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Computing Riemann Theta Functions

Bernard Deconinck, Matthias Heil, Alexander Bobenko, Mark van Hoeij, and
Markus Schmies.

The Riemann theta function is a complex-valued function of g complex
variables. It appears in the construction of many (quasi-) periodic solutions of
various equations of mathematical physics. In this paper, algorithms for its
computation are given. First, a formula is derived allowing the pointwise
approximation of Riemann theta functions, with arbitrary, user-specified
precision. This formula is used to construct a uniform approximation formula,
again with arbitrary precision.

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See this NSF nugget on this topic.
Maple implementation.