tlimit (limits using Taylor polynomials) takes less than one second:
(%i1) f : (sin(tan(x))-tan(sin(x)))/(asin(atan(x))-atan(asin(x)));
sin(tan(x)) - tan(sin(x))
(%o1) -----------------------------
asin(atan(x)) - atan(asin(x))
(%i2) showtime : all;
Evaluation took 0.0000 seconds (0.0000 elapsed)
(%o2) all
(%i3) tlimit(f,x,0);
Evaluation took 0.0468 seconds (0.0470 elapsed)
--Barton
________________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of James Cloos [cloos at jhcloos.com]
Sent: Wednesday, May 15, 2013 05:50
To: maxima at math.utexas.edu
Subject: CPU-hungry limit
I happened to look at Arnold-Trivium-1991.pdf again last night, and
tried the limit therein in maxima to see how well it would do.
It took about 20 minutes of CPU time using sbcl.
(A url to the pdf was posted some time ago in, I think, math-fun.)
(%i1) f : (sin(tan(x))-tan(sin(x)))/(asin(atan(x))-atan(asin(x)));
(%i2) limit(f,x,0);
It returned 1.
Which looks right, given plot2d(f,[x,-1,1]).
Is it expected that maxima would take so long to calculate such a limit?
-JimC
--
James Cloos <cloos at jhcloos.com> OpenPGP: 1024D/ED7DAEA6
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