The command

`evala(AFactors(-t^7-t^3-2*t^6-2*t^2+2))`

didn’t terminate after several hours. Is it normal that it takes so long or might it be a bug?

Yes, you are asking it to compute the splitting ﬁeld which may be degree `7! = 5040`

– it will
have to factor a polynomial of degree 5040 over Z.

The computation blows up. Even degree 5 is non trivial in the general case.

This polynomial is the product of a linear factor and an irreducible degree 6 factor. The
degree 6 factor has galois group S6, so you’re asking maple to construct a degree `6!`

extension (as a degree 2 ext. of a degree 3ext etc.) This is a huge task, so I’d consider it
normal that this takes so long. I can imagine that the answer wouldn’t even ﬁt in your
computer.

IMO there is not a bug here: your polynomial is just too complicated for being decomposed into linear factors by Maple. Look at the following (simple) example:

> restart; > alias(alpha=RootOf(Z^6+Z^5+Z^4+Z^3+Z^2+Z+1)); > expr1:=t^7-1; > evala(AFactor(expr1)); 4 (t - 1) (t - alpha) (t - alpha ) 2 3 4 5 (t + 1 + alpha + alpha + alpha + alpha + alpha ) 2 3 5 (t - alpha ) (t - alpha ) (t - alpha )

Anyway, your polynomial may in fact be partially decomposed into linear factors:

> -t^7-2*t^6-t^3-2*t^2+2; 7 6 3 2 -t - 2 t - t - 2 t + 2 > factor(%); 6 5 4 3 -(1 + t) (t + t - t + t + 2 t - 2) > expr2:=remove(type,%,{linear,constant}); 6 5 4 3 expr2 := t + t - t + t + 2 t - 2 > alias(beta=RootOf(Z^6+Z^5-Z^4+Z^3+2*Z-2)); > map(collect,factor(expr2,beta),[t]); 4 2 3 5 (beta + 2 + beta - beta + beta 4 2 3 + (beta + beta - beta + beta ) t 3 2 2 4 + (beta + 1 - beta + beta ) t + (1 + beta) t 2 3 5 + (beta - 1 + beta ) t + t ) (t - beta)

Apparently, the nonlinear part of this is very complicated. Maple might not be able to decompose it any further.