Re: [Maxima-discuss] Is there a way to expand ((1 + y )^ (1/n)) for y and n > 0?

[Richard F. <fa...@be...>]

On 10/19/2018 8:25 AM, Ray wrote:
> It's my experience, after some time, that rephrasing the question as
> A-B=0
> is proper in a large number of cases. 
There are two distinct problems:

   The zero-equivalence problem, which tests: is A-B  zero.
This is easier to compute and there are even heuristics, like evaluating 
A-B at
some number of random points, or expanding in Taylor series.
  In general, however, it is undecidable,
but in restricted domains, or in particular examples, it can be easily 
computed.

The simplification problem, which is:
given an expression E,  find the expression E'  with the lowest
"complexity"   (e.g.  fewest number of characters...)  such that
E-E' is equivalent to zero.

In the simplification problem, the practical issue is which direction
to drive known transformations, e.g.  A(x)--> B(x)  for some x in E,
or the reverse, B-->A.

For instance, should sin(x) be converted to exponentials, simplified, and
maybe converted back?  What about sin(x)^2   or  sin(2*x)  or ....
And that is not even going beyond high-school mathematics.