When to simplify complete elliptic integrals?

It seems to me that some people might prefer elliptic functions over 
gamma functions, so making the transformation all the time may be 
unsatisfactory to some people.
How to control this situation is analogous to lots of others, though.

In general, we have many identities to call upon in simplification, and 
controlling their direction is difficult.
For a simple example,
which is preferable,  2*sin(x)*cos(x) or sin(2*x)   ?  Do you want 
powers or products of trig, or multiple-angles?

One way of addressing the user-interface aspect of this has been adopted 
by some rival CAS...
that is, a simplification command that says you prefer to see the answer 
in terms of some set of functions.

So simplify( ....., gamma)    would try to make the result appear in 
terms of gamma functions.
    simplify(...., elliptic_ec)    the other way.
    simplify(cos(x),exp)  would produce complex exponentials
   simplify(atan(x),log)    etc  might be useful.
   simplify(...., factor)  might do the obvious thing too.

now how to specify  trig(multiple angles)  is, to me, not obvious.
Nor is it obvious how to write the simplification program that does all 
this.

But if you look at the many Maxima flags and special programs, maybe 
they can be unified under a common interface.
[This does not mean that the internals should be made inefficient by 
converting them all to "rules".  there is still a need for programs like 
ratsimp etc.]

Note that almost all the work of a CAS can be characterized by such a 
call to simplify...

simplify ( [describe problem to be solved], [kind of solution expected])





Thus Dieter Kaiser wrote:
> Hello Ray,
>
> I would prefer that the function can simplify itself accordingly. It seems to me
> more useful to put as much knowledge about a function into the simplier as
> possible.
>
> A call to an extra function which can do a simplification only for some special
> values seems to me not very efficient.
>
> Dieter Kaiser
>
> -----Urspr?ngliche Nachricht-----
> Von: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] Im
> Auftrag von Raymond Toy
> Gesendet: Freitag, 27. Februar 2009 20:25
> An: Maxima List
> Betreff: [Maxima] When to simplify complete elliptic integrals?
>
> Just noticed that the documentation for elliptic_kc and elliptic_ec says
> to use makegamma to convert these functions to gamma functions when
> possible.  Thus elliptic_ec(1/2) remains elliptic_ec(1/2).  But call
> makegamma and we get an expression involving gamma(1/4).
>
> Is that how the simplification of elliptic_ec should be done?  Should
> elliptic_ec(1/2) returned the gamma expression itself?
>
> Ray
>
>
>
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