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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- 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
- RingHom.compproof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.monomialstatement and proof · cited by 256
- Polynomial.C_mul_X_pow_eq_monomialproof · cited by 53
Cited by18
Results whose statement or proof uses this declaration.
- Polynomial.eval₂_eq_eval_mapproof · cited by 29
- Polynomial.map_surjectiveproof · cited by 18
- Polynomial.eval_one_mapproof · cited by 3
- PolyEquivTensor.toFunBilinear_apply_eq_sumproof · cited by 2
- Polynomial.eval_intCast_mapproof · cited by 2
- Polynomial.map_frobenius_expandproof · cited by 2
- Polynomial.exists_support_eq_of_mem_liftsproof · cited by 1
- denomsClearable_C_mul_X_powproof · cited by 1
- Polynomial.Bivariate.aeval_aeval_eq_aeval_algEquivAdjoinproof · cited by 1
- Polynomial.Bivariate.aveal_eq_map_swapproof · cited by 1
- PolynomialModule.map_smulproof · cited by 1
- bernoulliFun_oneproof · cited by 1