Magma V2.25-3 Patch Notes

Cyclic Covers¶

• An infinite loop with RankBound was fixed. Reported by M. Stoll.

Groups¶

• A crash when computing the commutator subgroup of two matrix groups has been fixed.
• The database of transitive permutation groups has been extended to include Derek Holt's collection of degree 48 transitive groups. There are 195,826,352 groups stored as 15GB of data. This collection is believed to be all transitive groups of degree 48, up to conjugacy in the symmetric group, but this has not yet been checked. This is an optional database that must be downloaded separately: files TrnGps48_pt0.tar.gz to TrnGps48_pt9.tar.gz from http://magma.maths.usyd.edu.au/magma/download/db/.
• A bug when using the OrderEqual filter in the Subgroups command, when the group has type GrpPC, and all subgroups have already been computed, has been fixed. Bug reported by Michael Zieve.

Hyperelliptic Curves¶

• A major upgrade of the machinery for computing with hyperelliptic curves and, more generally, curves of genus $2$ has been provided by M. Stoll. The highlights are listed in the five points below:-
• The implementations of the HeightConstant (for Jacobians) and ReducedBasis (for sets of Jacobian points) have been updated for greater efficiency. CanonicalHeight for genus 2 Jacobians over the rationals has also been improved, now using error functions on the Kummer surface.
• New intrinsics DoubleRichelotIsogenies applying to genus 2 curves or genus 2 Jacobians over the rationals have been added. These isogenies are defined over the rationals but are composites of two Richelot isogenies defined over a quadratic field.
• Also included is the intrinsic TwoPowerIsogenies which computes principally polarised abelian varieties of dimension two which are isogenous over the rationals to a genus 2 Jacobian over the rationals by an isogeny of degree a power of two.
• Intrinsics to compute the Mordell-Weil group of hyperelliptic Jacobians of genus 2 over the rationals, MordellWeilGroupGenus2, or, more generally, Mordell-Weil groups of hyperelliptic Jacobians of genus 1 or 2 over, respectively, a number field or the rationals, MordellWeilGroup have been added.
• New intrinsics to compute the minimisation and/or reduction of binary homogeneous forms over the rationals have been added. These are MinimizeAtP and MinRedBinaryForm.

IO¶

• Fixed a bug which only wrote the first 2^31 - 1 bytes when using WriteObject to a file. Reported by M. Grassl.
• Fixed a similar bug that could prevent ReadObject from a file from working with items with 2^31 bytes or more.

Lattices¶

• A bug giving incorrect results in the maps for DualQuotient has been fixed. Reported by M. Zimet.

Local Fields¶

• A problem with applying an automorphism to zero in a p-adic field was fixed. Reported by C. Birkbeck.

Number Fields¶

• A problem with the Round Four algorithm was fixed. Reported by J. Jones.
• IsQuadratic now returns true for all degree 2 fields and also returns an isomorphic radical extension as a FldQuad. Requested by T. Breuer.
• Compositum of two number fields has been made potentially more efficient by checking the smaller degree field for normality first. Reported by A. Sutherland.

Scheme Maps¶

• A new intrinsic ImproveParametrization has been added that, for a given scheme map from the projective line P^1 to an ordinary projective scheme over the rationals, finds a simpler such map by precomposing with a suitable automorphism (over the rationals) of P^1. Contributed by M. Stoll.

System¶

• The database types (as returned by DatabaseType) have changed for almost all databases. User code that checks these types will need to be changed (but should probably use extended types instead; see the next point).
• The database type DB can now be extended with an appropriate string (as returned by DatabaseType). For instance, the extended type for the lattice database is DB["Lat"]. Most intrinsics taking a database as argument now use the extended type.
• Extended types may now be indexed to get the corresponding parameter (which will be either another extended type or a string).
• Extended types may have # applied to them to give the number of parameters of the type.
• The undocumented "custom" database type has been removed.