[Maxima-bugs] [ maxima-Bugs-2588816 ] exp doesn't taylorize

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Bugs item #2588816, was opened at 2009-02-11 12:39
Message generated for change (Comment added) made by crategus
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Category: None
Group: None
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: exp doesn't taylorize

Initial Comment:
exp(taylor polynomial) --/--> taylor polynomial:

 (%i5) exp(taylor(x,x,0,3));
 (%o5) %e^x

Some powers do taylorize:

 (%i6) (1 + taylor(x,x,0,3))^(3/8);
 (%o6) 1+(3*x)/8-(15*x^2)/128+(65*x^3)/1024+...

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>Comment By: Dieter Kaiser (crategus)
Date: 2009-02-14 16:35

Message:
Code to handle a taylor expansion as argument to the function exp() has
been added.
This code has been added to the existing function simpexp in file
simp.lisp.

Now Maxima gets:

(%i41) exp(taylor(x,x,0,3));
(%o41) 1+x+x^2/2+x^3/6 /* with linear display the continuation is not
shown */

No more changes. The handling of noun/verb expressions is still
inconsistent.

Examples:

(%i43) 'exp(1.0);
(%o43) 'exp(1.0)  /* Does not evaluate as expected */

(%i42) 'exp(taylor(x,x,0,3));
(%o42) 'exp(x)    /* Does not taylorize correctly */

The original bug is fixed. Closing this bug report.

Dieter Kaiser

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Comment By: Dieter Kaiser (crategus)
Date: 2009-02-11 18:05

Message:
This could be the code to handle noun/verb properties more consistent. This
code includes the handling of a taylor expansion as argument:


(defmfun $exp (x)
  ;; Do not simplify. 
  ;; There are tests which depend on an unsimplified 
  ;; verb expression.
  (list '(mexpt) '$%e x))

(defprop %exp simp-exp operators)
(defprop $exp %exp alias)
(defprop %exp $exp reversealias)

(defun simp-exp (x y z)
  (oneargcheck x)
  (setq y (simpcheck (cadr x) z))
  (cond (($taylorp (second x))
         ;; taylorize exp(taylor(...))
         (return-from simp-exp
           (meval
             (list '($taylor)
                   (list '(mexpt) '$%e ($ratdisrep (second x)))
                   (cadr ($taylorinfo (second x)))))))
        (t (simplifya (list '(mexpt) '$%e y) z))))


This could be the results for %e^taylor(x,x,0,5) and exp(taylor,x,x,0,5):

(%i10) %e^(taylor(x,x,0,5));
(%o10) 1+x+x^2/2+x^3/6+x^4/24+x^5/120

(%i11) exp(taylor(x,x,0,5));
(%o11) 1+x+x^2/2+x^3/6+x^4/24+x^5/120

Dieter Kaiser

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