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 jasonp 2006-09-20 04:46

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

 Chris Card 2006-09-20 14:09

Hi Jason,
[QUOTE=jasonp;87527]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[/QUOTE]
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

 jasonp 2006-09-20 15:17

[QUOTE=Chris Card;87555]Just be careful, there are a few typos in Cohen that confuse the issue.
[/QUOTE]
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

 Chris Card 2006-09-20 16:03

[QUOTE=jasonp;87561]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[/QUOTE]

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

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