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# GAP - history of changes

## GAP 4.12.0 (August 2022)

The following gives an overview of the changes compared to the previous release. This list is not complete, many more internal or minor changes were made, but we tried to keep it to changes which we think might affect some users directly.

### Highlights

• Added the missing perfect groups of order up to two million

Added perfect groups of orders that had been missing in the Holt/Plesken book (newly computed). This increases the number of groups in the perfect groups library from 1098 to 15768. Also added five groups that were found missing in the existing lists. See PR #3925 and #4530 for details.

• The windows installer for GAP has been completely rewritten

There are many changes and minor fixes, the most significant are:

• GAP can be installed globally into "Program Files".
• GAP can also be installed without admin access into the user's home directory.
• Almost all packages work, including those with kernel modules and external programs.
• The default directory for saving is the user's "Documents" folder.
• There is no longer possible to choose which packages are installed.
• Windows versions before 8 are no longer supported.
• Initial support for make install available

This is mostly of interest for downstream packagers, e.g. for Linux distributions. One major caveat is that it does not deal with installing packages (handling that still requires some more planing and thought). The feature is also still rather new and as such is likely to still have rough edges, but we welcome you to try it, and share your feedback with us. See PR #4492.

### Changes to the libgap interface

• #4215 Add GAP_MarkBag, GAP_CollectBags, a minimal interface to the garbage collector
• #4501 Add GAP_CallFunc[0-3]Args
• #4531 Add GAP_IsMatrix
• #4621 Add GAP_NewRange, GAP_NewObjIntFromInt, GAP_ValueInt to the libgap API
• #4644 Make libgap-api.h safe to use from C++ code

### Changes to the GAP compiler

• #4746 Rewrite gac to not use libtool
• #4778 Remove support for static linking from gac, it was rarely if ever used but required a disproportionate amount of effort to keep it working
• #4933 Improve gac to print errors to stderr and in color

### Changes in the documentation

• #4168 Improve the documentation concerning GASMAN, add CollectGarbage
• #4339 Document TensorProduct, ExteriorPower and SymmetricPower (they existed since at least GAP 4.4)
• #4438 Improve documentation for random sources
• #4475 Improve argument checking and documentation for FreeGroup, FreeMonoid, FreeSemigroup, FreeMagmaWithOne, and FreeMagma
• #4529 Document IsNoImmediateMethodsObject officially, so that packages are free to use it (it already existed for a long time)
• #4672 Clarify documentation of IsFFECollection
• #4925 Document IsSquareInt (it has been around for a long time)

### Performance improvements

• #3721 Add optimised SmallestMovedPoint implementation
• #3740 Speed up printing of large permutations
• #4186 Speed up CoefficientsQadic for long results
• #4331 Speed up building stabchain from base and strong generators
• #4411 Speed up automorphism group and group isomorphism computations
• #4411 Speed up IntermediateSubgroups if the smaller subgroup has many orbits
• #4599 Speed up PositionSublist by using Position to search for first entry
• #4622 Speed up AlgebraicExtension and AlgebraicExtensionNC for larger degrees
• #4683 Speed up Embedding for wreath products
• #4836 Speed up calculation of character tables, in particular for solvable groups
• #4874 Speed up computation of the intersection of group cosets in the generic cases and even more so for permutation groups
• #4902 Speed up Exponent for groups with known conjugacy classes
• #4905 Speed up IrrBaumClausen (used for computing character tables of supersolvable groups, including $p$-groups)
• #4910 Speed up LinearCharacters for $p$-groups, and IrrConlon (used for computing character tables of supersolvable groups, including $p$-groups)

### Changes to HPC-GAP

• #3759 Fix an issue with error reporting in parallel threads
• #3761 Fix bugs in HPC-GAP serialization code and improve its tests
• #3822 Make the assertion level (which controls Assert statements) thread local when using HPC-GAP

### New features

• #3858 Add DeclareGlobalName; together with BindGlobal it can be used to replace uses of DeclareGlobalVariable & InstallValue (which are not thread safe and have other dangers)
• #3914 Add InnerAutomorphismGroup attribute for groups
• #3992 Add Pluralize function for strings
• #4074 Add IteratorOfPartitionsSet an iterator for all unordered partitions of a set into pairwise disjoint nonempty sets
• #4104 Add TaylorSeriesRationalFunction and improve Derivative for univariate rational functions
• #4126 Add command line option --version
• #4128 Add OutputGzipFile, in order to create a gzip compressed file
• #4207 Add group constructors PGammaL, PSigmaL, and their methods for permutation groups
• #4219 Add CompositionSeriesThrough
• #4249 Add ARCH_IS_WSL to detect Windows Subsystem for Linux
• #4295 Add OpenExternal, a function for opening files in the OS
• #4334 Add group constructors PGO and PSO
• #4410 Add ListWreathProductElement and WreathProductElementList
• #4465 Add command line option --print-gaproot
• #4557 Add InstallEarlyMethod which allows installing special methods that bypass method selection (and thus its overhead)
• #4893 Add HexSHA256 function for computing SHA256 checksums

### Improved and extended functionality

• #3355 Allow packages to use ISO 8601 dates in their PackageInfo.g files (so YYYY-MM-DD instead of DD/MM/YYYY)
• #3628 Add Info statement triggered when re-assigning already assigned attributes and the info level InfoAttributes is at least 3
• #3643 Start the process of making vector and matrix objects official
• #3668 Support several package instances with same version
• #3713 Add tracing and counting of built-in operations
• #3861 Extend the range of precomputed simple groups from orders up to 10^18 to orders up to about 10^27
• #3901 Allow function-call syntax for general mappings.
• #3920 Admit CentralIdempotentsOfAlgebra for algebras without One
• #3933 Add libtool versioning to libgap shared library
• #3939 Improve handling of temp directory in GAP for Windows
• #3986 Add methods taking machine floats for Sinh, Cosh, Tanh, Asinh, Acosh, Atanh, CubeRoot, Erf, Gamma
• #4000 Enhance NormalClosure to accept a list of normal generators (instead of a group) as second argument
• #4050 Use Pluralize to give correct pluralization in many GAP library methods
• #4099 Passing a .tst file as a command line argument to gap will now invoke Test on it
• #4105 Add an optional third argument to OrderMod that is a multiple of the order one wants to compute
• #4111 Enhance FreeGroup to support the option generatorNames to prescribe the names of the generators
• #4142 Extend BindConstant, MakeConstantGlobal to all object types.
• #4144 Avoid overflows when converting rationals with large denominator and/or numerator to floating point
• #4145 Improve errors messages for various set operations (AddSet, UniteSet, ...)
• #4146 Fix Cite to honor GAPInfo.TermEncoding for its printing; let BibEntry always use encoding "UTF-8"
• #4170 Improve Test to use colors to highlight failures and diffs
• #4201 Support optional transformFunction in Test, similar to compareFunction.
• #4231 Add LoadKernelExtension, IsKernelExtensionAvailable
• #4274 Enable color prompt by default
• #4275 Enable SaveAndRestoreHistory by default
• #4296 Allow function-call syntax for evaluating univariate polynomials
• #4332 Rewrite and officially document PlainListCopy
• #4333 Add GO(1,q), SO(1,q), Omega(1,q), Omega(-1,2,q)
• #4361 Add \in method for GO(e,d,q) and SO(e,d,q) that is based on the stored invariant quadratic form
• #4366 Improve (New)ZeroMatrix, (New)IdentityMatrix, (New)ZeroVector to better reject invalid input
• #4373 Support IsCommutative/IsAssociative for IsCollection, rather than just for IsMagma
• #4483 Write --help output to *stdout* not *errout*
• #4489 The functions GO, GU, Omega, SO, SU, and Sp now allow to specify an invariant form for the group in question; the methods that do the work are provided by the Forms package
• #4506 Change the default representation for perfect groups to IsPermGroup (previously IsFpGroup)
• #4517 Add basic operations for row/column reductions in matrix objects
• #4528 Improve SizeOfFieldOfDefinition such that fail is no longer returned when the first argument is a (Brauer) character
• #4537 Implement IsMinimalNonmonomial for nonsolvable groups
• #4555 Fix PrintFormattingStatus and SetPrintFormattingStatus for the standard output (i.e., when the first argument is "*stdout*" and add a variant that deals with the current output (whatever that may be), reachable by using "*current*" as first argument
• #4632 Document and unify the order in which GAP evaluates function arguments and options
• #4639 Add LatticeSubgroups method for the case IsHandledByNiceMonomorphism
• #4653 Add IsQuasisimpleGroup, IsQuasisimpleCharacterTable
• #4668 Add SpinorNorm
• #4764 Admit g^chi and chi^g for Brauer characters chi and group elements g
• #4810 Enhance SimplifiedFpGroup and IsomorphismSimplifiedFpGroup to transfer attributes (such as size, being abelian etc.) to the simplified group

### Removed or obsolete functionality

• #3694 Deprecate undocumented extra arguments for DeclareGlobalFunction and InstallGlobalFunction
• #3702 Make TmpNameAllArchs obsolete by enhancing TmpName
• #3796 Remove command line option -B which could be used to override the architecture
• #3862 Rename QUIT_GAP, FORCE_QUIT_GAP and GAP_EXIT_CODE to QuitGap, ForceQuitGap and GapExitCode (the old names remain available as synonyms)
• #4493 Remove optional crc argument to LoadDynamicModule and LoadStaticModule
• #4504 Turn IsLexicographicallyLess into an obsolete synonym for \<
• #4519 Make third argument of DeclareRepresentation and NewRepresentation optional, and document that it and the fourth argument are (and always were) unused
• #4655 Rename RadicalGroup to SolvableRadical (the old name is still supported as an obsolete synonym)
• #4697 Disable NaturalHomomorphism for FactorGroup, as it has side effects (code using this should be rewritten to use NaturalHomomorphismByNormalSubgroup instead)

### Fixed bugs that could lead to incorrect results

• #4035 Fix DirectoriesPackagePrograms to ignore case of package name, like LoadPackage does
• #4206 Fix DirectoriesPackageLibrary, DirectoriesPackagePrograms when they are called during package loading
• #4219 Fix IntermediateGroup to not return fail if the index is large but subgroups exist
• #4320 Fix missing outer automorphisms of certain Chevalley groups of type O_n-(q), n>=8 even; this also fixes calculation of certain normalizers in S_n
• #4327 Fix InvariantQuadraticForm for Omega(-1, 2*d, 2^n)
• #4372 Fix argument checking in FreeSemigroup, prevent creation of inconsistent objects
• #4373 Fix AsSemigroup to reject non-associative inputs
• #4396 Fix computation of all maximal subgroups (under specific circumstances, an incomplete list was returned)
• #4411 Fix RankAction to reject intransitive actions instead of returning potentially misleading results
• #4482 Fix bug in MakeImagesInfoLinearGeneralMappingByImages that could lead to errors resp. wrong results if multiplication with coefficients from the right is not defined resp. not commutative
• #4634 Fix test for subgroup conjugacy for cyclic permutation groups (If A,B are cyclic conjugate subgroups of G, and A <= C, with C abelian, the error could have caused a claim of C being conjugate to B)
• #4660 Fix (rare) wrong result for stabilizer computations
• #4664 Fix WreathProduct to return correct generators when given a matrix group and an intransitive top group
• #4665 Fix RootSystem to use the correct field for determining eigenvectors
• #4703 Fix Coefficients for large finite fields created via a polynomial
• #4718 Fix LatticeSubgroup sometimes returning wrong results for matrix groups
• #4822 Fix bug in computing canonical class representative for pc groups which could yield wrong results in larger groups
• #4907 Fix IsTransitive to require that the group actually acts on the given domain (strictly speaking, the previous behavior was "as documented", but it made no sense and led to bugs elsewhere)
• #4992 Fix Gcd for multivariate polynomials to always return a standard associate element

### Fixed bugs that could lead to crashes

• #3808 Fix a crash when using a constant global variable (created via MakeConstantGlobal, such as IsHPCGAP) as index variable of a for loop
• #3825 Fix some crashes caused by running out of memory
• #4407 Fix crash when accessing mat[i,j] and mat[i] is unbound
• #4442 Fix crash when incorrectly accessing a compressed vector v via v{...}[...] or v{...}{...} as if it was a matrix
• #4508 Fix crash in LocationFunc when the input has incomplete location information
• #4544 Forbid installing an operation as method for itself, as that leads to crashes
• #4579 Fix crash when methods for mutable attribute do not return a value
• #4823 Fix crash when QuitGap is called while reading from an InputTextString

### Fixed bugs that could lead to break loops

• #3693 Fix ViewString for string to correctly escape characters needing it
• #3747 Fix unexpected error when testing permutation groups for conjugacy
• #3903 Fix Cycles((),[ ]) to correctly return [ ]
• #4023 Fix the floating point number parser for certain exotic formats, e.g. 1.0e0i_ and 1.0e0i_y now work as intended
• #4037 Change IsPackageLoaded and TestPackage to ignore case of package name, like LoadPackage does
• #4108 Fix some unexpected error when inverting or computing random elements of algebraic extensions of finite fields of size > 256
• #4239 Add missing \= method for IsMultiplicativeElement and IsObjWithMemory (the other direction was already present)
• #4245 Admit non-fields as left acting domains for free (associative or Lie) algebras, and fix the zero-dimensional case
• #4411 Fix an assertion error in AllHomomorphismClasses
• #4427 Fix QuaternionAlgebra bug that caused QuaternionAlgebra( [1], 2, 5 ).1 to error the second time it was invoked
• #4566 Fix an unexpected error in FrobeniusCharacterValue when the rows of the equation system have different lengths
• #4875 Fix an unexpected error when computing conjugacy classes in certain large permutation groups (and other improvements)

### Other fixed bugs

• #3695 Fix Test to correctly handle test outputs which do not end with a newline when using rewriteToFile
• #3931 Do not ignore #@ comments after empty line at start of test file
• #4132 Fix a long standing bug which prevented SetPrintFormattingStatus( "*stdout*", false ); from working as expected
• #4232 Fix a bug where calling NextIterator on a "done" list iterator caused it to seemingly switch back to "not done" status
• #4317 Fix Cite to again properly compute the year in which GAP was released
• #4386 Fix the broken --strict option to BuildPackages.sh, but only if --parallel is not also specified
• #4451 Fix printing of GAP code containing nested logical operators to correctly use parentheses (try e.g. Print(x -> (x = x) = true);)
• #4759 Fix Earns to always returns a list, as documented (and other improvements)
• #4794 Remove incorrect line breaks in the output of StringFormatted
• #4855 Fix SubgroupsSolvableGroup to honor retnorm option even for trivial groups
• #4928 Fix off-by-one error in CopyListEntries that could end up creating lists in which the last element is unbound

### Package distribution

#### New packages redistributed with GAP

• classicpres 1.22: Classical Group Presentations, by Alexander Hulpke, Eamonn O'Brien, Charles Leedham-Green, Madeleine Whybrow, Giovanni de Franceschi
• StandardFF 0.9.4: Standard finite fields and cyclic generators, by Frank Lübeck
• UGALY 4.0.3: Universal Groups Acting LocallY, by Khalil Hannouch, Stephan Tornier

#### Updated packages redistributed with GAP

The GAP 4.12.0 distribution contains 154 packages, of which 121 have been updated since GAP 4.11.1. The full list of updated packages is given below:

## GAP 4.11.1 (March 2021)

### Fixed bugs that could lead to incorrect results

• #4178 Fixed bugs in RestrictedPerm with second argument a range

### Fixed bugs that could lead to crashes

• #3965 Fix potential garbage collector crashes on 64bit ARM systems
• #4076 Fix an infinite loop in BoundedRefinementEANormalSeries if large factors could not be refined, fix protected option of IsomorphismSimplifiedFpGroup, improve documentation of IsAutomorphismGroup

### Fixed bugs that could lead to error messages

• #3980 Fixed Gcd for rational polynomials

### Other fixed bugs

• #3963 Provide automatic decompression of filenames ending .gz (as is in the documentation of InputTextFile)
• #3944 The error checking in PartialPerm has been corrected such that invalid inputs (numbers < 1) are detected
• #4006 Fix gac to ensure that binaries it creates on Linux can load and run, even if a GAP package with a compiled kernel extension (such as IO) is present

### Improved and extended functionality

• #3790 Add further information to the library of simple groups
• #3840 Speed up garbage collection

### Packages

• #4016 Improved etc/Makefile.gappkg (used by GAP packages that want to build a simple GAP kernel extension)

### Fixes/improvements in the experimental way to allow 3rd party code to link GAP as a library (libgap)

• #4081 Enhance GAP_ValueGlobalVariable to supported automatic variables (see DeclareAutoreadableVariables)
• #4258 Fixed GAP_Enter macro so that GAP's recursion depth counter is saved/restored. Without this, if too many GAP errors occurred during runtime a segmentation fault could occur in the program using libgap

### Fixes and improvements for the Julia integration

• #4042 Avoid access to JuliaTLS members by using jl_threadid() and jl_get_current_task() helpers, fix compiler constness warnings in weakptr.c
• #4053 Fix the logic for scanning tasks in the Julia GC
• #4058 Refine the logic for scanning Julia stacks
• #4071 Make the Julia GC threadsafe when used from GAP.jl

### Other changes

• #3922 Build system: New feature to execute BuildPackages.sh in parallel mode by adding --parallel
• #4041 Build system: Fix make check in out-of-tree builds

### Packages no longer redistributed with GAP

PolymakeInterface: Following the withdrawal of the package Convex in GAP 4.11.0 because of being superseded by NConvex, the PolymakeInterface has also been withdrawn. These two packages are now replaced by NormalizInterface and NConvex.

### Updated packages redistributed with GAP

The GAP 4.11.1 distribution contains 151 packages, of which 49 have been updated since GAP 4.11.0. The changes include extending the Transitive Groups Library with representatives for all transitive permutation groups of degree at most 47 (due to Derek Holt), and fixing the ordering of groups of orders 3^7, 5^7, 7^7, 11^7 in the Small Groups Library. For other changes, we refer to the documentation of the packages. The full list of updated packages in the GAP 4.11.1 distribution is given below:

## GAP 4.11.0 (February 2020)

### New features and major changes

• Removed ability to return objects from many error break loops

Many error break loops in GAP used to allow replacing an object in a computation by another one. This ability was very tricky to use, and leads to computation results that are difficult to reproduce. At the same time, supporting this adds complexity to the GAP kernel. We therefore decided to remove this feature. Right now, this is not yet fully done, but we removed about 3/4 of these, and will remove the rest in a future GAP release. (See e.g. PR #2966).

• GAP now contains some C++ code

Therefore, in order to compile it, you need a C++ compiler. See #2667 for the rationale.

• HPC-GAP

The ward tool has been decommissioned in PR #2870. In the future, guard checks will be performed in a different way; however, this code is not yet complete (see PR #2845). In the meantime, guard checking is broken. If you are interested in using HPC-GAP, please consider helping us to fix this and other issues with it.

• Syntax trees

Functions were added which allow converting a GAP function object into an abstract syntax tree which can be parsed and modified from within GAP code (see PR #2628). Moreover, it is possible to convert such a syntax tree (possibly after modifying it) back into a GAP function object (see PR #3371).

### Improved and extended functionality

• #1633 Allow local variables in test files via #@local <list of variables to be local>, and conditional execution of tests via #@if, #@else, #@endif
• #2520 Overhaul tracking of current statement, fixing several bugs where the break loop error message referenced the wrong statement
• #2772 Add support for profiling interpreted code
• #2773 Reorder methods after new implications are added
• #2830 Undocumented functionality has now been extended and documented that allows one to construct the Green's classes of a semigroup that are contained in another Green's class (e.g. constructing the H-classes contained in an R-class)
• #2856 Make AtExit a stack and make DirectoryTemporary more robust
• #2869 Fix + and * methods for a DirectProductElement and a non-list collection
• #2873 The GAP kernel version is now available in the configure script
• #2876 IsomorphismTransformationSemigroup now returns an IdentityMapping for a transformation semigroup
• #2923 Extend obsolete to support multiple levels
• #2936 Add back ViewObj method for generic fields
• #2952 Add command line option --bare to start GAP without even needed packages (developer tool)
• #2960 Add List method accepting an iterator and a function
• #2946, #2955, #2974, #3372 Improve many error messages
• #2985 Improve support for custom list object implementations
• #2998, #2999, #3007 Expose additional functionality related to chars, floats and integers via the libgap API
• #2900 Teach Test to abort test if ctrl-C is pressed
• #2910 Add custom SetDimension implementation, and call SetDimension(A,0) in places creating trivial modules or algebras
• #2924 Improve performance of NormalizerViaRadical
• #3031 Improve performance of ConjugacyClasses for solvable groups
• #3053 More properties can now be preserved when constructing direct products of semigroups
• #3075 Special redispatch for Nat.Hom.ByNS if group is found out to be finite
• #3076 Add IsAutoGlobal for testing whether a variable was declared using DeclareAutoreadableVariables
• #3077 Allow appending to the command line history
• #3078 Avoid memory issues in solvable conjugacy classes routine
• #3080 Method to compute Hall subgroups of arbitrary finite groups.
• #3093 Methods transforming small matrix groups into permutation groups now work for objects of type IsMatrixObj
• #3099 Show a warning when GroupWithGenerators called on a domain
• #3104 Extend IntegratedStraightLineProgram to the situation that some of the input programs return lists of elements
• #3118 Make Refinements an AtomicRecord so it can be added to by users
• #3129 BrauerTableOp now works for cyclic defect such that all Brauer characters lift to characteristic zero
• #3168 Allow input and output to be mixed in Test
• #3207 Display for functions with large literals is improved
• #3626 Customisable names of classes and characters in Display of character tables
• #3621 Add Display method for PC group
• #3209 Enable backtraces with --enable-debug
• #3226 Make last, last2, last3,time and memory_allocated read-only
• #3231 Speed up IsConjugate for IsNaturalSymmetricGroup
• #3247 CloseMutableBasis now returns true if the basis was extended and false otherwise
• #3252 Improve gac to preserve argument names of compiled functions
• #3253 CharacterTableIsoclinic now works for groups of type p.G.p
• #3267 Change StructureDescription of an infinite cyclic group from C0 to Z
• #3278 Improve method for IsSolvableGroup
• #3335 Reduce memory usage on windows when running external programs
• #3365 Add First(list), Last(list) and Last(list,func)
• #3370 Pragmas are now available
• #3376 SortedList now accepts a function as the second argument
• #3383 Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via TwoCohomologyGeneric
• #3384 Improve performance of subgroup calculations (e.g. via ConjugacyClassesSubgroups) in some cases
• #3385 Add FlipBlist, ClearAllBlist, SetAllBlist
• #3387 Add ShowUsedInfoClasses
• #3394 Make the descriptions for TNUMs (which we print in some error messages) more user friendly
• #3399 Support floating point numbers when specifying how much memory GAP should use, for example "-o 2.5G"
• #3420 Give more library methods human-readable names. These are used when profiling
• #3423 Improve gac to support calls to custom function objects
• #3430 NameFunction now is an attribute so that custom function objects can implement support for it
• #3454 Improve error handling for Image, Images, PreImage and PreImages
• #3455 New function DirectProductFamily
• #3459 Add ShowDeclarationsOfOperation helper
• #3473 Improve an AsList method for domains with stored GeneratorsOfDomain
• #3483 Change the pre-set memory limit default from 2GB to 3/4 of physical memory. Use the -o option if you want to change this limit.
• #3501 MaximalSubgroups now works even if tomlib is not available
• #3504 make bootstrap now uses curl if wget is unavailable under macOS
• #3516 Improve performance of the Julia GC integration
• #3520 Clarify when nonabelian simple groups are meant in the documentation
• #3522 Add IsNonabelianSimpleGroup
• #3542 Add --add-package-config-<PACKAGENAME>="<CONFIG_ARGS>" option to BuildPackages.sh where <CONFIG_ARGS> are passed through to the configure script of package <PACKAGENAME>
• #3543 Add PositionSortedBy
• #3551 Add new kernel operations ELM_MAT, ASS_MAT
• #3513 Use posix_spawn in iostreams if available
• #3554 Add basic libgap APIs for working with matrices
• #3564 Add WhereWithVars, an extended version of Where which prints the values of all arguments and locals
• #3566 Optimise operations involving identity permutations, improve printing of permutations
• #3630 Speed up MaximalAbelianQuotient for subgroups of fp groups
• #3579 Speed up writing to global variables
• #3592 The values of computed attributes will no longer be stored automatically in mutable attribute-storing objects
• #3604 Add EuclideanDegree and QuotientRemainder for Z/nZ
• #3619 Randomize is now documented, and its definition changed: note that it is now Randomize(random_source, obj)
• #3620 make html can be used to compile only HTML versions of the GAP manuals, without a PDF.
• #3683 Add etc/Makefile.gappkg, for use in the build system of GAP package with kernel extensions
• #3690 Improve NullspaceModQ to support arbitrary moduli, and renamed it to NullspaceModN (the old name is still available as a synonym)
• #3711 Adjust TestPackage to return information about the test result
• #3715 Allow HPC-GAP to run as a forkable server process
• #3745 Add a new kernel header gap_all.h for use by package authors instead of compiled.h
• #3746 Allow package build systems to detect GAP version by inserting GAP_VERSION into sysinfo.gap
• #3606 Add BindingsOfClosure helper (Work in progress)

### Changed documentation

• #3886 Convert Changes manuals book into markdown
• #2798 Clarify MemoizePosIntFunction documentation
• #2946 Document what a "small integer" resp. "immediate integer" is
• #2953 Document that PermutationGModule works not just for finite fields
• #3101 Remove Section 87.2-5 on "Avoiding multiplication of permutations" in the reference manual (the described functionality does not actually work)
• #3348 Add explanation for a workaround regarding the ^-key on OSX to INSTALL.md
• #3358 Document the two-argument version of Set
• #3360 Improve discoverability of rewriteToFile option in Test
• #3363 Add some information in the documentation of IsPrimitive.
• #3374 Document that InputTextFile should not be used for binary files
• #3449 Clarify and corrects documentation of CompositionMapping
• #3453 Improve documentation of GeneratorsOfDomain
• #3468 New PrintObj method for general domains which know their GeneratorsOfDomain
• #3469 DeclareCategoryCollections, constructors are now documented and parts of the reference manual are refactored
• #3472 Document IsRangeRep and improve the documentation of ConvertToRangeRep, IsRange, and the section Ranges
• #3529 Document CharacteristicSubgroups
• #3591 Improve parts of the documentation in Chapter 41.
• #3615 Document basic representations of objects (IsInternalRep, IsDataObjectRep, IsComponentObjectRep, IsPositionalObjectRep, IsAttributeStoringRep, IsPlistRep)
• #3612 Improves the documentation of Quotient to make it sensible for non-commutative rings, and rings with zero divisors

### Fixed bugs that could lead to crashes

• #3151 Fix crash when ApplicableMethod is called incorrectly
• #3221 Handle infinite recursion in attribute methods
• #3491 Fix crashes when passing invalid arguments to functions for records: \., IsBound\., Unbind\. and \.\:\=
• #3738 Fix bug in CycleStructurePerm for a single cycle of length 2^16 that caused wrong answers and memory corruption

### Fixed bugs that could lead to incorrect results

• #2938 Fix bug related to ImaginaryPart for quaternion algebras
• #3103 This fixes #3097, a problem with Order of automorphism and #3100, a problem with GroupHomomorphismByImages
• #3392 Prevent blist functions that modify an argument in-place (such as UniteBlist) from modifying immutable blists
• #3522 IsSimpleGroup does not imply IsAlmostSimpleGroup anymore
• #3575 Fix bug in calculating x/p for an integer x and permutation p, if p has been 'trimmed'.
• #3603 Fix bug where the result of StandardAssociateUnit could be not a unit.
• #3611 Fix StandardAssociateUnit for polynomial rings to return a polynomial, not an element of the coefficient ring
• #3646 Fix bug in MinimalFaithfulPermutationDegree that reported a too large degree for certain groups representable as subdirect product
• #3662 Fix bug in MaximalSubgroupClassReps that could lead to a wrong result
• #3689 Fix bug in BlistList for two ranges that could lead to wrong results
• #3690 Fix bug NullspaceModQ that could lead to wrong results
• #3733 Fix ConstituentsOfCharacter for Brauer character: its result, when called with a Brauer character as its only argument, was not reliable. (This bug has been reported by Gabriel Navarro.) Also, calling it with a Brauer character table and a virtual Brauer character caused error messages

### Fixed bugs that could lead to break loops

• #3038 Fix RankOfPartialPermSemigroup for partial perm groups with empty GeneratorsOfGroup
• #3052 Fix the viewing of empty transformation semigroups
• #3110 Workaround for Issue #3055 and fix for GQuotient
• #3142 Fix Int and Rat for float values nan, inf, -inf
• #3192 Catch some corner cases for trivial group
• #3331 Fix an issue with IsomorphismGroups if one group is finite and the other is infinite.
• #3375 Improve warnings when using tabs in continuations
• #3401 SSortedLists is not required to be homogeneous anymore
• #3437 Fix a bug with in calculating SubdirectProducts which could sometimes fail on valid input.
• #3559 Fix IsUpperTriangularMat for non-square matrices
• #3571 Fix NrCols and NumberColumns for empty matrices in IsMatrix
• #3763 Fix bug in IrrConlon leading to unexpected errors
• #3865 Fix the code setting up a subgroup data structure by the solvable radical method, which could lead to unexpected errors

### Other fixed bugs

• #2595 Fix missing syntax warning for using undefined global variable
• #2756 Reject invalid AND-filters such as Center and IsAssociative
• #2903 Kernel: make OnLeftInverse use LQUO
• #2908 Fix profiling when IO_Fork from the IO package is used
• #2977 This fixes an infinite recursion if the rank of IsGroup and IsFinite becomes very large
• #3189 Ensure IsHomogeneousList("") return true
• #3229 Fix the fact that the ^^^^ markers on unbound globals would point to the wrong place.
• #3320 Fix the problem whereby if GAP on windows sees a \r, it will remove the next \n, no matter how far away it is.
• #3325 Fix libgap's GAP_ENTER_DEBUG macro (using it previously lead to a linker error)
• #3390 Corrects input limit on 64Bit SetCyclotomicsLimit
• #3395 PrintObj(1.) now correctly prints 1.
• #3400 Fix the line breaking hints in the ViewString method for finite lists.
• #3428 Fix GNU readline detection on OpenBSD, and make the configure test for it more robust
• #3444 Remove obsolete -a command line option
• #3481 Fix bug which caused code which calls PrintCSV many times with a filename to fail eventually
• #3580 Fix potential infinite loop or recursion when computing the size of infinite cyclic groups
• #3847 Fix printing of certain words in free groups (if subexpressions occur as powers iteratedly then nonsense could be displayed, but the data internally was correct)
• #3610 Invalid use of / on ZmodZ (e.g. dividing a unit by a zero divisor) will produce an Error
• #3612 fixes some methods for Quotient, in particular Quotient(R, x, Zero(R)) now returns fail

### Removed or obsolete functionality

• #2237 The undocumented (!) functions InfoRead1 and InfoRead2 are obsolete
• #2237, #2961 Remove the obsolete synonyms MutableIdentityMat (for IdentityMat), MutableNullMat (for NullMat) and SHALLOW_SIZE (for SIZE_OBJ), DEBUG_LOADING (for GAPInfo.CommandLineOptions.D)
• #2919 The undocumented (!) function SetFeatureObj is obsolete; use SetFilterObj resp. ResetFilterObj instead.
• #3185 (Un)HideGlobalVariables is obsolete
• #3269 TemporaryGlobalVarName is obsolete
• #3409 Remove BANNER, QUIET

### Packages

• #3215 Issue tracker, maintainers and contributors are printed in package banners
• #3286 Teach ValidatePackageInfo about the optional License field

### Other changes

• #2709 Rename MultRowVector to MultVector (the old name is still supported, but marked as obsolete)
• #2729 Rename QuaternionGroup to DicyclicGroup, document IsDihedralGroup and IsQuaternionGroup
• #3010 Read lib/transatl.g before any gap.ini file, when GAP is loaded
• #3406 Remove RXVT-shell support for Windows
• #3480 BuildPackages.sh now executes make clean before full build

### New packages redistributed with GAP

• AGT A library of strongly regular graphs on at most 40 vertices, and functionality to inspect combinatorial and algebraic properties of graphs in GRAPE format, by Rhys J. Evans
• CddInterface GAP interface to cdd, by Kamal Saleh
• DifSets Enumeration of the difference sets (up to equivalence) in groups, by Dylan Peifer
• ferret C++ reimplementation of Jeffery Leon’s Partition Backtrack framework for solving problems in permutation groups, by Christopher Jefferson
• images Finding minimal and canonical images in permutation groups, by Christopher Jefferson, Markus Pfeiffer, Rebecca Waldecker, Eliza Jonauskyte
• NCOnvex Polyhedral constructions and computations for cones, polyhedrons, polytopes and fans, by Kamal Saleh, Sebastian Gutsche
• NoCK Computation of Tolzanos’s obstruction for compact Clifford-Klein forms, by Maciej Bocheński, Piotr Jastrzębski, Anna Szczepkowska, Aleksy Tralle, Artur Woike
• RepnDecomp Algorithms for decomposing linear representations of finite groups, by Kaashif Hymabaccus

## GAP 4.10.2 (June 2019)

### Improvements in the experimental way to allow 3rd party code to link GAP as a library:

• Add GAP_AssignGlobalVariable and GAP_IsNameOfWritableGlobalVariable to the libGAP API (#3438).

### Fixes in the experimental support for using the Julia garbage collector:

• Fix of a problem where the Julia GC during a partial sweep frees some, but not all objects of an unreachable data structure, and also may erroneously try to mark the deallocated objects (#3412).

• Fix stack scanning for the Julia GC when GAP is used as a library (#3432).

### Fixed bugs that could lead to crashes:

• Fix a bug in TransformationListList which could cause a crash (#3463).

### Fixed bugs that could lead to incorrect results:

• Fix a bug in ClassPositionsOfLowerCentralSeries. (Reported by Frieder Ladisch) (#3321).

• Fix a dangerous bug in the comparison of large negative integers, introduced in GAP 4.10.1: if x and y were equal, but not identical, large negative numbers then x < y returned true instead of false. (#3478).

### Fixed bugs that could lead to break loops:

• If the group has been obtained as subgroup from a Fitting free/solvable radical computation, the data is inherited and might not guarantee that the factor group really is Fitting free. Added a check and an assertion to catch this situation (#3154).

• Fix declaration of sparse action homomorphisms (#3281).

• LatticeViaRadical called ClosureSubgroupNC assuming that the parent contained all generators. It now calls ClosureSubgroup instead, since this cannot always be guaranteed (this could happen, for example, in perfect subgroup computation). Also added an assertion to ClosureSubgroupNC to catch this situation in other cases. (Reported by Serge Bouc) (#3397).

• Fix a "method not found" error in SubdirectProduct (#3485).

### Other fixed bugs:

• Fix corner case in modified Todd-Coxeter algorithm when relator is trivial (#3311).

### New and updated packages since GAP 4.10.1

GAP 4.10.2 distribution contains 145 packages, including updated versions of 55 packages from GAP 4.10.1 distribution,

A new package MonoidalCategories by Mohamed Barakat, Sebastian Gutsche and Sebastian Posur have been added to the distribution. It is based on the CAP package and implements monoidal structures for CAP.

Unfortunately we had to withdraw the QaoS package from distribution of GAP, as the servers it crucially relies on for its functionality have been permanently retired some time ago and are not coming back (details).

## GAP 4.10.1 (February 2019)

### Fixes in the experimental way to allow 3rd party code to link GAP as a library:

• Do not start a session when loading workspace if --nointeract command line option is used (#2840).

• Add prototype for GAP_Enter and GAP_Leave macros (#3096).

• Prevent infinite recursions in echoandcheck and SyWriteandcheck (#3102).

• Remove environ arguments and sysenviron (#3111).

### Fixes in the experimental support for using the Julia garbage collector:

• Fix task scanning for the Julia GC (#2969).

• Fix stack marking for the Julia GC (#3199).

• Specify the Julia binary instead of the Julia prefix (#3243).

• Export Julia CFLAGS, LDFLAGS, and LIBS to sysinfo.gap (#3248).

• Change MPtr Julia type of GAP objects to be a subtype of the abstract Julia GapObj type provided by the Julia package GAPTypes.jl (#3497).

### Improved and extended functionality:

• Always generate sysinfo.gap (previously, it was only generated if the "compatibility mode" of the build system was enabled) (#3042).

• Add support for writing to ERROR_OUTPUT from kernel code (#3043).

• Add make check (#3285).

### Changed documentation:

• Fix documentation of NumberFFVector and add an example (#3079).

### Fixed bugs that could lead to crashes:

• Fix readline crash when using autocomplete with colored-completion-prefix turned on in Bash (#2991).

• Fix overlapping memcpy in APPEND_LIST (#3216).

### Fixed bugs that could lead to incorrect results:

• Fix bugs in the code for partial permutations (#3220).

• Fix a bug in Gcd for polynomials not returning standard associates, introduced in GAP 4.10.0 (#3227).

### Fixed bugs that could lead to break loops:

• Change GroupWithGenerators to accept collections again (to avoid regressions in code that relied on this undocumented behavior) (#3095).

• Fix ShallowCopy for for a Knuth-Bendix rewriting system (#3128). (Reported by Ignat Soroko)

• Fix IsMonomialMatrix to work with compressed matrices (#3149). (Reported by Dominik Bernhardt)

### Removed or obsolete functionality:

• Disable make install (previously it displayed a warning which often got ignored) (#3005).

### Other fixed bugs:

• Fix some errors which stopped triggering a break loop (#3013).

• Fix compiler error with GCC 4.4.7 (#3026).

• Fix string copying logic (#3071).

### New and updated packages since GAP 4.10.0

GAP 4.10.1 distribution contains 145 packages, including updated versions of 35 packages from GAP 4.10.0 distribution, and also the following five new packages:

• MajoranaAlgebras by Markus Pfeiffer and Madeleine Whybrow, which constructs Majorana representations of finite groups.

• PackageManager by Michael Torpey, providing a collection of functions for installing and removing GAP packages, with the eventual aim of becoming a full pip-style package manager for the GAP system.

• Thelma by Victor Bovdi and Vasyl Laver, implementing algorithms to deal with threshold elements.

• walrus by Markus Pfeiffer, providing methods for proving hyperbolicity of finitely presented groups in polynomial time.

• YangBaxter by Leandro Vendramin and Alexander Konovalov, which provides functionality to construct classical and skew braces, and also includes a database of classical and skew braces of small orders.

## GAP 4.10.0 (November 2018)

### New features and major changes

• Reduce impact of immediate methods GAP allows declaring so-called "immediate methods". The idea is that these are very simple and fast methods which are immediately called if information about an object becomes known, in order to perform some quick deduction. For example, if the order of a group is set, there might be immediate methods which update the filters IsFinite and IsTrivial of the group suitably.

While this can be very elegant and useful in interactive GAP sessions, the overhead for running these immediate methods and applying their results can become a major factor in the runtime of complex computations that create thousands or millions of objects.

To address this, various steps were taken:

• some immediate methods were turned into regular methods;

• a special handlers for SetSize was created that deduces properties which previously were taken care of by immediate methods;

• some immediate methods were replaced by implications (set via InstallTrueMethod), a mechanism that essentially adds zero overhead, unlike immediate methods;

• various group constructors were modified to precompute and preset properties of freshly created group objects, to avoid triggering immediate methods for these.

As a result of these and other changes, consider the following example; with GAP 4.9, it takes about 130 seconds on one test system, while with GAP 4.10 it runs in about 22 seconds, i.e., more than six times faster.

