Theorems · Theorem · commutative algebra

PowerSeries.IsWeierstrassDivision.isWeierstrassFactorization

∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] {g q : PowerSeries A} {r : Polynomial A}
  (hg : (PowerSeries.map (IsLocalRing.residue A)) g ≠ 0)
  (H : (PowerSeries.X ^ ((PowerSeries.map (IsLocalRing.residue A)) g).order.toNat).IsWeierstrassDivision g q r),
  g.IsWeierstrassFactorization (Polynomial.X ^ ((PowerSeries.map (IsLocalRing.residue A)) g).order.toNat - r) ↑⋯.unit⁻¹

Defined in

Mathlib.RingTheory.PowerSeries.WeierstrassPreparation

Cited by

1 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsLocalRing