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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:

"{{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:

(* True *)

(* True *)

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

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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

1 Answer 1

Apart from Sjoerd's suggestion of taking the symmetric part of your matrix (mat + Transpose[mat])/2, here is another way:

makesym[mat_?SquareMatrixQ] := 
        UpperTriangularize[mat] + Transpose[UpperTriangularize[mat, 1]]

SiegelTheta[Ω[0.01] // makesym, s]
   1. + 0.*I
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