Theorems · Theorem · commutative algebra
Polynomial.coe_pow
∀ {R : Type u_1} [inst : Semiring R] {φ : Polynomial R} (n : ℕ), ↑(φ ^ n) = ↑φ ^ n- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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
- Polynomialstatement and proof · cited by 5,681
- PowerSeriesstatement · cited by 797
- Polynomial.toPowerSeriesstatement · cited by 96
- RingHom.map_powproof · cited by 22
- Polynomial.coeToPowerSeries.ringHomproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_mapproof · cited by 2
- Polynomial.IsDistinguishedAt.map_ne_zero_of_eq_mulproof · cited by 2
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionproof · cited by 1
- PowerSeries.IsWeierstrassDivision.isWeierstrassFactorizationproof · cited by 1
- PowerSeries.binomialSeries_natproof · cited by 1