G:=PcGroupCode( 741231213963541373679312045151639276850536621925972119311,11664);;
IsomorphismGroups(G,PcGroupCode(CodePcGroup(G),Size(G)))<>fail;


Relevant pull requests and issues: #2386, #2387, #2522.

• Change definition of IsPGroup to not require finiteness This is a small change in terms of amount of code changed, but we list it here as it has a potential (albeit rather unlikely) impact on the code written by GAP users: In the past, the GAP manual entry for IsPGroup defined p-groups as being finite groups, which differs from the most commonly used definition for p-groups. Note however that there was not actual implication installed from IsPGroup to IsFinite, so it always was possible to actually created infinite groups in the filter IsPGroup. In GAP 4.10, we adjusted (in #1545) the documentation for IsPGroup to the commonly accepted definition for p-groups. In addition, code in the GAP library and in packages using IsPGroup was audited and (in a very few cases) adjusted to explicitly check IsFinite (see e.g. #2866).

• Experimental support for using the Julia garbage collector It is now possible to use the garbage collector of the Julia language instead of GAP's traditional GASMAN garbage collector. This is partly motivated by a desire to allow tight integration with GAP and Julia in the future. Warning: right now, this is slower, and also requires a patched version of Julia.

Relevant pull requests: #2092, #2408, #2461, #2485, #2495, #2672, #2688, #2793, #2904, #2905, #2931.

• libGAP (work in progress) We now provide a experimental way to allow 3rd party code to link GAP as a library; this is based on the libGAP code by SageMath, but different: while we aim to provide the same functionality, we do not rename any symbols, and we do not provide the same API. We hope that a future version of SageMath can drop its custom modifications for GAP and use this interface instead. Work is underway to achieve this goal. If you are interested in this kind of interface, please get in touch with us to help us improve it. See also this email.

To get an idea how libGAP works, you can configure GAP as normal, and then execute make testlibgap which will build a small program that uses some of the existing API and links GAP. Relevant pull requests:

• #1690 Add a callback to FuncJUMP_TO_CATCH

• #2528 Add IsLIBGAP constant

• #2702 Add GAP kernel API

• #2723 Introduce command line options --norepl and --nointeract

### Improved and extended functionality

• #2041 Teach FrattiniSubgroup methods to check for solvability

• #2053 Faster computation of modular inverses of integers

• #2057 Various changes, including:

• Improve computation of automorphism groups for fp groups (we still recommend to instead first convert the group to a computationally nice representation, such as a perm or pc group)

• Add MinimalFaithfulPermutationDegree attribute for finite groups

• Improve performance of GQuotients(F,G) when F is an fp group

• Some other performance and documentation tweaks

• #2061, #2086, #2159, #2306 Speed up GcdInt, LcmInt, PValuation, RootInt, SmallestRootInt, IsPrimePowerInt

• #2063 Teach GAP that BPSW pseudo primes less than 2^64 are all known to be prime (the previous limit was 10^13)

• #2091 Refactor DeclareAttribute and NewAttribute (arguments are now verified stricter)

• #2115, #2204, #2272 Allow (optionally) passing a random source to many more Random methods than before, and also to RandomList

• #2136 Add shortname entry to record returned by IsomorphismTypeInfoFiniteSimpleGroup

• #2181 Implement Union(X,Y), where X and Y are in PositiveIntegers, NonnegativeIntegers, Integers, GaussianIntegers, Rationals, GaussianRationals, Cyclotomics, at least where a suitable output object exists (we already provided Intersection(X,Y) for a long time)

• #2185 Implement IsCentral(M,x), where M is a magma, monoid, group, ring, algebra, etc. and x an element of M (the documentation already claimed that these exist for a long time)

• #2199 Optimize true/false conditions when coding if-statements

• #2200 Add StringFormatted, PrintFormatted, PrintToFormatted

• #2222 Turn hidden implications into actual implications

• #2223 Add operation PositionsBound which returns the set of all bound positions in a given list

• #2224, #2243, #2340 Improve ShowImpliedFilters output

• #2225 Improve LocationFunc for kernel function

• #2232 Make ValueGlobal faster

• #2242 Add global function CycleFromList

• #2244 Make rank argument to InstallImmediateMethod optional, similar to InstallMethod

• #2274 Ensure uniform printing of machine floats nan, inf, -inf across different operating systems

• #2287 Turn IsInfiniteAbelianizationGroup into a property and add some implications involving it

• #2293, #2602, #2718 Improved and documented various kernel and memory debugging facilities (requires recompiling GAP with --enable-debug, --enable-valgrind resp. --enable-memory-checking)

• #2308 Method selection code was rewritten from GAP to C

• #2326 Change SimpleGroup to perform better input validation and improve or correct error message for type 2E

• #2375 Make last2 and last3 available in break loops

• #2383 Speed improvements for automorphism groups

• #2393 Track location of InstallMethod and InstallImmediateMethod

• #2422 Improve tracking of InstallMethod and DeclareOperation

• #2426 Speed up InverseMatMod with integer modulus

• #2427 Fix and complete support for custom functions (i.e., objects which can be called like a function using obj(arg) syntax)

• #2456 Add PrintString and ViewString methods for character tables

• #2474 Change IsConstantRationalFunction and IsUnivariateRationalFunction to return false if input isn't a rational function (instead of an error)

• #2474 Add methods for multiplying rational functions over arbitrary rings by rationals

• #2496 Finite groups whose order is known and not divisible by 4 are immediately marked as solvable

• #2509 Rewrite support for .gz compressed files to use zlib, now works on Windows

• #2519, #2524, #2531 Test now rejects empty inputs and warns if the input contains no test

• #2574 When reporting syntax errors, GAP now "underlines" the complete last token, not just the position where it stopped parsing

• #2577, #2613 Add quadratic and bilinear add forms for Omega(e,d,q)

• #2598 Add BannerFunction to PackageInfo.g

• #2606 Improve PageSource to work on functions that were read from a file given by a relative path

• #2616 Speed up computation of quotients of associative words by using existing (but previously unused) kernel functions for that

• #2640 Work on MatrixObj and VectorObj

• #2654 Make Sortex stable

• #2666, #2686 Add IsBiCoset attribute for right cosets, which is true if the right coset is also a left coset

• #2684 Add NormalSubgroups methods for symmetric and alternating permutation groups

• #2726 Validate PackageInfo.g when loading packages

• #2733 Minor performance improvements, code cleanup and very local fixes

• #2750 Reject some invalid uses of ~

• #2812 Reduce memory usage and improve performance the MTC (modified Todd-Coxeter) code that was rewritten in GAP 4.9, but which was much slower than the old (but buggy) code it replaced; the difference is now small, but the old code still is faster in some case.

• #2855, #2877 Add IsPackageLoaded

• #2878 Speed up conjugacy tests for permutation by using random permutation of points when selecting base in centraliser

• #2899 TestDirectory reports number of failures and failed files

### Changed documentation

• #2192 Add an example for PRump

• #2219 Add examples to the relations chapter.

