Discussion related to cado-nfs

[Zimmermann Paul <Paul.Zimmermann@inria.fr>]

       Dear Meng,

> Date: Sat, 29 Mar 2014 08:46:39 +0800 (CST)
> From: meng  <qsmeng@126.com>
> 
> Dear Paul,
>    Thank you for your email. I just now read the params.c220. 
>    In recent version some partial parameters  on polynomial are: degree , P 
> ,  nq.  In versions before March,2013 there is another parameter  lq, which 
> disappeared in later version. Different  polynomials will be generated for 
> different set of parameters.  So the number of polynomials is very big. Is 
> there some general consideration on the choice of these parameters? 
>    I expect some discuss on this problem in this mail list.
>    Thank you.
>    Best regards,
> Qingshu Meng

lq was the number of small primes q used in Kleinjung's 2008 polynomial
selection algorithm : for each leading coefficient a_d, we tried values of
\ell = p_1 p_2 q_1 q_2 ... q_{lq} with P < p1, p2 < 2P.

Now we only use the parameter nq, which is the number of values of
q_1 q_2 ... q_{lq} (together with corresponding roots) tried for each
p_1 p_2 product.

Since for degree d there can be up to d roots for each q_j, there might be
up to d^{lq} roots for each q_1 q_2 ... q_{lq} term, thus in most cases we
try only one q_1 q_2 ... q_{lq} product. For example with degree 5 and
nq=625 we can take lq=4.

I hope this clarifies things. Feel free to propose improvements.

Paul