Magma V2.19 introduces an important collection of tools for identifying the type of a surface and computing its basic invariants.
Other aspects of the package include the ability to recognise various special hypergeometric motives (or data) in terms of Artin representations or (hyper)elliptic curves.
Arithmetic Geometry (Modular Forms)
The performance is greatly enhanced by pre-computing auxiliary tables
so that the initial computation of the logarithms of a factor base
can be avoided. This means that logarithms of individual elements
can be computed immediately if the relevant table is present for the
field under consideration. Tables are currently available for most
finite fields of characteristic 2, 3, 5 or 7 with cardinality up to
2400
(i) Short presentations on standard generators for the orthogonal groups have been installed. As a consequence, short presentations on standard generators are now available for all families of classical groups.
(ii) A new function has been provided for writing an element of a classical
group G
The availability of presentations enables rapid verification of the Composition
Tree for any group whose composition factors exclude exceptional groups of
Lie type. It is planned to add short presentations for the exceptional groups
in the near future.
Linear Algebra and Module Theory
The main functionality is concerned with computing the semisimplification
of a given