mersenneforum.org > Math Text for computational algebraic number theory?
 Register FAQ Search Today's Posts Mark Forums Read

 2006-09-20, 04:46 #1 jasonp Tribal Bullet     Oct 2004 3·1,181 Posts Text for computational algebraic number theory? Does anyone have a recommendation for a text on this subject? I've realized that I'm not going to be able to implement an NFS square root (or understand NFS, for that matter) without understanding this subject better. There's Cohen's 'A Course In Computational Algebraic Number Theory', but I'm concerned that it's a bit dated by now. I'd prefer something more modern, that can deal with the algorithms used by latter-day NFS. It doesn't have to be a basic text either, I'll just keep rereading it until I understand :) Thanks, jasonp
2006-09-20, 14:09   #2
Chris Card

Aug 2004

13010 Posts

Hi Jason,
Quote:
 Originally Posted by jasonp Does anyone have a recommendation for a text on this subject? I've realized that I'm not going to be able to implement an NFS square root (or understand NFS, for that matter) without understanding this subject better. There's Cohen's 'A Course In Computational Algebraic Number Theory', but I'm concerned that it's a bit dated by now. I'd prefer something more modern, that can deal with the algorithms used by latter-day NFS. It doesn't have to be a basic text either, I'll just keep rereading it until I understand :) Thanks, jasonp
I implemented the NFS square root algorithm based on studying (over many months I should say) Cohen, and the papers by Montgomery and Nguyen. I think everything you need is in there, although it's probably a good idea to have a few other books on ANT to refer to. The trickiest algorithms you need (IMO) are those for calculating an integer basis (Round2) and decomposition of ideals into prime ideals - if you can crack those you'll be a long way down the road. Just be careful, there are a few typos in Cohen that confuse the issue.

Chris

2006-09-20, 15:17   #3
jasonp
Tribal Bullet

Oct 2004

DD716 Posts

Quote:
 Originally Posted by Chris Card Just be careful, there are a few typos in Cohen that confuse the issue.
Does anyone have the 2000 reprinting of this book? I wonder if those typos got fixed. The local university library appears to have it too...

jasonp

2006-09-20, 16:03   #4
Chris Card

Aug 2004

2028 Posts

Quote:
 Originally Posted by jasonp Does anyone have the 2000 reprinting of this book? I wonder if those typos got fixed. The local university library appears to have it too... jasonp
I have the 2000 reprinting, and there are typos in it which weren't in the Errata published on the web. I reported several typos to M. Cohen at the time, but I haven't checked recently to see if they've been added to the Errata.

Chris

 Similar Threads Thread Thread Starter Forum Replies Last Post Nick Number Theory Discussion Group 17 2017-12-23 20:10 MattcAnderson Miscellaneous Math 8 2016-01-03 19:43 wreck Math 4 2010-04-15 07:11 mfgoode Puzzles 2 2006-05-30 09:46 math Homework Help 2 2004-05-02 18:09

All times are UTC. The time now is 04:06.

Sun Jan 23 04:06:35 UTC 2022 up 183 days, 22:35, 0 users, load averages: 0.77, 0.98, 1.05