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

[Ray <ray...@gm...>]

On 10/19/2018 11:00 AM, Richard Fateman wrote:
> I think this question really has two parts.
>
> 1. Given some formula  (say, the binomial expansion), can Maxima
> substitute particular values (like 3.5   or 1/3) for particular names,
> like n.
>
> 2. Can Maxima be prompted to show that it knows this formula
> or something equivalent by issuing some command  (for this
> particular case, powerseries()  or taylor() ).
>
> The answer to part 1, is generally yes, unless the formula violates some
> general rules (like it divides by zero, or is incompatible with the
> Maxima
> simplification process)
>
> The answer to part 2 depends on the particular form.  There are huge
> collections of identities and special forms catalogued in math reference
> books.  Steering Maxima to come up with a particular arrangement of
> a formula may or may not succeed.  The question then changes to --
> is there a practical reason to include this particular arrangement in
> Maxima's algorithms?
>
> We can (as humans) refer to the online  collection
> https://dlmf.nist.gov/
>
> Less clear is how to match the capabilities of existing
> (or prospective) computer systems to
> make use of this kind of information in solving problems.
>
> As a very simple general statement,  if the reference document
> says   A=B
> should the program simplify A to B   or the reverse?
> (Or neither.  Or ... depends...)
>
> RJF
It's my experience, after some time, that rephrasing the question as
A-B=0
is proper in a large number of cases.  And then the whole expression is
simplified to zero.  This is common in Algebraic Geometry and /should
/be common in Electronic Engineering: E-I*R=0 actually reflects reality
better than the various forms E=I*R, I=E/R, R=E/I.   In the 80's I found
that the computer verification of identity problems could flow through
easily, whereas A=B confounded them.

RayR