Theorems · Theorem · field theory
Polynomial.map_pow
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] (f : R →+* S) (n : ℕ),
Polynomial.map f (p ^ n) = Polynomial.map f p ^ n- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement · cited by 806
- Polynomial.mapRingHomproof · cited by 98
- RingHom.map_powproof · cited by 22
Cited by59
Results whose statement or proof uses this declaration.
- Polynomial.derivative_mapproof · cited by 17
- Polynomial.prod_cyclotomic_eq_X_pow_sub_oneproof · cited by 11
- Polynomial.cyclotomic_primeproof · cited by 7
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- WeierstrassCurve.map_Ψ₂Sqproof · cited by 5
- WeierstrassCurve.Affine.map_polynomialproof · cited by 4
- Polynomial.mem_map_rangeSproof · cited by 4
- Polynomial.prod_cyclotomic_eq_geom_sumproof · cited by 4
- WeierstrassCurve.map_preΨ₄proof · cited by 4
- WeierstrassCurve.map_Ψ₃proof · cited by 4
- Polynomial.int_coeff_of_cyclotomic'proof · cited by 3
- Cubic.map_toPolyproof · cited by 3