[Maxima] constants, simplification, numerical evaluation

Stavros Macrakis macrakis at alum.mit.edu
Sat Mar 15 03:24:37 CDT 2008


Treating exp(x) as an elementary function distinct from %e^x is a terrible idea.

It would simplify numer, but would complicate many other cases.

  exp(x)-%e^x => 0
  log(exp(x)) => x
  exp(x+y)/exp(x) => exp(y)
  factor(exp(2*x)-1)
  integrate
  radcan
  limit
etc. etc.

I suppose you could uniformly represent a^b as exp(b*log(a)) but then
you'd have to change everything in Maxima that handled "^" to handle
exp instead. Do you really want to represent x^2 as exp(2*log(x))?

          -s

On Sat, Mar 15, 2008 at 12:56 AM, Robert Dodier <robert.dodier at gmail.com> wrote:
>  It seems like we could make Maxima simpler and more consistent
>  by treating exp(x) like other "elementary" functions (trig, hyperbolic,
>  etc) and applying to exp(x) the same rules for numeric computation
>  as for the other functions. Instead of simplifying exp(x) to %e^x,
>  exp(x) should be preserved. With no %e in sight during simplification,
>  we can be rid of %enumer which is nothing but trouble anyway,
>  and get useful and predictable numerical behavior without making
>  up more special cases.
>
>  Robert
>
>
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