Theorems · Theorem · field theory
Polynomial.map_comp
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) (p q : Polynomial R),
Polynomial.map f (p.comp q) = (Polynomial.map f p).comp (Polynomial.map f q)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.mapstatement and proof · cited by 806
- pow_succproof · cited by 374
- Polynomial.eval₂proof · cited by 267
- Polynomial.compstatement and proof · cited by 193
- Polynomial.map_Xproof · cited by 122
- Polynomial.map_Cproof · cited by 107
Cited by14
Results whose statement or proof uses this declaration.
- ascPochhammer_mapproof · cited by 5
- Ideal.IsFractionRing.normalproof · cited by 3
- descPochhammer_mapproof · cited by 3
- Polynomial.map_taylorproof · cited by 2
- minpoly_add_algebraMap_splitsproof · cited by 2
- Field.primitive_element_inf_auxproof · cited by 1
- IsPrimitiveRoot.minpoly_dvd_expandproof · cited by 1
- ascPochhammer_eval_compproof · cited by 1
- cyclotomic_prime_pow_comp_X_add_one_isEisensteinAtproof · cited by 1
- Polynomial.dickson_one_one_mulproof · cited by 1
- minpoly_neg_splitsproof · cited by 1