The most important changes between **GAP** 4.2 and **GAP** 4.3 were:

The performance of several routines has been substantially improved.

The functionality in the areas of finitely presented groups, Schur covers and the calculation of representations has been extended.

The data libraries of transitive groups, finite integral matrix groups, character tables and tables of marks have been extended.

The Windows installation has been simplified for the case where you are installing

**GAP**in its standard location.Many bugs have been fixed.

The most important changes between **GAP** 4.1 and **GAP** 4.2 were:

A much extended and improved library of small groups as well as associated

`IdGroup`

(smallgrp: IdGroup) routines.The primitive groups library has been made more independent of the rest of

**GAP**, some errors were corrected.New (and often much faster) infrastructure for orbit computation, based on a general "dictionary" abstraction.

New functionality for dealing with representations of algebras, and in particular for semisimple Lie algebras.

New functionality for binary relations on arbitrary sets, magmas and semigroups.

Bidirectional streams, allowing an external process to be started and then controlled "interactively" by

**GAP**A prototype implementation of algorithms using general subgroup chains.

Changes in the behavior of vectors over small finite fields.

A fifth book "New features for Developers" has been added to the

**GAP**manual.Numerous bug fixes and performance improvements

The changes between the final release of **GAP** 3 (version 3.4.4) and **GAP** 4 are wide-ranging. The general philosophy of the changes is two-fold. Firstly, many assumptions in the design of **GAP** 3 revealed its authors' primary interest in group theory, and indeed in finite group theory. Although much of the **GAP** 4 library is concerned with groups, the basic design now allows extension to other algebraic structures, as witnessed by the inclusion of substantial bodies of algorithms for computation with semigroups and Lie algebras. Secondly, as the scale of the system, and the number of people using and contributing to it has grown, some aspects of the underlying system have proved to be restricting, and these have been improved as part of comprehensive re-engineering of the system. This has included the new method selection system, which underpins the library, and a new, much more flexible, **GAP** package interface.

Details of these changes can be found in the document "Migrating to GAP 4" available at the **GAP** website, see https://www.gap-system.org/Gap3/migratedoc.pdf.

It is perhaps worth mentioning a few points here.

Firstly, much remains unchanged, from the perspective of the mathematical user:

The syntax of that part of the

**GAP**language that most users need for investigating mathematical problems.The great majority of function names.

Data libraries and the access to them.

A number of visible aspects have changed:

Some function names that need finer specifications now that there are more structures available in

**GAP**.The access to information already obtained about a mathematical structure. In

**GAP**3 such information about a group could be looked up by directly inspecting the group record, whereas in**GAP**4 functions must be used to access such information.

Behind the scenes, much has changed:

A new kernel, with improvements in memory management and in the language interpreter, as well as new features such as saving of workspaces and the possibility of compilation of

**GAP**code into C.A new structure to the library, based upon a new type and method selection system, which is able to support a broader range of algebraic computation and to make the structure of the library simpler and more modular.

New and faster algorithms in many mathematical areas.

Data structures and algorithms for new mathematical objects, such as algebras and semigroups.

A new and more flexible structure for the

**GAP**installation and documentation, which means, for example, that a**GAP**package and its documentation can be installed and be fully usable without any changes to the**GAP**system.

Very few features of **GAP** 3 are not yet available in **GAP** 4.

Not all of the

**GAP**3 packages have yet been converted for use with**GAP**4.The library of crystallographic groups which was present in

**GAP**3 is now part of a**GAP**4 package**CrystCat**by V. Felsch and F. Gähler.

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