Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] {g : PowerSeries A} {f : Polynomial A} {h : PowerSeries A}
(H : g.IsWeierstrassFactorization f h), f.degree = ↑(((PowerSeries.map (IsLocalRing.residue A)) g).order.lift ⋯)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Top.topstatement · cited by 9,680
- Polynomialstatement and proof · cited by 5,681
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- PowerSeriesstatement and proof · cited by 797
- Polynomial.degreestatement · cited by 643
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.ResidueFieldstatement · cited by 156
- PowerSeries.orderstatement · cited by 92
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionproof · cited by 1