Skip to main content

For calculations in the curve complex

Project description

PyPI version PyPI license Travis build status

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 – 3.8. 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.

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

curver-0.4.1.tar.gz (129.7 kB view hashes)

Uploaded Source

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page