Theorems · Definition · commutative algebra
PowerSeries.divXPowOrder
{R : Type u_1} → [Semiring R] → PowerSeries R → PowerSeries RGiven a non-zero power series f, divXPowOrder f is the power series obtained by
dividing out the largest power of X that divides f, that is its order
- Defined in
- Mathlib.RingTheory.PowerSeries.Order
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 69 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffproof · cited by 324
- ENat.toNatproof · cited by 143
- PowerSeries.orderproof · cited by 92
- PowerSeries.mkproof · cited by 52
Cited by21
Results whose statement or proof uses this declaration.
- PowerSeries.Inv_divided_by_X_pow_orderproof · cited by 6
- PowerSeries.coeff_divXPowOrderstatement · cited by 5
- PowerSeries.Unit_of_divided_by_X_pow_orderproof · cited by 4
- PowerSeries.divXPowOrderHomproof · cited by 3
- PowerSeries.Inv_divided_by_X_pow_order_leftInvstatement and proof · cited by 3
- PowerSeries.Inv_divided_by_X_pow_order_rightInvstatement and proof · cited by 3
- PowerSeries.X_pow_order_mul_divXPowOrderstatement and proof · cited by 3
- PowerSeries.divXPowOrder_zerostatement · cited by 2
- PowerSeries.Unit_of_divided_by_X_pow_order_nonzerostatement and proof · cited by 2
- PowerSeries.firstUnitCoeffproof · cited by 2
- PowerSeries.divXPowOrder_Xstatement · cited by 1
- PowerSeries.constantCoeff_divXPowOrderstatement and proof · cited by 1