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Curver is a program for performing calculations in the curve complex. It implements the Bell–Webb algorithm to determine the Nielsen–Thurston type of a mapping class. This algorithm runs in polynomial time but the constants involved currently make this implementation impractical.

Curver officially supports Python 3.6 – 3.9. Unoffically, it also runs on PyPy and Sage with some care.


Curver is available on PyPI, so it can be installed via:

$ pip install curver --user --upgrade

Once installed, try it inside of Python:

>>> import curver
>>> S = curver.load(0, 5)
>>> S('s_0.s_1.s_0') == S('s_1.s_0.s_1')
>>> f = S('s_0.s_1.s_2.s_3')
>>> g = S('s_0.s_1.s_3.s_2')
>>> h = S('s_0.s_1.S_2.S_3')
>>> f.order(), g.order(), h.order()
(5, 5, 5)
>>> f.is_conjugate_to(g)
>>> f.is_conjugate_to(g)


  • Solves the word problem for mapping class groups.
  • Performs Nielsen–Thurston classification of mapping classes.
  • Solves the conjugacy problem for periodic mapping classes.
  • Computes the asymptotic translation length of mapping classes on the curve complex.
  • Computes geodesics in the curve complex.
  • Computes quotient orbifolds and their quotient maps.
  • Computes the action of mapping classes on H_1.
  • Determines the topological type of multicurves.

The API Documentation

If you are looking for information on a specific function, class, or method, this part of the documentation is for you.

The Contributor Guide

If you want to contribute to the project, this part of the documentation is for you.

There are no more guides. You are now guideless. Good luck.

Indices and tables