Theorems · Definition · commutative algebra
HahnSeries.SummableFamily.powers
{Γ : Type u_1} →
{R : Type u_3} →
[inst : AddCommMonoid Γ] →
[inst_1 : LinearOrder Γ] →
[IsOrderedCancelAddMonoid Γ] → [inst : CommRing R] → HahnSeries Γ R → HahnSeries.SummableFamily Γ R ℕA summable family of powers of a Hahn series x. If x has non-positive orderTop, then
return a junk value given by pretending x = 0.
- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.orderTopproof · cited by 103
- HahnSeries.SummableFamilystatement · cited by 88
Cited by28
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.powers_toFunstatement and proof · cited by 14
- HahnSeries.SummableFamily.powerSeriesFamilyproof · cited by 13
- HahnSeries.SummableFamily.powers_of_orderTop_posstatement · cited by 4
- HahnSeries.SummableFamily.powers_zerostatement · cited by 4
- HahnSeries.inv_singleproof · cited by 3
- HahnSeries.SummableFamily.binomialFamily_applyproof · cited by 3
- HahnSeries.SummableFamily.one_sub_self_mul_hsum_powersstatement and proof · cited by 2
- HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_posproof · cited by 2
- HahnSeries.SummableFamily.binomialFamily_orderTop_posproof · cited by 2
- HahnSeries.SummableFamily.hsum_powerSeriesFamily_mulproof · cited by 1
- HahnSeries.isUnit_of_isUnit_leadingCoeff_AddUnitOrderproof · cited by 1
- HahnSeries.SummableFamily.powerSeriesFamily_hsum_zeroproof · cited by 1