScalarsproof · cited by 6
- Polynomial.separable_mapproof · cited by 6
- IntermediateField.splits_of_splitsproof · cited by 5
- Polynomial.Splits.image_rootSetproof · cited by 4
- Normal.of_algEquivproof · cited by 4
- Polynomial.Splits.of_algHomproof · cited by 3
- IsIntegral.minpoly_splits_tower_top'proof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3