On Mon, Oct 5, 2009 at 1:38 PM, Leo Butler <l.butler at ed.ac.uk> wrote:
> On Mon, 5 Oct 2009, Stavros Macrakis wrote:
>
> < Yes, it is accurate. You could also show the same thing with '+', which
> < might motivate the behavior better:
> <
> < 1+2.0 => 3.0
> < '(1+2.0) => 3.0
> < '(x+1+2.0) => x+3.0
>
> These examples muddy the water,
The intent was to *clarify* the water by showing the parallel between the
operation of adding 1 (or x+1) to 2.0 to the operation of taking the sin of
2.0.
> because they clearly are
> 'simplifications'. There is some arbitrary line that separates a
> 'simplification' from an 'evaluation' (e.g. in your examples above, one
> can say that the '+' function is being evaluated.).
Why would you say that 1+2=>3 is an "evaluation" (though not in Maxima
terms), but x+2*x => 3*x is an "evaluation"? What about %i+2*%i?
The line is not arbitrary at all for mathematical functions. As I mentioned
in my last mail, where it gets somewhat more arbitrary is with operators
like "integrate".
> I was trying to find the line, because it is not where I would naively put
> it.
>
The line is very simple (except as I say for cases like 'integrate'). ALL
automatic transformations of expressions involving Maxima functions are
simplifications.
Things also get muddy for user-defined routines (better not to call them
functions...) -- users can define mathematical functions but only through
the pattern-matching mechanism.
-s