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#313 sqrt(x,0) should not give 1 in RealClosedField ←	↑	→ #315 segmentation fault when the compiler processes badly indented macro that contain $Lisp

#314 Wrong answer for integrate(2*atan(x)/(1+x^2),x)

Edit detail for #314 Wrong answer for integrate(2*atan(x)/(1+x^2),x) revision 1 of 8

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Editor: Time: 2007/11/17 22:25:13 GMT-8
Note: Yes, it is related to #293

changed:
-
The antiderivative should be $\atan(x)^2$, however:
\begin{axiom}
integrate(2*atan(x)/(1+x^2),x)
D(%,x)
D(atan(x)^2,x)
\end{axiom}

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

From kratt6 Tue Aug 29 04:55:37 -0500 2006
From: kratt6
Date: Tue, 29 Aug 2006 04:55:37 -0500
Subject: Yes, it is related to #293
Message-ID: <20060829045537-0500@wiki.axiom-developer.org>

Look at 
\begin{axiom}
f x == 2*atan(x)+atan(2*x/(x^2-1))
\end{axiom}
Differentiating, we see that $f$ is constant
\begin{axiom}
D(f x, x)
\end{axiom}

However, $f$ is not continuous at 1, and indeed,
\begin{axiom}
numeric f(%pi)
\end{axiom}

Drawing  the function makes the situation quite clear...

The antiderivative should be , however:

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

(1)

Type: Union(Expression Integer,...)

axiom
D(%,x)

(2)

Type: Expression Integer

axiom
D(atan(x)^2,x)

(3)

Type: Expression Integer

Maybe this is related to bug #293, i.e., Axiom choosing the wrong branch of , 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 is constant

axiom
D(f x, x)

axiom

Compiling function f with type Variable x -> Expression Integer

(4)

Type: Expression Integer

However, is not continuous at 1, and indeed,

axiom
numeric f(%pi)

axiom

Compiling function f with type Pi -> Expression Integer

(5)

Type: Float

Drawing the function makes the situation quite clear...