Alec,

Perfect, that's just what I needed.  Much better.

Since the NumberField constructor should complain if the next
polynomial (the quotient of the division) is not irreducible, the
students can just proceed on faith that the result of the division is
the remaining portion of a factorization and assume it is correct when
there is no error.

Thanks!

Rob

On Apr 14, 8:06 pm, Alec Mihailovs <alec.mihail...@gmail.com> wrote:
> On Apr 14, 2:08 pm, Rob Beezer <goo...@beezer.cotse.net> wrote:
>
> > Rinse, repeat.  First iteration is below.  By the time I get to degree
> > 3 the factorizations are taking about 8 hours.  My question: is there
> > a more efficient way to do this?
>
> Divisions are faster than the factorization - divide by (x-a), then by
> (x-b), then by (x-c). Now, the last step takes a long time, but it is
> not actually necessary - the polynomial is x^2 + (c + b + a)*x + c^2 +
> (b + a)*c + b^2 + a*b + a^2, so dividing it by (x-d), we get (x+a+b+c
> +d).
>
> Alec

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