[Maxima] Rational powers and simplification

Richard Fateman fateman at cs.berkeley.edu
Sun Aug 30 14:51:30 CDT 2009

Stefano Ferri wrote:
> I think this could be a nice feature. This would only affect display
> and not internal representation right? Maybe it could be useful in
> association to a display variable to let users choose between the
> display of rational exponents and  square roots.
> In a humble user opinion :-)

Usually it is a bad idea for the display to stray too far from the 
internal representation because then some obvious properties become false.

Like 2*sqrt(2)  looks like it is a product of two items, but internally 
it is an exponentiation.
Already there is some divergence, in that the expression (a+1)/(b+1)   
is internally (a+1)* (b+1)^(-1),
although the problems it causes are probably outweighed by the benefits.

Also, there are generalizations that you might consider as an issue.

Is 3^(5/3)  supposed to be 3 * 3^(2/3) ?   or do you mean to mess with 
the display of Just SquareRoots?
How about 2^(x+1),  should that become 2*2^x?
How about 2^(x+1/2), should that become 2^x*sqrt(x)?

How about exp(3/2), should that become %e*sqrt(%e) ?

I'm sure there are other cases that would have to be explored.

Also, you may think it is relatively effortless to add a feature, since 
only one programmer (and the computer program) need
be aware of it , but the reading of explanation in documentation is a 
burden on every human who looks at the manual.

Anyway, these are considerations.


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