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Curver is a program for performing calculations in the curve complex. It implements the Bell–Webb algorithm [BellWebb16] 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 2.7 and 3.4 – 3.6. It also runs on PyPy and Sage.


The use of Python 3 is highly preferred over Python 2. Consider upgrading your applications and infrastructure if you find yourself still using Python 2 in production today. If you are using Python 3, congratulations — you are indeed a person of excellent taste. — Kenneth Reitz

A taste of curver:

>>> S = curver.load(0, 5)
>>> S('s_0.s_1.s_0') == S('s_1.s_0.s_1')
>>> S('S_2.S_3.S_4').is_periodic()


  • Performs Nielsen–Thurston classification of mapping classes.
  • Solves the word problem for mapping class groups.
  • Computes the asymptotic translation length of mapping classes on the curve complex.
  • Computes geodesics in the curve complex.
  • 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