Thank you for your comments. Some replies below.
On Mon, Oct 15, 2012 at 1:14 PM, Peter Mueller <[email protected]> wrote: > I'm just teaching algebra, and I was about to recommend to my students to > make some experiments with groups and permutation groups in Sage. Unless I'm > overlooking something, some of the functionality and in particular the > documentation is a mess. > > Let's start with something like > > sage: a = SymmetricGroup(3)('(1,2)') > sage: b = SymmetricGroup(3)('(2,3)') > > For someone who is used to Gap and Magma, the first surprise is that > > sage: 1^a > > produces a NotImplementedError This might be an issue of over-riding the exponentiation of an integer. I guess it could be implemented, at a cost of slowing down the much more common computation of exponentiation on ZZ. > > I don't see in the documents how to apply a permutation group element to an > element. Well, There are various ways: sage: G = SymmetricGroup(3) sage: a = G("(1,3)") sage: b = G("(2,3)") sage: a*b (1,2,3) sage: a(1) 3 sage: a.orbit(1) [1, 3] sage: a.orbit(1)[1] 3 > > sage: a*b > (1,3,2) > > indicates that Sage uses the right action, as do Gap and Magma. After some > experimenting one finds out that a group element a applied to x is a(x). In > my opinion, this quite irritating, for this produces things like > > sage: (a*b)(1) == a(b(1)) > False In Sage, permutations are (correctly, IMHO) implemented as right actions (so that (1)(a*b) = ((1)a)b). The only thing implemented by Sage is the left action. I agree with you that this is unfortunate. > > Are there any plans (or possibilities) to fix such a misconception? (I know, > everyone is invited to help improve and extend Sage, and at some point I > hope to do so ...) > > As to the docs, it seems to me that neither the thematic tutorial, nor the > permutation group pages in the Reference Manual and Constructions Manual > explain or give examples about how to apply permutations. > > The thematic tutorial `Group Theory and Sage' looks particularly odd: It > starts with number theory which has nothing to do with what I would expect > under this heading. The second part then contains no material at all about > how to create and work with self-made permutation groups. I'm not sure what you mean. That paper starts with the basic interface then moves to abelian groups. Do you mean that abelian groups should not be covered in a paper titled "Group theory and Sage"? > > Considering the great possibilities which Sage offers, it is a pity that > especially for finite groups the docs appear unorganized and miss important > topics. Thanks for your interest in improving Sage! > > -- Peter Mueller > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
