Re: nfisincl question

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Mar 15, 2018 at 07:31:32PM -0300, Ariel Martin Pacetti wrote:
> 
> Hello, today I came with the problem of determining whether (the field given
> by) a quadratic polynomial is contained in a huge and nasty degree 480
> polynomial. I did not wanted the morphism, just a boolean answer (0,1). I
> tried to run nfisincl (which seems like the natural routine), but after one
> hour, and a lot of memory I gave up.
> 
> Instead, I tried polcompositum(p,q), and I checked that the output had the
> same degree as q (the 480 one). This took less than a minute. My question
> (now that I solved the theoretical question) is whether there is some flag
> (I did not find it) that allows nfisincl to give a boolean answer without
> serching for the morphism (as did polcompositum).
> 
> As I said, I solved the problem, but there might be another (more efficient)
> way to do it that I do not know of.

The problem is that nfisincl tries to factor the small polynomial over the
quotient field of the big one. It is usually much faster to do the
opposite. Then you only need to check if there is a factor of the right
degree.

Cheers,
Bill.