[Maxima-bugs] [ maxima-Bugs-910008 ] Combining Taylor series of different orders

[SourceForge.net <no...@so...>]

Bugs item #910008, was opened at 2004-03-04 12:06
Message generated for change (Settings changed) made by robert_dodier
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=910008&group_id=4933

Please note that this message will contain a full copy of the comment thread,
including the initial issue submission, for this request,
not just the latest update.
>Category: Lisp Core - Taylor
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: Combining Taylor series of different orders

Initial Comment:
taylor(exp(x),x,0,2) - taylor(exp(x),x,0,0)
    => x + x^2/2 + ...

This is wrong.  The result should be 0+... (order 0).

taylor(exp(x),x,0,2) - taylor(exp(x),x,0,1)
      =>  0 + ...

taylor(exp(x),x,0,2) * taylor(exp(x),x,0,5)
       => 1 + 2*x + 2*x^2 + ...

This time, the printed results are correct: the
expansion is only as good as the longest of the
component expansions.

But taylorinfo of the result is [[x,0,2]], that is,
taylor thinks that it is 0 + 0*x + 0*x^2 + ...

taylor(taylor(exp(x),x,0,2),x,0,5)
    => 1 + x + x^2/2 + ...

This is correct, and the taylorinfo is correctly
[[x,0,2]], but shouldn't it give a warning?

taylor(x^2,x,0,1)/x politely gives a warning ("0+...
assumed to be zero in Taylor"), but the result has
taylorinfo [[x,0,2]].  Shouldn't it have taylorinfo
[[x,0,1]]?

         -s


----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=910008&group_id=4933