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Submitted by : (unknown) at: 2007-11-17T22:25:13-08:00 (10 years ago)
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The antiderivative should be \atan(x)^2, however:

axiom
integrate(2*atan(x)/(1+x^2),x)

\label{eq1}{\arctan \left({x}\right)}^2(1)
Type: Union(Expression(Integer),...)
axiom
D(%,x)

\label{eq2}{2 \ {\arctan \left({x}\right)}}\over{{x^2}+ 1}(2)
Type: Expression(Integer)
axiom
D(atan(x)^2,x)

\label{eq3}{2 \ {\arctan \left({x}\right)}}\over{{x^2}+ 1}(3)
Type: Expression(Integer)

Maybe this is related to bug #293, i.e., Axiom choosing the wrong branch of \atan, or #141?

Yes, it is related to #293 --kratt6, Tue, 29 Aug 2006 04:55:37 -0500 reply
Look at
axiom
f x == 2*atan(x)+atan(2*x/(x^2-1))
Type: Void

Differentiating, we see that f is constant

axiom
D(f x, x)
axiom
Compiling function f with type Variable(x) -> Expression(Integer)

\label{eq4}0(4)
Type: Expression(Integer)

However, f is not continuous at 1, and indeed,

axiom
numeric f(%pi)
axiom
Compiling function f with type Pi -> Expression(Integer)

\label{eq5}3.1415926535897932385(5)
Type: Float

Drawing the function makes the situation quite clear...

Category: Aldor Library Compiler => Axiom Library Status: open => fix proposed

Status: fix proposed => fixed somewhere

no patch available

http://fricas.svn.sourceforge.net/viewvc/fricas/trunk/src/algebra/gaussian.spad.pamphlet?r1=257&r2=358&view=patch

This was done in rev 418 of wh-sandbox, not FriCAS...

Yes, but the link is to Fricas not the wh-sandbox.

Status: fixed somewhere => fix proposed




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