[GAP Forum] Solving Cubic and Quartic Equations in GAP

[Bill Allombert]

On Wed, Jun 08, 2005 at 11:01:02AM -0400, MCKAY john wrote:
> What does the answer below mean???
> 
> "if at all possible" - for 3-ics and 4-ics it is ALWAYS possible.
> 
> has the answerer provided an expression in radicals for ALL solvable
> polynomial in Z[x]?
> 
> If so, then let's hear about it.
> 
> It is a scandal that no-one to date has done this in symbolic computation.

This is off-topic here, but in my Ph.D. thesis I have developed an algorithm
that could solve this problem for super-solvable Galois extensions of Q
This is quite practical, you can handle polynomial of degree 100 and
more, and it is available in PARI/GP but not in GAP.

The major problem is that the expressions returned are quickly extremely large. 

Cheers,
Bill.