Generapy documentation

Generapy provides arbitrary-precision numerical algorithms for algebraic curves, Riemann theta functions, Abelian functions, and integrable systems. It uses mpmath for numerical types, arithmetic, matrices, and precision contexts.

The public API is independent of the mpmath namespace. Functions use mpmath.mp by default and accept a keyword-only ctx argument when a separate numerical context is required.

For an overview of the mathematical conventions and available methods, start with Algebraic curves and Abelian functions.

Contents:

• Algebraic curves
  • Conventions
  • The Curve class
  • Topology
  • Periods and Riemann data
  • Places, paths, and integration
  • Abel maps and lattice reduction
  • Validation and result records
• Abelian functions
  • Riemann theta functions
  • Curve data for Kleinian functions
  • Kleinian functions
• Examples
  • Baker’s genus-two addition formula
  • Bernatska’s genus-three trigonal curve
  • The Bobenko–Reyman–Semenov-Tian-Shansky top
  • Computing the Bobenko curve data
  • Kovalevskaya’s original theta-function solution
  • Manakov motion from genus-two Kleinian functions
  • Neumann–Moser motion on a genus-three curve
  • Ônishi’s sigma and determinant identities
• References