[GAP Forum] degree <5 univariate polynomials solving

[Dima Pasechnik]

Dear Andreas, dear GAP Forum,
> 
> If I understand your problem correctly, you want to use the splitting field of 
> the minimal polynomial. You can use the command SplittingField to create it.
[...]
> To use the commands Eigenvectors or Eigenvalues you have to embed the entries 
> of the matrix in the splitting field first. The result of
> 
> gap> Eigenvectors( L, One(L)*mat );
> 
> may be what you have been searching for.
exactly. Thanks.

It did not cross my mind that one must use  "One(L)*mat" here rather than
just "mat".
IMHO this is inconsistent with the convention when you work with 
GF, as there GF(p) is a subset of GF(p^k), no need for such a cast.

> An idea: Possibly your problem can be examined more efficiently over a finite 
> field, as your matrices have 0-1 entries only.
well, not always (they are actually "collapsed adjacency matrices" of graphs).

Best,
Dmitrii.