heyoka.py is a Python library for the integration of ordinary differential equations (ODEs) via Taylor's method. Notable features include:

  • support for both double-precision and extended-precision floating-point types (80-bit and 128-bit),
  • the ability to maintain machine precision accuracy over tens of billions of timesteps,
  • high-precision zero-cost dense output,
  • accurate and reliable event detection,
  • batch mode integration to harness the power of modern SIMD instruction sets,
  • interoperability with SymPy,
  • a high-performance implementation of Taylor's method based on automatic differentiation techniques and aggressive just-in-time compilation via LLVM.

heyoka.py is based on the heyoka C++ library.

If you are using heyoka.py as part of your research, teaching, or other activities, we would be grateful if you could star the repository and/or cite our work. For citation purposes, you can use the following BibTex entry, which refers to the heyoka.py paper (arXiv preprint):

    author = {Biscani, Francesco and Izzo, Dario},
    title = "{Revisiting high-order Taylor methods for astrodynamics and celestial mechanics}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {504},
    number = {2},
    pages = {2614-2628},
    year = {2021},
    month = {04},
    issn = {0035-8711},
    doi = {10.1093/mnras/stab1032},
    url = {https://doi.org/10.1093/mnras/stab1032},
    eprint = {https://academic.oup.com/mnras/article-pdf/504/2/2614/37750349/stab1032.pdf}


The full documentation can be found here.


  • Francesco Biscani (Max Planck Institute for Astronomy)
  • Dario Izzo (European Space Agency)