Sorry, I was in the mountains for a bit and missed some conversation. Mike H: Do you want any assistance in your current task?
Robert B: In response to your question after my last e-mail, assuming I understand it correctly, I am under the assumption that only points declared explicitly in the generators are considered. (And perhaps fixed points should be declared with 1-cycle generators?) I realize this may not be backwards compatible, and so I'm wondering what the best course of action here is. Someone asked me a great question a couple of days ago that made me realize that something should be emphasized here, even if it is a bit basic. A permutation group as defined in Sage (and GAP) is three objects: a set, an action/representation, and an underlying group. Unfortunately, the best way to define a permutation group is usually to instead define the corresponding action/representation. Of course, this gives a group and it also brings along more structure (transitivity, primitivity, etc.). But, technically, it is not "a group" and is more appropriately "an action." GAP blurs this difference, but always maintains the action as the primary structure (as Rob's recent example illustrates), even if its primary purpose is to examine the underlying group and even if it calls the structure "a group". Traditionally, the set on which the action acts is a formal object (formal in the mathematical sense, it has no underlying structure). This is true in GAP, although the domain of an action is limited to natural numbers (although there is no underlying structure or order that is assumed). In Sage, this isn't true, and the underlying set is assumed to be well-ordered (the natural numbers as a set plus the structure of order). At least, this is true in Sage currently before an arbitrary action set is implemented. Rob: In response to your question about a coset class.. We have discussed briefly the idea of a PermutationSubgroup class which would inherit certain information from a parent group/action, and I think the idea of a method for a complete list of coset reps, or transversal reps, etc., fits well into such a class. Jason -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
