# Curver¶

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.
• 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 User Guide¶

This part of the documentation, which is mostly prose, begins with some background information about Curver, then focuses on step-by-step instructions for getting the most out of Curver.

## 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.