Theorems · Theorem · commutative algebra
Polynomial.polynomial_map_coe
∀ {U : Type u_2} {V : Type u_3} [inst : CommSemiring U] [inst_1 : CommSemiring V] {φ : U →+* V} {f : Polynomial U},
↑(Polynomial.map φ f) = (PowerSeries.map φ) ↑f- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
- PowerSeriesstatement · cited by 797
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.toPowerSeriesstatement · cited by 96
- PowerSeries.mapstatement · cited by 82
- PowerSeries.extproof · cited by 69
- Polynomial.coeff_coeproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassFactorizationAt.map_ne_zero_of_ne_topproof · cited by 3
- Polynomial.IsDistinguishedAt.map_ne_zero_of_eq_mulproof · cited by 2
- Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_mapproof · cited by 2