-- Wolfram Research QA process defect: Bug in Mathematica 6 - Sum - 2 (Cos, invalid Indeterminate, regression bug) - BUG THE LONG LIVER: 2002-2008
Vladimir Bondarenko
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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Bug in Mathematica 6 - Sum - 1 - (Log, Exp, invalid value)
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-- NOT FIXED BUGS ARE DANGEROUS: THEY TEND TO GET MORE SEVERE --
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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.
First, in 1996, Mathematica 3.0 returns a correct answer. Then,
in 2002, in Mathematica 4.2 fails to calculate this sum.
The functionality is broken!
Next, in 2005, in Mathematica 5.2, the functionality is broken
even deeper, to the extent that it returns a false answer.
The same holds for Mathematica 6.0.2.
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N[(E^(-2*I-Sqrt[3])*((-I)*(-I+Sqrt[3])*E^(I+2*Sqrt[3])*Beta[E^(-2
*I),(1-I*Sqrt[3])/2,0]+I*(I+Sqrt[3])*E^I*Beta[E^(-2*I),(1+I*Sqrt[
3])/2,0]+(-1-I*Sqrt[3])*E^(3*I)*Beta[E^(2*I),(1-I*Sqrt[3])/2,0]+I
*(I+Sqrt[3])*E^(3*I+2*Sqrt[3])*Beta[E^(2*I),(1+I*Sqrt[3])/2,0]+E^
(4*I+Sqrt[3])*(2*I-I*Pi+Log[Csc[1]^2/4])+I*E^Sqrt[3]*(-2+Pi+I*Log
[4*Sin[1]^2]) + 2*E^(2*I+Sqrt[3])*(-4+2*EulerGamma+(1+I*Sqrt[3])*
PolyGamma[0,(1-I*Sqrt[3])/2]+(1-I*Sqrt[3])*PolyGamma[0,(1+I*Sqrt[
3])/2])))/24]
NSum[Cos[n]^2/(n^3 + 1), {n, 1, Infinity}]
0.217243
0.217243
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Sum[Cos[n]^2/(n^3 + 1), {n, 1, Infinity}]
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VERSION OUTPUT RESOLUTION
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Mathematica 6.0 Indeterminate <----------------------- BUG #2
Mathematica 5.2 Indeterminate <----------------------- BUG #2
Mathematica 4.2 Unevaluated <------------------------- BUG #1
Mathematica 3.0 Correct answer OK
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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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