# Algebraic Power Series Rings

- [Introduction](introduction.md)

- [Basics](basics.md)

  - [Data Structures](basics.md#data-structures)

  - [Verbose Output](basics.md#verbose-output)

- [Constructors](cons.md)

  - [`PolyToSeries(s): RngMPolElt → RngPowAlgElt`](cons.md#function-polytoseries-rngmpolelt)

  - [`AlgebraicPowerSeries(dp, ip, L, e): RngUPolElt, RngMPolElt, Lat, RngIntElt → RngPowAlgElt`](cons.md#function-rpa-aps)

  - [`AlgebraicPowerSeries(dp, ip, e): RngUPolElt, RngMPolElt, RngIntElt → RngPowAlgElt`](cons.md#function-algebraicpowerseries-rngupolelt-rngmpolelt-rngintelt)

  - [`AlgebraicPowerSeries(dp, ip): RngUPolElt, RngMPolElt → RngPowAlgElt`](cons.md#function-algebraicpowerseries-rngupolelt-rngmpolelt)

  - [`EvaluationPowerSeries(s, nu, v): Tup, SeqEnum, SeqEnum → RngPowAlgElt`](cons.md#function-rpa-eval)

  - [`ImplicitFunction(dp): RngUPolElt → RngPowAlgElt`](cons.md#function-rpa-imp)

  - [Rational Puiseux Expansions](cons.md#rational-puiseux-expansions)

    - [`RationalPuiseux(p): RngUPolElt → Tup, SeqEnum, RngIntElt`](cons.md#function-rpa-pui)

    - [`Example: constructors`](cons.md#example-ex-da4682)

- [Accessors and Expansion](accessors.md)

  - [`Domain(s): RngPowAlgElt → RngMPol`](accessors.md#function-domain-rngpowalgelt)

  - [`ExponentLattice(s): RngPowAlgElt → Tup`](accessors.md#function-exponentlattice-rngpowalgelt)

  - [`DefiningPolynomial(s): RngPowAlgElt → RngUPolElt`](accessors.md#function-rpa-defp)

  - [`Order(s): RngPowAlgElt → RngIntElt`](accessors.md#function-order-rngpowalgelt)

  - [`Expand(s,ord): RngPowAlgElt, RngIntElt → BoolElt, RngMPolElt`](accessors.md#function-rpa-exp)

  - [`Example: accessors`](accessors.md#example-ex-4231eb)

- [Arithmetic](arith.md)

  - [`AlgComb(c,ss): RngMPolElt, SeqEnum → RngPowAlgElt`](arith.md#function-algcomb-rngmpolelt-seqenum)

  - [`s + t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt`](arith.md#operation-op-plus-rngpowalgelt-rngpowalgelt)

  - [`s - t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt`](arith.md#operation-op-minus-rngpowalgelt-rngpowalgelt)

  - [`s * t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt`](arith.md#operation-op-times-rngpowalgelt-rngpowalgelt)

  - [`Example: arith`](arith.md#example-ex-46bd4b)

- [Predicates](preds.md)

  - [`IsZero(s): RngPowAlgElt → BoolElt`](preds.md#function-rpa-zer)

  - [`s eq t: RngPowAlgElt, RngPowAlgElt → BoolElt`](preds.md#operation-op-eq-rngpowalgelt-rngpowalgelt)

  - [`IsPolynomial(s): RngPowAlgElt → BoolElt, RngMPolElt`](preds.md#function-rpa-isp)

  - [`Example: preds`](preds.md#example-ex-e6b227)

- [Modifiers](mods.md)

  - [`ScaleGenerators(s,ls): RngPowAlgElt, SeqEnum → RngPowAlgElt`](mods.md#function-scalegenerators-rngpowalgelt-seqenum)

  - [`ChangeRing(s,R): RngPowAlgElt, RngMPol → RngPowAlgElt`](mods.md#function-changering-rngpowalgelt-rngmpol)

  - [`SimplifyRep(s): RngPowAlgElt → RngPowAlgElt`](mods.md#function-rpa-simp)

  - [`Example: scale`](mods.md#example-ex-e60c95)