# [Maxima] solve and nth roots of ( - 1 )

Edwin Woollett woollett at charter.net
Sun May 24 15:32:09 CDT 2009

```On May 23 Richard Fateman wrote:

>  Let me try to be clear:  If you use a single expression that includes
> (-1)^(1/4),  you are asking for trouble.  If solve produces an
>  expression that includes (-1)^(1/4), it probably also includes 3 more
> expressions with that form.  That's sort of OK, if you keep the 4
>  expressions together as a set of solutions.

My example shows that in, the present incarnation, maxima solve *does*
return a list
with each element containing the factor ( - 1 )^(1/4).

For the neophyte (like me), there is the practical problem of turning this
into useful information for other uses. One of my interests is to understand
and
explain (for fellow neophytes) a safe path to a useful result, given the
present
state of maxima.

The result of the  exploration is that a safe path,
I think,  is to replace all of those unwanted factors at
once with
ratsubst( rectform( ( - 1 )^(1/4) ),  ( -1 )^(1/4),  solvelist ) .

Although this appears to be safe, it is certainly a step
which will be unwelcome to practival users, who
simply want an immediate list of practical roots
of an equation.

>  Or you can pick a particular solution (in the complex plane) and then
>  instead of having the 4 solutions that circulate around, you have fixed
>  them all in place. But then you should remove (-1)^(1/4) in all the
>  roots in the solution set.

This speaks to the design of maxima's solve function. I would welcome
a retooled version which simply listed the four unique complex roots
of  ( - 1 )^(1/4).

Thanks for the feedback on this issue.

Ted Woollett

```