For calculations in the curve complex

Project description

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.

Quickstart

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('s_0.s_1.s_0') == S('s_1.s_0.s_1')
True
>>> 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)
True
>>> f.is_conjugate_to(g)
False

Features

• Solves the word problem for mapping class groups.

• Performs Nielsen–Thurston classification of 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

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