On 5/16/06, Robert Dodier <robert.dodier at gmail.com> wrote:
>
> On 5/15/06, Stavros Macrakis <macrakis at gmail.com> wrote:
>
> > I think you need to declare F complex *as a function*, not just declare
> it
> > to be both complex and a function. After all, as Barton points out,
> > ordinary mathematical notation often uses the same symbol for both a
> > function and a constant.
>
> I don't see how Maxima can allow the same symbol to be
> declared a constant and a function, because that makes
> expressions like F + G ambiguous, right?
Well, it would if Maxima supported this notation with the interpretation F +
G = lambda([x],F(x)+G(x)); does the positional derivative package do this
?
Of course, since Maxima in general doesn't impose any semantics, you can
certainly *use* that notation; it would be nice if we had a standard
functional composition operator, too. "." can be used, but there is only
one of those.
If F as a variable and F as a function were the same thing, then you
couldn't assign F a value (F:3) and a functional value (F(x):=x) at the same
time. But you can. Of course, you can also assign F a functional value
(F:lambda([x],x).... That said, Maxima in general doesn't manipulate
lambda-expressions intelligently.
So far as I know there are no symbols which are both
> constants and functions in Maxima at present.
> The gamma function is gamma and the Euler-Mascheroni
> constant is %gamma; nothing else comes to mind.
You have a point there....
-s