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Hi all, here’s a brief summary of the 12th week of my GSoC:
# line 29: set the next element from the current branch and update # accorndingly c[l] += 1 element = ~(computed_words[l - 1])
should be replaced with
# line 29: set the next element from the current branch and update # accorndingly c[l] += 1 if l == 0: element = identity else: element = ~(computed_words[l - 1])
since we might be at the bottom level with . In this case, python doesn’t yell at you for looking up computed_words[-1] since negative indices wrap around the list in python. Yet another silly mistake that’s incredibly hard to track down! I hope that it will work properly from now on, and I’ll have to include some more tests to it.
def center(self): return self.centralizer(self)
was used. This can be updated later when I (or someone else) figures out the polynomial-time algorithm.
In : from sympy.combinatorics.named_groups import * In : S = SymmetricGroup(4) In : ds = S.derived_series() In : len(ds) Out: 4 In : ds == AlternatingGroup(4) Out: True In : ds == DihedralGroup(2) Out: True In : ds == PermutationGroup([Permutation([0, 1, 2, 3])]) Out: True
demonstrating the well-known normal series of groups that solves the symmetric group on 4 letters. Note that the normal closure algorithm was already there thanks to the work of Mario, I just improved it a bit and added some applications.
I wrote docstrings for the new stuff, and my current work can be found on my week10 branch. There will be some comprehensive test following the new additions (and I’ll need GAP to verify the results of some of them, probably). It seems that Todd-Coxeter won’t happen during GSoC since there’s just one more week; instead, I plan to focus on improving disjoint cycle notation and group databases.
 Derek F. Holt, Bettina Eick, Bettina, Eamonn A. O’Brien, “Handbook of computational group theory”, Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2005. ISBN 1-58488-372-3
Exploring and venting about quantitative issues
Adventures of a would-be do-gooder.
Mathematics related discussions
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
Most of the blog moved to blog.krastanov.org