Theorems · Theorem · commutative algebra
Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} (f h : PowerSeries R) {g : Polynomial R},
g.IsDistinguishedAt I →
PowerSeries.constantCoeff h ∉ I → f = ↑g * h → ↑g.natDegree = ((PowerSeries.map (Ideal.Quotient.mk I)) f).order- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement · cited by 1,105
- PowerSeriesstatement and proof · cited by 797
- Ideal.Quotient.mkstatement and proof · cited by 610
- PowerSeries.constantCoeffstatement and proof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.IsDistinguishedAt.isWeierstrassDivisorAtproof · cited by 1