# Find the representative cycle location in the persistence diagram

I know that some toolbox such as Dionysus can also return the representative points which are on the boundaries of the cycles (topological features of a point cloud). I can clearly extract these points using the TDA toolbox in R which acts as a wrapper on the Dionysus and several other TDA toolbox. However, I wonder what is the theory behind it. Can someone please explain it in short or guide me to the papers where I can read more about it. I'm familiar with the reduced boundary matrix and how it is possible to compute the persistence homology using this matrix, however, I'm curious if Dionysus takes advantage of this matrix to detect the boundaries.