[Maxima-bugs] [ maxima-Bugs-593357 ] Various problems with Limit and Atan2

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Bugs item #593357, was opened at 2002-08-09 23:36
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: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: Various problems with Limit and Atan2

Initial Comment:
limit(-atan2(sin(x),1/x),x,0)

returns

   - FALSE

Note that this only happens when the argument 
expression is negated (!).

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

limit(atan2(x,2*x),x,0)
and
limit(atan2(2*x^2,x^2),x,0)

give the error

Atan2(0,0) has been generated.

But the first should give IND, and the second should give 
atan(2).

-----------

limit(atan2(x*abs(a),x),inf)

correctly gives atan(abs(a)), but

limit(atan2(x,abs(a)*x),x,inf)

gives the noun form

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



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>Comment By: Raymond Toy (rtoy)
Date: 2006-11-08 22:05

Message:
Logged In: YES 
user_id=28849

Current CVS (including the fix for bug 626697 does this:

limit(-atan2(sin(x),1/x),x,0) -> nounform
limit(atan2(x*abs(a),x),inf) -> atan(a)
limit(atan2(x,abs(a)*x),x,inf) -> atan(1/a)

limit(atan2(x,2*x),x,0) and limit(atan2(2*x^2,x^2),x,0) both
return atan2(0,0) generated.

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