Abstract: Given a fixed number of generators for a DGA (differential graded algebra), if there are fewer relations among them, the DGA tends to be larger as a vector space. The extreme cases are polynomial DGAs and DGAs with trivial products. To compute the homology efficiently, one may need to use different algorithms depending on the number of relations. In this talk, I will demonstrate several algorithms I use in my computation of some Ext rings in algebraic topology. Most of the algorithms rely on the theory of Groebner bases. I will give an introduction to Groebner bases before the algorithms.
