[Maxima] solve and nth roots of ( - 1 )
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
explain (for fellow neophytes) a safe path to a useful result, given the
state of maxima.
The result of the exploration is that a safe path,
I think, is to replace all of those unwanted factors at
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.
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