TITLE: Computational software in Algebraic Topology?
QUESTION [30 upvotes]: I was wondering if there is any good software out there that allows you to do specific computations in algebraic topology. For example:

Create a simplicial complex/set and ask questions about its homology, cohomology;
Build manifolds using handle decompositions;
Calculate homotopy limits, colimits.

Something quite flexible and robust in the vein of MAGMA
Thank you.

REPLY [2 votes]: Although it might now be exactly what you are looking for (e.g. lack of homotopy-theoretic constructions), but there is a nice computational package called javaPlex that "implements persistent homology and related techniques from computational and applied topology, in a library designed for ease of use, ease of access from Matlab and java-based systems, and ease of extensions for further research projects and approaches." 
JavaPlex allows straightforward construction of chain complexes and things like the Mayer-Vietoris sequences, as well as computational techniques for persistent homology.
Link: http://git.appliedtopology.org/javaplex/