[ maxima-Bugs-609464 ] 1+%e,numer and %e^%e,numer

Hello Richard,

I have thought about the problem of the extra test in simplifya, but I have
found no other solution. (I have not tried to find a complete new concept to
handle the constants. You know I have not your experience.)

Because we don't do the numerical evaluation for the symbol $%e in meval1, we
have to check again every symbol in simplifya to get the desired consistent
results. Perhaps the order of the tests can be optimized. I have chosen:

(defmfun simplifya (x y)
  (cond ((and $numer $%enumer (atom x) (eq x '$%e))
         (setq x %e-val))
        ...

When we add at last the following code to the function simpcheck every function
will simplify accordingly too:

(defmfun simpcheck (e flag)
  (cond ((specrepp e) (specdisrep e)) 
        (flag e) 
         ;; Set $%enumer to allow numerical simplification
        (t (let (($%enumer $numer)) (simplifya e nil)))))

We will get numerical results for sin(%e), gamma(%e), ... when $numer is TRUE,
but no numerical evaluation for $%e in expressions like sin(%e^x).

In one of my last postings I have reported a wrong change. The change has to be
added to the function pls and not plusin (I have tried both places):

(defun pls (x out)
  (prog (fm plusflag)
     (if (mtimesp x) (setq x (testtneg x)))
     (when (and $numer (atom x) (eq x '$%e))
       ;; Numercical value for $%e when $numer is TRUE
       (setq x %e-val))
     ...

With the four changes to the simplifier the numerical evaluation and
simplification of $%e is consistent and works for the user like the other
constants %i, %pi, ... Even nested expressions like %e^(%e^(2*x+1)) will work
fine. The testsuite and the share_testsuite will have no problems. Only one test
changes: gamma(%e),numer; will simplify to a numerical result.

The only way of doing this faster and without a change to the simplifier I have
found is to cut out the flag %enumer, but then %e^x will simplify to 2,17...^x.

So, should we implement the changes to the simplifier?

Dieter Kaiser


-----Urspr?ngliche Nachricht-----
Von: Richard Fateman [mailto:fateman at cs.berkeley.edu] 
Gesendet: Montag, 18. Mai 2009 07:07
An: Dieter Kaiser
Cc: maxima at math.utexas.edu
Betreff: Re: [Maxima] [ maxima-Bugs-609464 ] 1+%e,numer and %e^%e,numer

Can these patches be put somewhere else?  You are checking the setting  
of $numer and $enumer   an enormous number of times.
At least once for every atom in every expression that is ever simplified..

I think that this should be done in a different way, if at all possible.

for example,

have two core simplifiers.  One for $numer=true   and another where 
$numer = nil.  Then it doesn't have to be checked everywhere.

RJF