Theorems · Definition · commutative algebra
MvPowerSeries.order
{σ : Type u_1} → {R : Type u_2} → [Semiring R] → MvPowerSeries σ R → ℕ∞The order of a multivariate power series is the the minimum total degree over all
exponents d with nonzero coefficient coeff d f.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- ENatstatement · cited by 4,985
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.weightedOrderproof · cited by 37
Cited by45
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_of_lt_orderstatement and proof · cited by 5
- PowerSeries.order_eq_orderstatement and proof · cited by 4
- MvPowerSeries.le_orderstatement · cited by 4
- MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zeroproof · cited by 3
- PowerSeries.le_order_subststatement and proof · cited by 2
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zerostatement and proof · cited by 2
- MvPowerSeries.order_lestatement and proof · cited by 2
- MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zerostatement · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2
- MvPowerSeries.le_order_powstatement · cited by 2
- MvPowerSeries.exists_coeff_ne_zero_and_orderstatement and proof · cited by 1
- PowerSeries.le_order_subst_leftstatement · cited by 1