Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsLocalRing A] {g : PowerSeries A} {f : Polynomial A}
{h : PowerSeries A},
g.IsWeierstrassFactorization f h → f.natDegree = ((PowerSeries.map (IsLocalRing.residue A)) g).order.toNat- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
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Cites15
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
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- PowerSeriesstatement and proof · cited by 797
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.ResidueFieldstatement · cited by 156
- ENat.toNatstatement · cited by 143
- PowerSeries.orderstatement · cited by 92
- PowerSeries.mapstatement · cited by 82
- IsLocalRing.residuestatement · cited by 71
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