Re: if-expression and variables

On 05/03/2011 04:21 AM, Ralf Hemmecke wrote:
> Dear Stefan,
>
> as others already have pointed out, for Axiom, your question is not 
> really well posed.
>
> In Axiom
>
>   if x<10 then 2*x else 5*x^2
>
> is *not* an expression (as you might know it from other untyped CAS 
> like Mathematica or Maple), but rather a programming language 
> construct. In other words, if Axiom sees this, it is evaluated. So the 
> result is either 2*x or 5*x^2 depending on the (boolean) outcome of 
> the evaluation of x<10.
>
> I think, Bill suggested to use something like InputForm. There it 
> would be possible to represent an if-expression unevaluated.
>
> But you should rather say what you actually want (it's not the same 
> what you expect).
>
> In order for us to suggest you a proper way to handle your use case, 
> you should tell us why you want a piecewise function and (more 
> important) what you later want to do with that function.
>
> Until we have that information, everything would be just digging in 
> the dark.
>
> Ralf
Ralf

But the question is not intrinsically a "programing construct".  With 
some (bulky) symbolic logic constructs one can express it in a 
mathematical sense.
That is: set membership and "exclusive or".  I wouldn't have the 
slightest idea how to implement it in Axiom; nonetheless questions like 
this have non programmatic expressions.  For instance Prolog has an 
explicit resolution syntax that is reasonably obvious and supports 
embedding logic conditions on and on.   As I recall you can even extend 
it to second order logic.