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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
Assumes
SemiringSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ascPochhammer_map · cited by 5ascPochhammer_mapIdeal.IsFractionRing.normal · cited by 3IsFractionRing.normalIsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow · cited by 3Rat.isIntegralClosure_adj…descPochhammer_map · cited by 3descPochhammer_mapPolynomial.map_taylor · cited by 2Polynomial.map_taylorminpoly_add_algebraMap_splits · cited by 2minpoly_add_algebraMap_sp…Field.primitive_element_inf_aux · cited by 1Field.primitive_element_i…IsPrimitiveRoot.minpoly_dvd_expand · cited by 1IsPrimitiveRoot.minpoly_d…ascPochhammer_eval_comp · cited by 1ascPochhammer_eval_compcyclotomic_prime_pow_comp_X_add_one_isEisensteinAt · cited by 1cyclotomic_prime_pow_comp…Polynomial.dickson_one_one_mul · cited by 1Polynomial.dickson_one_on…minpoly_neg_splits · cited by 1minpoly_neg_splitsdescPochhammer_succ_comp_X_sub_one · cited by 0descPochhammer_succ_comp_…ascPochhammer_succ_comp_X_add_one · cited by 0ascPochhammer_succ_comp_X…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringRingHom · cited by 10189RingHomPolynomial · cited by 5681PolynomialPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CPolynomial.map · cited by 806Polynomial.mappow_succ · cited by 374pow_succPolynomial.eval₂ · cited by 267Polynomial.eval₂Polynomial.comp · cited by 193Polynomial.compPolynomial.map_X · cited by 122Polynomial.map_XPolynomial.map_C · cited by 107Polynomial.map_CPolynomial.map_mul · cited by 90Polynomial.map_mulPolynomial.map_add · cited by 50Polynomial.map_addPolynomial.induction_on · cited by 23Polynomial.induction_onPolynomial.map_compCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.