I am developing a Python package for computations in algebraic topology (namely: cohomology and Massey products on manifolds). Basically all the stuff I'm doing requires an explicit triangulation of the manifold $M$ we're working on, by which I mean a simplicial complex $K$ homeomorphic to $M$ with the additional requirement that the individual simplices are embedded (I'm not sure whether it's a standard requirement or not). Now, writing down an explicit triangulation and all the boundary maps is a pain in the ass, already for the torus you have almost too many simplices hanging around. My question is: is there a simple way to generate triangulations for manifolds starting from other data (e.g. a cellular decomposition)?
More precisely, what I would like is:
Given data which can be easily and systematically written down if we know our manifold, obtain a triangulation (given by an array containing the number of cells in each dimension and the boundary maps given as matrices) in an algorithmic way.