-----------------------------------------------------------------
Maple is OK, while none of the Mathematica versions can calculate
this integral correctly.
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-- NOT FIXED BUGS ARE DANGEROUS: THEY TEND TO GET MORE SEVERE --
-----------------------------------------------------------------
Quality of CASs is our #1 care.
So our little demo continues.... Hello again from the VM machine
which hopefully soon will be used by CAS manufacturers to the
benefit of their customers.
This example demonstrates YET ANOTHER case of bad defects in the
Wolfram Research Quality Assurance process. Consider, it cannot
trap & fix efficiently regression bugs.
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N[-Sqrt[3] Log[2-Sqrt[3]]/6 - Sqrt[2] Log[Sqrt[2]-1]/6 - Pi/12]
NIntegrate[1/((1+z^2)^(1/2) + (1+z^2)^(7/2)), {z, 0, Infinity}]
0.326115
0.326115
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N[Integrate[1/((1+z^2)^(1/2) + (1+z^2)^(7/2)), {z, 0, Infinity}]]
-----------------------------------------------------------------
VERSION OUTPUT RESOLUTION
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Mathematica 6.0 0.849714 <---------------------------- BUG #2
Mathematica 5.2 Unevaluated <------------------------- BUG #1
Mathematica 4.2 0.849714 <---------------------------- BUG #2
Mathematica 3.0 Unevaluated <------------------------- BUG #1
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Explanation.
The Unevaluated output is interpreted as a defect in accordance
with our extended point of view of bug we had described, taking
into account its economical aspect.
All Maple versions since 1996 to 2007 calculate this integral
correctly.
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If the same bugs exists through numerous software releases,
I think that is valuable public information.
It just should not happen.
-- Brad Cooper
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Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/
Cyber Tester, LLC
http://maple.bug-list.org/
Maple Bugs Encyclopaedia
http://www.CAS-testing.org/
CAS Testing
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"We must understand that technologies
like these are the way of the future."
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