[GAP Forum] GaloisType is running very long

[Daniel Blazewicz]

Dear GAP forum,

I was executing GaloisType method for several irreducible polynomials of the form x^12+ax+b to find solvable examples. And my loop "hung" at x^12+63*x-450. After 2 days I decided to break the execution. FYI, I use 4 years old laptop with ~2GHz CPU. Do you know if it is expected that GaloisType method can take days (weeks?) for polynomials of 12th degree? GAP forum audience is relatively big. Perhaps someone has an experience in this area...

The only information I found was

1) http://mail.gap-system.org/pipermail/forum/2006/001456.html : "Also the type returned by `GaloisType' is proven correct -- at the cost that such a test might take very long for certain polynomials."
2) http://www.gap-system.org/Manuals/doc/ref/chap66.html : "This function is provided for rational polynomials of degree up to 15. However, in some cases the required calculations become unfeasibly large. For a few polynomials of degree 14, a complete discrimination is not yet possible, as it would require computations, that are not feasible with current factoring methods."

Best regards,
Daniel Błażewicz