• #2360 Document IdealDecompositionsOfPolynomial (also accessible via its synonym DecomPoly) and NormalizerViaRadical

• #2366 Do not recommend avoiding X which is a synonym for Indeterminate

• #2432 Correct a claim about the index of Omega(e,p,q) in SO(e,p,q) (see SO)

• #2549 Update documentation of the -T command line option

• #2551 Add new command line option --alwaystrace which ensures error backtraces are printed even if break loops are disabled

• #2681 Documented ClassPositionsOfSolvableRadical and CharacterTableOfNormalSubgroup

• #2834 Improve manual section about Info classes

### Fixed bugs that could lead to crashes

• #2154, #2242, #2294, #2344, #2353, #2736 Fix several potential (albeit rare) crashes related to garbage collection

• #2196 Fix crash in HasKeyBag on SPARC Solaris 11

• #2305 Fix crash in PartialPerm([1,2,8],[3,4,1,2]);

• #2477 Fix crash if ~ is used to modify list

• #2499 Fix crash in the kernel functions {8,16,32}Bits_ExponentSums3

• #2601 Fix crash in MakeImmutable(rec(x:=~));

• #2665 Fix crash when an empty filename is passed

• #2711 Fix crash when tracing buggy attribute/property methods that fail to return a value

• #2766 Fix obscure crashes by using a!{l} syntax inside a function (this syntax never was fully implemented and was unusable, and now has been removed)

### Fixed bugs that could lead to incorrect results

• #2085 Fix bugs in JenningsLieAlgebra and PCentralLieAlgebra that could e.g. lead to incorrect LieLowerCentralSeries results

• #2113 Fix IsMonomial for reducible characters and some related improvements

• #2183 Fix bug in ValueMolienSeries that could lead to ValueMolienSeries(m,0) not being 1

• #2198 Make multiplication of larger integers by tiny floats commutative (e.g. now 10.^-300 * 10^400 and 10^400 * 10.^-300 both give infinity, while before 10^400 * 10.^-300 gave 1.e+100); also ensure various strange inputs, like rec()^1;, produce an error (instead of setting a^1 = a and 1*a = a for almost any kind of object)

• #2273 Fix TypeOfOperation for setters of and-filters

• #2275, #2280 Fix IsFinitelyGeneratedGroup and IsFinitelyGeneratedMonoid to not (incorrectly) assume that a given infinite generating set implies that there is no finite generating set

• #2311 Do not set IsFinitelyGeneratedGroup for finitely generated magmas which are not groups

• #2452 Fix bug that allowed creating empty magmas in the filters IsTrivial and IsMagmaWithInverses

• #2689 Fix LogFFE to not return negative results on 32 bit systems

• #2766 Fix a bug that allowed creating corrupt permutations

### Fixed bugs that could lead to break loops

• #2040 Raise error if eager float literal conversion fails (fixes #1105)

• #2582 Fix ExtendedVectors for trivial vector spaces

• #2617 Fix HighestWeightModule for Lie algebras in certain cases

• #2829 Fix ShallowCopy for IteratorOfCartesianProduct

### Other fixed bugs

• #2220 Do not set IsSubsetLocallyFiniteGroup filter for finite fields

• #2268 Handle spaces in filenames of gzipped filenames

• #2269, #2660 Fix some issues with the interface between GAP and XGAP (or other similar frontends for GAP)

• #2315 Prevent creation of groups of floats, just like we prevent creation of groups of cyclotomics

• #2350 Fix prompt after line continuation

• #2365 Fix tracing of mutable variants of One/Zero/Inv/AInv

• #2398 Fix PositionStream to report correct position

• #2467 Fix support for identifiers of length 1023 and more

• #2470 Do not display garbage after certain syntax error messages

• #2533 Fix composing a map with an identity map to not produce a range that is too big

• #2638 Fix result of Random on 64 bit big endian system to match those on little endian, and on 32 bit big endian

• #2672 Fix MakeImmutable for weak pointer objects, which previously failed to make subobjects immutable

• #2674 Fix SaveWorkspace to return false in case of an error, and true only if successful

• #2681 Fix Display for the character table of a trivial group

• #2716 When seeding a Mersenne twister from a string, the last few characters would not be used if the string length was not a multiple of 4. Fixing this may lead to different series of random numbers being generated.

• #2720 Reject workspaces made in a GAP with readline support in a GAP without, and vice versa, instead of crashing

• #2657 The subobjects of the mutable values of the attributes ComputedClassFusions, ComputedIndicators, ComputedPowerMaps, ComputedPrimeBlockss are now immutable. This makes sure that the values are not accidentally changed. This change may have side-effects in users' code, for example the object returned by 0 * ComputedPowerMaps( CharacterTable( "A5" ) )[2] had been a mutable list before the change, and is an immutable list from now on.

### Removed or obsolete functionality

• Remove multiple undocumented internal functions. Nobody should have been using them, but if you were, you may extract it from a previous GAP release that still contained it. (#2670, #2781 and more)

• #2335 Remove several functions and variables that were deprecated for a long time: DiagonalizeIntMatNormDriven, DeclarePackageDocumentation, KERNEL_VERSION, GAP_ROOT_PATHS, LOADED_PACKAGES, PACKAGES_VERSIONS, IsTuple, StateRandom, RestoreStateRandom, StatusRandom, FactorCosetOperation, ShrinkCoeffs, ExcludeFromAutoload, CharacterTableDisplayPrintLegendDefault, ConnectGroupAndCharacterTable, IsSemilatticeAsSemigroup, CreateCompletionFiles, PositionFirstComponent, ViewLength

• #2502 Various kernel functions now validate their inputs more carefully (making it harder to produce bad effects by accidentally passing bad data to them)

• #2700 Forbid constructors with 0 arguments (they were never meaningful)

### Packages

GAP 4.10.0 distribution includes 140 packages.

• The francy package by Manuel Martins, which provides an interface to draw graphics using objects. This interface allows creation of directed and undirected graphs, trees, line charts, bar charts and scatter charts. These graphical objects are drawn inside a canvas that includes a space for menus and to display informative messages. Within the canvas it is possible to interact with the graphical objects by clicking, selecting, dragging and zooming.

• The JupyterVis package by Nathan Carter, which is intended for use in Jupyter Notebooks running GAP kernels and adds visualization tools for use in such notebooks, such as charts and graphs.

No longer redistributed with GAP:

• The linboxing package has been unusable (it does not compile) for several years now, and is unmaintained. It was therefore dropped from the GAP package distribution. If anybody is willing to take over and fix the package, the latest sources are available at https://github.com/gap-packages/linboxing.

• The recogbase package has been merged into the recog package, and therefore is no longer distributed with GAP.

## GAP 4.9.3 (September 2018)

### Fixed bugs that could lead to break loops:

• Fixed a regression in HighestWeightModule caused by changes in sort functions introduced in GAP 4.9 release (#2617).

### Other fixed bugs and further improvements:

• Fixed a compile time assertion that caused compiler error on some systems (#2691).

### New and updated packages since GAP 4.9.2

This release contains updated versions of 18 packages from GAP 4.9.2 distribution. Additionally, it has three new packages:

• The curlInterface package by Christopher Jefferson and Michael Torpey, which provides a simple wrapper around libcurl to allow downloading files over http, ftp and https protocols.

• The datastructures package by Markus Pfeiffer, Max Horn, Christopher Jefferson and Steve Linton, which aims at providing standard datastructures, consolidating existing code and improving on it, in particular in view of HPC-GAP.

• The DeepThought package by Nina Wagner and Max Horn, which provides functionality for computations in finitely generated nilpotent groups given by a suitable presentation using Deep Thought polynomials.

## GAP 4.9.2 (July 2018)

### Fixed bugs that could lead to break loops:

• Fixed a bug in iterating over an empty cartesian product (#2421). (Reported by @isadofschi)

### Fixed bugs that could lead to crashes:

• Fixed a crash after entering return; in a "method not found" break loop (#2449).

• Fixed a crash when an error occurs and OutputLogTo points to a stream which internally uses another stream (#2596).

### Fixed bugs that could lead to incorrect results:

• Fixed a bug in computing maximal subgroups, which broke some other calculations, in particular, computing intermediate subgroups. (#2488). (Reported by Seyed Hassan Alavi)

### Other fixed bugs and further improvements:

• Profiling now correctly handles calls to longjmp and allows to generate profiles using version 2.0.1 of the Profiling package (#2444).

• The bin/gap.sh script now respects the GAP_DIR environment variable (#2465). (Contributed by RussWoodroofe)

• The bin/BuildPackages.sh script now properly builds binaries for the simpcomp package (#2475).

• Fixed a bug in restoring a workspace, which prevented GAP from saving the history if a workspace was loaded during startup (#2578).

### New and updated packages since GAP 4.9.1

This release contains updated versions of 22 packages from GAP 4.9.1 distribution. Additionally, it has three new packages. The new JupyterKernel package by Markus Pfeiffer provides a so-called kernel for the Jupyter interactive document system. This package requires Jupyter to be installed on your system (instructions). It also requires GAP packages IO, ZeroMQInterface, json, and also two new packages by Markus Pfeiffer called crypting and uuid, all included into GAP 4.9.2 distribution. The JupyterKernel package is not yet usable on Windows.

