#### 6.11 afactors (17.3.99)

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.