[Maxima-bugs] [ maxima-Bugs-2843954 ] limit of trig expression

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Bugs item #2843954, was opened at 2009-08-24 20:42
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Limit
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Barton Willis (willisbl)
Assigned to: Nobody/Anonymous (nobody)
Summary: limit of trig expression

Initial Comment:
(%i55) e : (2*sin(x)*z+cos(x)*sin(2*x)-2*cos(x)^2*sin(x))/(z^2+(-sin(2*x)^2-4*sin(x)^2-cos(x)^2-1)*z+sin(2*x)^2-4*cos(x)*sin(x)*sin(2*x)+4*cos(x)^2*sin(x)^2);
(%o55) (2*sin(x)*z+cos(x)*sin(2*x)-2*cos(x)^2*sin(x))/(z^2+(-sin(2*x)^2-4*sin(x)^2-cos(x)^2-1)*z+sin(2*x)^2-4*cos(x)*sin(x)*sin(2*x)+4*cos(x)^2*sin(x)^2)
(%i56) limit(e,z,0);
(%o56) cos(x)/(sin(2*x)-2*cos(x)*sin(x))

Bogus:
(%i57) trigexpand(%);
Division by 0
 -- an error.  To debug this try debugmode(true);

OK:

(%i58) limit(trigexpand(e),z,0);
(%o58) -(2*sin(x))/((4*cos(x)^2+4)*sin(x)^2+cos(x)^2+1)

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>Comment By: Raymond Toy (rtoy)
Date: 2010-03-25 21:05

Message:
I think limit basically evaluates the limit of the numerator and
denominator.  It thinks there are are no problems with either because the
terms without z look fine, but, in fact, are exactly zero for all x.

Not sure what can be done in this case.  I do see that in limitsimp there
is a hack to handle sin(x)^2+cos(x)^2.  I suppose we could do trigexpand in
addition to the hack, but that seems as if it could potentially complicate
limit a lot.


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