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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 4 of 8

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Editor: japp Time: 2008/10/14 06:03:22 GMT-7
Note: From Fricas

added:

From japp Tue Oct 14 06:03:22 -0700 2008
From: japp
Date: Tue, 14 Oct 2008 06:03:22 -0700
Subject: From Fricas
Message-ID: <20081014060322-0700@axiom-wiki.newsynthesis.org>

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

The antiderivative should be $\atan(x)^2$ , however:

fricas

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

$\label{eq1}{\arctan \left({x}\right)}^{2}$

(1)

Type: Union(Expression(Integer),...)

fricas

D(%,x)

$\label{eq2}\frac{2 \ {\arctan \left({x}\right)}}{{{x}^{2}}+ 1}$

(2)

Type: Expression(Integer)

fricas

D(atan(x)^2,x)

$\label{eq3}\frac{2 \ {\arctan \left({x}\right)}}{{{x}^{2}}+ 1}$

(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

fricas

f x == 2*atan(x)+atan(2*x/(x^2-1))

Type: Void

Differentiating, we see that is constant

fricas

D(f x, x)

fricas

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

$\label{eq4}0$

(4)

Type: Expression(Integer)

However, is not continuous at 1, and indeed,

fricas

numeric f(%pi)

fricas

Compiling function f with type PiDomain -> Expression(Integer)

$\label{eq5}3.1415926535 \<u> 897932385$

(5)

Type: Float

Drawing the function makes the situation quite clear...

fixed in FriCAS? --kratt6, Thu, 20 Dec 2007 00:56:46 -0800 reply

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

... --gdr, Sun, 18 May 2008 13:42:27 -0700 reply

Status: fix proposed => fixed somewhere

no patch available

From Fricas --japp, Tue, 14 Oct 2008 06:03:22 -0700 reply

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