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Hi all, here’s a brief summary of the 11th week of my GSoC.
In : from sympy.combinatorics.named_groups import * In : A = AlternatingGroup(9) In : G = A.pointwise_stabilizer([2, 3, 5]) In : G == A.stabilizer(2).stabilizer(3).stabilizer(5) Out: True
(this is much faster than the naive implementation using .stabilizer() repeatedly), and the centralizer of a group inside a group :
In : from sympy.combinatorics.named_groups import * In : S = SymmetricGroup(6) In : A = AlternatingGroup(6) In : C = CyclicGroup(6) In : S_els = list(S.generate()) In : G = S.centralizer(A) In : G.order() Out: 1 In : temp = [[el*gen for gen in A.generators] == [gen*el for gen in A.generators] for el in S_els] In : temp.count(False) Out: 719 In : temp.count(True) Out: 1 In : G = S.centralizer(C) In : G == C Out: True In : temp = [[el*gen for gen in C.generators] == [gen*el for gen in C.generators] for el in S_els] In : temp.count(True) Out: 6
(it takes some effort to see that these calculations indeed prove that .centralizer() returned the needed centralizer). The centralizer algorithm uses a pruning criterion described in , and even though it’s exponential in complexity, it’s fast for practical purposes. Both of the above functions are available (albeit not documented yet) on my week10 branch.
That’s it for now!
 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
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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
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