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Bug introduced in 8.0 or earlier and persists through 11.0.1 or later


This may or may not be related to the bug reported in this question.

I was trying to verify the results of this challenge over on Code Golf with the following code:

p = {{5., 2., 0., 0.}, {2., 5., 2., -2.}, {0., 2., 5., 0.}, {0., -2., 0., 5.}}
SiegelTheta[I*p/Pi, ConstantArray[0, Length@p]]

While I do get the correct result, SiegelTheta throws a bunch of of messages via Range along the lines of:

Range::range: "Range specification in Range[-I,I] does not have appropriate bounds."

I've verified this with all of the example matrices in the linked challenge - the larger the matrix, the more of these messages are thrown. The same happens when I generate random positive definite matrices myself with the following code:

n = 5;
m = RandomChoice[{-1, 1}, {n, n}]
p = N@IdentityMatrix[n] + m\[Transpose].m;
PositiveDefiniteMatrixQ@p
SiegelTheta[I*p/Pi, ConstantArray[0, n]]

I have contacted Wolfram Support and they confirmed that this is a bug. If anyone can reproduce it in earlier Mathematica version, feel free to update the header.

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    $\begingroup$ Using TracePrint[SiegelTheta[(* stuff *)], Range[__], TraceInternal -> True] reveals that an internal auxiliary routine is making the bad Range[] call, so I would consider this a bug. Comparison with the result from version 5.2 (when SiegelTheta[] was a package function as opposed to a built-in) shows consistent results, so the sum is being computed correctly despite the bug. Please file a report when you find the time. $\endgroup$ – J. M. will be back soon Apr 5 '16 at 12:04
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    $\begingroup$ P.S. if you want to scare the people at code golf with the complexity of the problem, link them to this paper. $\endgroup$ – J. M. will be back soon Apr 5 '16 at 12:07

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