# SiegelTheta fails to evaluate when given proper arguments

SiegelTheta often returns error messages when I give it arguments that should be of the correct form. For instance, I have a numerical matrix like

M = N[{{1 + π/2, -1, 1 - π/2}, {-1, 1 + π/2, -1}, {1 - π/2, -1, 1 + π/2}}];


and I want to evaluate SiegelTheta[Ω[0.01], s], where

Ω[r_] := I*Inverse[M]/r

s = {0, 0, 0};


but I get the following error message:

SiegelTheta::invmat:
"{{0. + 56.831I,0. + 31.831I,0. + 25.I},{0. + 31.831I,0. + 63.662I,0. +31.831I},
{0. + 25.I,0. + 31.831I,0. + 56.831I}} must be a symmetric matrix with a positive definite
imaginary part."


However, Ω[0.01] does satisfy those conditions, even according to Mathematica:

PositiveDefiniteMatrixQ[Im[Ω[0.01]]]
(* True *)

SymmetricMatrixQ[Ω[0.01]]
(* True *)


I would appreciate any help resolving this issue. I am using Mathematica version 9.0.1.

-
While Im[Ω[0.01]] is positive definite, Ω[0.01] is not. –  bill s Jun 26 '13 at 20:43
Note that Ω[0.01][[2, 1]] === Ω[0.01][[1, 2]] returns False. Also, examine this: Rationalize[#, 0] &@Ω[0.01] –  Sjoerd C. de Vries Jun 26 '13 at 20:53
If you remove the N from the definition of M, you have SymmetricMatrixQ@Ω[0.01] (-> True) –  Jacob Akkerboom Jun 26 '13 at 21:12
@Sjoerd: You're right, I see. It seems from the source code that SiegelTheta determines whether the input matrix is symmetric by subtracting the transpose and finding whether the result is the zero matrix. And while Ω[0.01] == Transpose[Ω[0.01]] evaluates as True, apparently the difference between Ω[0.01] and its transpose is not zero (for instance MatrixRank[Ω[0.01] - Transpose[Ω[0.01]]] evaluates to 2). Do you have any suggestions for how to get around this and get an answer from SiegelTheta? –  Skyler Jun 26 '13 at 21:17
How about: SiegelTheta[(Ω[0.01] + Transpose[Ω[0.01]])/2,s] –  Sjoerd C. de Vries Jun 26 '13 at 21:21