Real and Complex Fields [HB 42]

Removals and Changes:

• The range of inputs to the intrinsics Eisenstein and WeierstrassSeries has been refined. The precision argument has been made into a parameter in the case of series and removed otherwise. The result from Eisenstein will be in a series ring over the field of fractions of the input coefficient ring if one exists and will give an error otherwise if division by zero occurs.

• A new algorithm for the DedekindEta function is used which evaluates a sum (as described by Cohen) rather than a product (as was done by the former algorithm). The algorithm for computing Delta has been switched so as to use the DedekindEta function rather than the the Eisenstein function. There have been significant improvements in speed in both cases. It is no longer necessary for a series to be over a field for Delta to be applied and the precision argument has been removed.

New Features:

• The classical multivariate $\theta$ function has been implemented for column matrices c and z and an element of the Siegel upper half-space.

Bug fixes:

• A bug in each of Eisenstein and WeierstrassSeries has been fixed.

• A bug in JacobiTheta when zero is given as the first argument has been fixed.