Subject: Discussion related to cado-nfs
List archive
- From: "Thomas D. Dean" <tomdean@wavecable.com>
- To: Pierrick Gaudry <pierrick.gaudry@loria.fr>, Paul Zimmermann <Paul.Zimmermann@inria.fr>
- Cc: cado-nfs@inria.fr
- Subject: Re: [cado-nfs] Cado-nfs Fails in Sqrt
- Date: Thu, 21 Apr 2022 10:02:07 -0700
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On 4/21/22 05:10, Pierrick Gaudry wrote:
After investigating with Pierrick Gaudry, it appears (in one run when he was
able to reproduce the issue) that the two smallest factors 7901783 and
30578437
do appear *both* in gcd(R-A,N) and gcd(R+A,N) for all dependencies that we've
checked, where R and A are the rational and algebraic square roots.
In fact, these factors are so small that they belong to the factor base.
I can not make an opinion whether this can produce strange behaviours
regarding the probability that a dependency can separate them.
Theoretical considerations meet practical implementation details, here.
This is definitely a very atypical input for NFS.
Regards,
Pierrick
I have an example that produces the same error for length 143.
I also have two examples where the factor completes for length 123!
- [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/19/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/19/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/20/2022
- Message not available
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Pierrick Gaudry, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Pierrick Gaudry, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Pierrick Gaudry, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Emmanuel Thomé, 04/22/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Pierrick Gaudry, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Thomas D. Dean, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Pierrick Gaudry, 04/21/2022
- Re: [cado-nfs] Cado-nfs Fails in Sqrt, Paul Zimmermann, 04/21/2022
- Message not available
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