Algebraic Power Series Rings

• Introduction
• Basics
  • Data Structures
  • Verbose Output
• Constructors
  • PolyToSeries(s): RngMPolElt → RngPowAlgElt
  • AlgebraicPowerSeries(dp, ip, L, e): RngUPolElt, RngMPolElt, Lat, RngIntElt → RngPowAlgElt
  • AlgebraicPowerSeries(dp, ip, e): RngUPolElt, RngMPolElt, RngIntElt → RngPowAlgElt
  • AlgebraicPowerSeries(dp, ip): RngUPolElt, RngMPolElt → RngPowAlgElt
  • EvaluationPowerSeries(s, nu, v): Tup, SeqEnum, SeqEnum → RngPowAlgElt
  • ImplicitFunction(dp): RngUPolElt → RngPowAlgElt
  • Rational Puiseux Expansions
    • RationalPuiseux(p): RngUPolElt → Tup, SeqEnum, RngIntElt
    • Example: Constructors for Algebraic Power Series
• Accessors and Expansion
  • Domain(s): RngPowAlgElt → RngMPol
  • ExponentLattice(s): RngPowAlgElt → Tup
  • DefiningPolynomial(s): RngPowAlgElt → RngUPolElt
  • Order(s): RngPowAlgElt → RngIntElt
  • Expand(s,ord): RngPowAlgElt, RngIntElt → BoolElt, RngMPolElt
  • Example: Accessing an Algebraic Power Series
• Arithmetic
  • AlgComb(c,ss): RngMPolElt, SeqEnum → RngPowAlgElt
  • s + t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt
  • s - t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt
  • s * t: RngPowAlgElt, RngPowAlgElt → RngPowAlgElt
  • Example: Substituting Series into Polynomials
• Predicates
  • IsZero(s): RngPowAlgElt → BoolElt
  • s eq t: RngPowAlgElt, RngPowAlgElt → BoolElt
  • IsPolynomial(s): RngPowAlgElt → BoolElt, RngMPolElt
  • Example: Testing Whether a Series Is Polynomial
• Modifiers
  • ScaleGenerators(s,ls): RngPowAlgElt, SeqEnum → RngPowAlgElt
  • ChangeRing(s,R): RngPowAlgElt, RngMPol → RngPowAlgElt
  • SimplifyRep(s): RngPowAlgElt → RngPowAlgElt
  • Example: Scaling the Generators of a Series
• Bibliography