Hi Martin,
Martin RUBEY writes:
> You are very right. The name TAYLOR is somewhat misleading. There is a
> bug(fix) you should consider (applying) when using taylor together with
> sums:
>
> http://sourceforge.net/tracker/index.php?func=detail&aid=663873&group_id=4933&atid=104933
>
Is this checked into CVS? If so, I have it already. Come to think of it,
I've been building from CVS, and thus is what I call rc4 the same as what
the rest are? I'm using the HEAD tag in updating.
> (well, the second of the two)
>
> The following happens in unpatched maxima if you feed taylor with a sum
> that contains the expansion variable as a limit:
>
> (C1) taylor(sum(k,k,0,m),m,0,3);
>
> (D1)/T/ k + . . .
>
> Concerning extensions: The algolib group at inria developed software for
> maple, it is certainly worth it to do the same for maxima. However, this
> is maybe a demanding task.
>
> http://algo.inria.fr/libraries/libraries.html#gdev
>
> (you are into chemistry, not maths, aren't you?)
>
I'm a theoretical chemist, so math is good part of what I do. As to
porting something from maple to maxima, sounds good, but I'd really
have to learn lisp then, right? :)
> Martin
>
>
> > 3. It seems that TAYLOR is somewhat more clever than the documentation
> > would indicate. Consider:
> >
> > (C1) f(x):=1+1/x+exp(-x)*(1+1/x);
> > 1 1
> > (D1) f(x) := 1 + - + EXP(- x) (1 + -)
> > x x
> > (C2) taylor(f(x),x,inf,2);
> > 1 1 - x
> > (D2)/T/ 1 + - + . . . + (1 + - + . . .) %E + . . .
> > x x
> >
> > This is neither a Taylor or Laurent series, but is very useful in
> > assymptotic analysis of expressions. I don't know how robust this
> > behavior is, for example:
> >
> > (C1) taylor(sin(x)/(1+x),x,inf,3);
> > TAYLOR encountered an essential singularity in:
> > SIN(x)
> > -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
> >
> > Rather than giving an error, it might be nice to have the option of
> > keeping the sin (or any other essentially singular function, like
> > exp(-x)) explicit and taylor expanding the rest; i.e.,
> >
> > sin(x)/x -sin(x)/x**2 + ...
> >
> >
> > In any event this behavior is undocumented.
> >
> > David
> > _______________________________________________
> > Maxima mailing list
> > Maxima@www.math.utexas.edu
> > http://www.math.utexas.edu/mailman/listinfo/maxima
> >
>
>
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