[sage-devel] Re: Group of units in Z_n
Hello, After more than 5 years, there is now a ticket implementing a unit_group() method for IntegerModRing: http://trac.sagemath.org/ticket/17317 (needs review). Peter Op zaterdag 19 september 2009 05:14:57 UTC+2 schreef Rob Beezer: Sage-Devel, I've got it in my head to implement the group of invertible elements in Z_n as a useful tool for teaching introductory group theory. There is of course, a very simple and straight-forward classification of these abelian groups. But for someone new to the topic, they display quite a bit of variety - sometimes, cyclic, sometimes not, a variety of orders for the elements, and a variety of subgroups. I'd say they might even look unpredictable to a novice. In IntegerModRing there are a few relevant methods whose name begins with unit and a few that begin with multiplicative. These are useful for students, and unit_gens will be useful for my purposes. My intent would be to implement the group so that all a student ever saw was the actual integers mod n. Under the hood, the classification and generators might provide an efficient implementation. For example, rather than having multiplicative_subgroups return each subgroup as a list of generators, it might be possible to actually build the subgroups so they can be queried about order, cyclic-ness, etc. So I'd try to make the group implementation general enough to also represent the subgroups. So this won't necessarily make Sage any more powerful, but it might be a great teaching tool for basic concepts of group theory, at least up until the classification of finite abelian groups. Has this group been implemented somewhere and I missed it? Is there some other powerful machinery for rings that might make this easier to implement? Any code elsewhere for a similar structure or purpose that I might look to for help in designing this? Any general advice or suggestions? Thanks! Rob -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: Group of units in Z_n
Rob, Please do this! I am always having to do some hack in my number theory class for this, and it is very annoying (as you have discovered) not to have this. It is somewhere very far down my to-do list for Sage. Actually, I'm surprised there isn't some hidden structure where it lurks, as you suggest in your last paragraph. Thanks! - kcrisman --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Group of units in Z_n
Hi Karl-Dieter, Well, I guess I *am* doing this as I put together something very quick and sloppy last night, which has helped formulate my ideas for a better version (this approach was due to some good advice from William). Let me know if you need something messy and incomplete, but serviceable, right away. ;-) Good chance I might call on you for some number-theoretic advice along the way. Rob On Sep 21, 6:17 am, kcrisman kcris...@gmail.com wrote: Rob, Please do this! I am always having to do some hack in my number theory class for this, and it is very annoying (as you have discovered) not to have this. It is somewhere very far down my to-do list for Sage. Actually, I'm surprised there isn't some hidden structure where it lurks, as you suggest in your last paragraph. Thanks! - kcrisman --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Group of units in Z_n
On Sep 21, 11:50 am, Rob Beezer goo...@beezer.cotse.net wrote: Hi Karl-Dieter, Well, I guess I *am* doing this as I put together something very quick and sloppy last night, which has helped formulate my ideas for a better version (this approach was due to some good advice from William). Let me know if you need something messy and incomplete, but serviceable, right away. ;-) Good chance I might call on you for some number-theoretic advice along the way. Nope, not teaching it (or anything at all, in fact) this semester; next up spring 2011. But I think this will help a lot of other people, since Sage is so natural for NT and plus William's book is already out there... - kcrisman Rob On Sep 21, 6:17 am, kcrisman kcris...@gmail.com wrote: Rob, Please do this! I am always having to do some hack in my number theory class for this, and it is very annoying (as you have discovered) not to have this. It is somewhere very far down my to-do list for Sage. Actually, I'm surprised there isn't some hidden structure where it lurks, as you suggest in your last paragraph. Thanks! - kcrisman --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Group of units in Z_n
Francis, On Sep 19, 2:12 am, fwc f.cla...@swansea.ac.uk wrote: I have a draft of an implementation of the group of units for a finite field, which overlaps, of course, with the group in question. I modelled it on John Cremona's unit group code for number fields (sage/ rings/number_field/unit_group.py). Thanks for the pointer to Cremona's work, and I'll take a close look at your patch. If you put it on Trac, can you cc me (rbeezer)? Rob --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
