Summer is ending :(

A beautiful summer is coming to an end and I am at the last leg of my Gsoc. I must apologize for the erratic posts but its mostly because I was “busy” with other things (mostly enjoying myself in the US of A, eating steaks, going out for barbecues, and enjoying the beautiful Maryland summer weather.)

In the last few weeks I spent a bit of time cleaning up Gray code. It went through a few API changes and I hope to have the subsets and partitions branches merged in within this week. I also implemented a demo of the Permutations branch that involves Polyhedron rotations. I hope to show one involving a Rubik’s cube when I have the Permutation group module in (more on that in a while). I also implemented a residue class and a residue group module as that was missing in the number theory branch of Sympy. That branch needs an overhaul both in terms of functionality as well as the code that is already there and I hope I can get some momentum going in that direction with the code I have written. I also wrote some generators for Permutation groups. This is fairly easy to do now, the basic algorithm is to generate all permutations and filter out those that do not fit the criteria. Of course, generating all permutations is inefficient, and some generators have certain special properties that we can use. For example, the Cyclic group can be generated in linear time as that simply involves a single rotation. Alternating group however requires the generation of all even permutations. Some group generators will probably make use of the specialized algorithms that have been implemented in the iterables section of Sympy.

I have also managed to implement the Schreier sims algorithm but its extremely ugly and unpythonic for now. Algorithms for generating orbits and stabilizer chains are also there but they are fairly inefficient. I hope to clean them up and submit them for a pull request in this week before the hard pencils down date.

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