#### afactors (17.3.99)

##### Werner Heiss

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?

##### Michael Monagan (18.3.99)

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.

##### Nils Bruin (19.3.99)

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.

##### Helmut Kahovec (19.3.99)

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.