Mathlib Map

Theorems · Theorem · field theory

Polynomial.map_monomial

∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) {n : ℕ} {a : R},
  Polynomial.map f ((Polynomial.monomial n) a) = (Polynomial.monomial n) (f a)
Defined in
Mathlib.Algebra.Polynomial.Eval.Defs
Cited by
18 results in Mathlib
Foundations
Depth 103 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.

Polynomial.eval₂_eq_eval_map · cited by 29Polynomial.eval₂_eq_eval_…Polynomial.map_surjective · cited by 18Polynomial.map_surjectivePolynomial.eval_one_map · cited by 3Polynomial.eval_one_mapPolyEquivTensor.toFunBilinear_apply_eq_sum · cited by 2PolyEquivTensor.toFunBili…Polynomial.eval_intCast_map · cited by 2Polynomial.eval_intCast_m…Polynomial.map_frobenius_expand · cited by 2Polynomial.map_frobenius_…Polynomial.exists_support_eq_of_mem_lifts · cited by 1Polynomial.exists_support…denomsClearable_C_mul_X_pow · cited by 1denomsClearable_C_mul_X_p…Polynomial.Bivariate.aeval_aeval_eq_aeval_algEquivAdjoin · cited by 1Bivariate.aeval_aeval_eq_…Polynomial.Bivariate.aveal_eq_map_swap · cited by 1Bivariate.aveal_eq_map_sw…PolynomialModule.map_smul · cited by 1PolynomialModule.map_smulbernoulliFun_one · cited by 1bernoulliFun_onePolynomial.mapAlgHom_monomial · cited by 0Polynomial.mapAlgHom_mono…Polynomial.Bivariate.swap_map_C · cited by 0Bivariate.swap_map_CPolynomial.eval_natCast_map · cited by 0Polynomial.eval_natCast_m…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapRingHom · cited by 10189RingHomPolynomial · cited by 5681PolynomialPolynomial.X · cited by 1639Polynomial.XPolynomial.C · cited by 1598Polynomial.CRingHom.comp · cited by 899RingHom.compPolynomial.map · cited by 806Polynomial.mapPolynomial.monomial · cited by 256Polynomial.monomialPolynomial.C_mul_X_pow_eq_monomial · cited by 53Polynomial.C_mul_X_pow_eq…Polynomial.eval₂_monomial · cited by 19Polynomial.eval₂_monomialPolynomial.map_monomialCITED BYCITES

Cites13

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

Cited by18

Results whose statement or proof uses this declaration.