1 | initial version |

From the documentation for generic cell complexes cited by @jpilab:

This module defines a class of abstract finite cell complexes. This is meant as a base class from which other classes (like SimplicialComplex, CubicalComplex, and DeltaComplex) should derive. As such, most of its properties are not implemented. It is meant for use by developers producing new classes, not casual users.

In particular, there is no way for a Sage user to use a "cell complex"; you can instead work with a simplicial complex, a Delta complex, or a simplicial set. There are plenty of examples of all of those in the documentation.

Simplicial sets can be very efficient; to define a 10-dimensional sphere, for example, you only have to specify a 10-dimensional simplex and a 0-dimensional simplex. Delta complexes are somewhat more efficient, and simplicial complexes are the least efficient, in terms of numbers of simplices required.

(Here's a question: if Sage were to implement CW complexes, for example, how should it encode the gluing maps? Is there a good way to describe a continuous function in a computer algebra system like Sage? With a good answer to this, we could think about how to handle the rest of the implementation.)

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.