Theorems · Theorem · commutative algebra
MvPowerSeries.weightedOrder_monomial
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {d : σ →₀ ℕ} {a : R} [inst_1 : Decidable (a = 0)],
MvPowerSeries.weightedOrder w ((MvPowerSeries.monomial d) a) = if a = 0 then ⊤ else ↑((Finsupp.weight w) d)The weightedOrder of the monomial a*X^d is infinite if a = 0 and weight w d otherwise.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- Finsuppstatement and proof · cited by 5,255
- ENatstatement · cited by 4,985
- AddMonoidHomstatement · cited by 3,230
- map_zeroproof · cited by 1,614
- MvPowerSeriesstatement and proof · cited by 659
- Finsupp.weightstatement and proof · cited by 90
- MvPowerSeries.monomialstatement and proof · cited by 69
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.weightedOrder_monomial_of_ne_zeroproof · cited by 2
- MvPowerSeries.order_monomialproof · cited by 0