Paper 5: Computing with the analytic Jacobian of a genus 2 curve by Paul B. van Wamelen The code for this paper takes around 12 seconds to run on a 64-bit 2.4GHz AMD processor. Changes since book release: V2.14: The intrinsic FrobeniusForm has been renamed to FrobeniusFormAlternating. V2.12: Minor updates made to reflect the change in real and complex fields since V2.11 (now based on MPFR rather than PARI). Algorithm changes (possibly due to the above) mean that the results of various calls, while still correct, may not be the same as before. There have been some additions to properly handle this possibility, in three places: + Since MAGens arises from a set, the first matrix may not be the correct choice. A test has been added to check for this, and use the second matrix if so. + The entries in the alpha matrices may now live in degree 8 fields rather than degree 4. The degree in the call to MyPowerRelation has been adjusted to reflect this. + The exact list may be different, leading to a different nullspace of the matrix. The computation of alpha has been changed to reflect this.