## GAP 4.9.1 (May 2018)

This is the first public release of GAP 4.9.

### Major changes:

• Merged HPC-GAP into GAP. For details, please refer to the end of these release notes.

• GAP has a new build system, which resolves many quirks and issues with the old system, and will be easier to maintain. For regular users, the usual ./configure && make should work fine as before. If you are interested in technical details on the new build system, take a look at README.buildsys.md.

• The guidelines for developing GAP packages were revised and moved from the Example package to the reference manual. (#484).

• In addition to supporting single argument lambda functions like a -> a+1, GAP now supports lambdas with fewer or more than one argument, or even a variable number. E.g. {a,b} -> a+b is a shorthand for function(a,b) return a+b; end. For details on how to use this, please refer to the reference manual. For technical details, e.g. why we did not choose the syntax (a,b) -> a+b, see #490.

• Function calls, list accesses and records accesses now can be nested. For example, you can now write y := f().x; (essentially equivalent to y := f();; y := y.x;), which previously would have resulted in an error; see #457 and #462).

• The libraries of small, primitive and transitive groups which previously were an integral part of GAP were split into three separate packages PrimgGrp, SmallGrp and TransGrp. For backwards compatibility, these are required packages in GAP 4.9 (i.e., GAP will not start without them). We plan to change this for GAP 4.10 (see #2434), once all packages which currently implicitly rely on these new packages had time to add explicit dependencies on them (#1650, #1714).

• The performance of GAP's sorting functions (such as Sort, SortParallel, etc.) has been substantially improved, in some examples by more than a factor of four: as a trivial example, compare the timing for Sort([1..100000000] * 0). As a side effect, the result of sorting lists with equal entries may produce different answers compared to previous GAP versions. If you would like to make your code independent of the exact employed sorting algorithm, you can use the newly added StableSort, StableSortBy and StableSortParallel. (For some technical details, see #609).

• We removed our old home-grown big integer code, and instead always use the GMP based big integer code. This means that the GMP library now is a required dependency, not just an optional one. Note that GAP has been using GMP big integer arithmetic for a long time by default, and we also have been bundling GMP with GAP. So this change mostly removed code that was never in use for most users.

• A number of improvements have been made to Random. These may lead to different sequences of numbers being created. On the up side, many more methods for Random (and other RandomXYZ operations) now optionally take an explicit RandomSource as first argument (but not yet all: help with issue #1098 is welcome). Some relevant pull requests:

• Allow creating random permutations using a random source (#1165)

• Let more Random methods use an alternative source (#1168)

• Help Random methods to use RandomSource (#810)

• Remove uses of old random generator (#808)

• Fix Random on long (>2^28) lists (#781)

• Fix RandomUnimodularMat (#1511)

• Use RandomSource in a few more places (#1599)

• The output and behaviour of the profiling system has been substantially improved:

• Make profiling correctly handle the same file being opened multiple times (#1069)

• Do not profile the return statements inserted into the end of functions (#1073)

• Ensure we reset OutputtedFilenameList in profiling when a workspace is restored (#1164)

• Better tracking of amounts of memory allocated and time spent in the garbage collector (#1806)

• Allow profiling of memory usage (#1808)

• Remove profiling limit on files with <= 2^16 lines (#1913)

• In many cases GAP now outputs the filename and location of functions in helpful places, e.g. in error messages or when displaying compiled functions. We also try to always use the format FILENAME:LINE, which various utilities already know how to parse (e.g. in iTerm2, cmd-clicking on such a string can be configured to open an editor for the file at the indicated line). For some technical details, see #469, #755, #1058.

• GAP now supports constant variables, whose value cannot change anymore during runtime; code using such constants can then be slightly optimized by GAP. E.g. if foo is turned into a constant variable bound to the value false, then GAP can optimize if foo then ... fi; blocks completely away. For details, see the documentation for MakeConstantGlobal. (#1682, #1770)

### Other changes:

• Enhance StructureDescription with a major rewrite, enhancing DirectFactorsOfGroup" and adding SemidirectDecompositions; the core algorithm now also works for infinite abelian groups. Further, it became faster by quickly finding abelian direct factors and recognizing several cases where the group is direct indecomposable. (#379, #763, #985)

• Mark FittingSubgroup and FrattiniSubgroup as nilpotent (#400)

• Add method for Socle for finite nilpotent groups (#402)

• Change ViewString and String methods for various inverse semigroups and monoids (#438, #880, #882)

• Enhance some nilpotent and p-group attributes (#442)

• Improve Union for a list with many ranges (#444)

• Add UserHomeExpand, a function to expand ~ in filenames. (#447)

• Extra hint in "No Method Found" error message if one of the arguments is fail (#460)

• Tell Sylow subgroups of natural A_n or S_n their size when we make them (#529)

• Some small enhancements on Sylow and Hall subgroup computations, mostly for nilpotent groups. (#535)

• Remove .zoo archive related tools (#540)

• Add new FrattiniSubgroup, MaximalNormalSubgroups, MinimalNormalSubgroups and Socle methods for abelian and/or solvable groups, even infinite ones. The new methods are only triggered if the group already knows that it is abelian and/or solvable. (#552, #583, #606)

• New attribute NormalHallSubgroups, returning a list of all normal Hall subgroups of a group. (#561)

• Add ComplementClassesRepresentatives fallback method for arbitrary groups (#563)

• (#612) Add parsing of hex literals in strings, e.g. "\0x61" is turned into "a" (#612)

• Collection of enhancements (#683)

• Various speed improvements to polynomial factorisation and the GAP MeatAxe (#720, #1027)

• The code and documentation for transformations is improved and corrected in many instances (#727, #732)

• Change RootFFE to optionally takes a field or field size as first argument, from which the roots will be taken (#761)

• Change Permanent from a global function to an attribute (#777)

• Add CallFuncListWrap to wrap return value to allow distinguishing between functions which return and functions which don't (#824)

• Allow repeated use of same DeclareSynonym call (#835)

• New implementation of modified Todd-Coxeter (the old one had bugs, see #302), #843)

• New functionality: Cannon/Holt automorphisms and others (#878)

• Add IsPowerfulPGroup property, and a FrattiniSubgroup method for powerful p-groups (#894)

• Improve performance for group isomorphism/automorphisms (#896, #968)

• Make ListX, SetX, SumX and ProductX support lists which are not collections (#903)

• Some improvements for LatticeByCyclicExtension (#905)

• Add helpers to retrieve information about operations and filters: CategoryByName, TypeOfOperation, FilterByName, FiltersObj, FiltersType, IdOfFilter, IdOfFilterByName, IsAttribute, IsCategory, IsProperty, IsRepresentation (#925, #1593)

• Give better error message if a help file is missing (#939)

• Add LowercaseChar and UppercaseChar (#952)

• Add PositionMaximum and PositionMinimum (#956)

• Switching default command history length from infinity to 1000 (#960)

• Allow conversion of -infinity to float via NewFloat and MakeFloat (#961)

• Add option NoPrecomputedData to avoid use of data libraries in certain computations (useful if one wants to verify the content of these data libraries) (#986)

• Remove one-argument version of AsPartialPerm for a transformation (#1036)

• Partial perms now have a MultiplicativeZero rather than a Zero, since they are multiplicative rather than additive elements (#1040)

• Various enhancements: (#1046)

• A bugfix in NaturalHomomorphismByIdeal for polynomial rings

• Improvements in handling solvable permutation groups

• The trivial group now is a member of the perfect groups library

• Improvements in using tabulated data for maximal subgroups

• New tests for group constructors and some fixes (e.g. GO(1,4,5) used to trigger an error) (#1053)

• Make HasSolvableFactorGroup slightly more efficient (#1062)

• Enhance HasXXFactorGroup (#1066)

• Remove GAP4stones from tests (#1072)

• AsMonoid and AsSemigroup are now operations, and various bugs were resolved related to isomorphisms of semigroups and monoids (#1112)

• Mark isomorphisms between trivial groups as bijective (#1116)

• Speed up RootMod and RootsMod for moduli with large prime factors; also add IS_PROBAB_PRIME_INT kernel function (#1141)

• The search for the documentation of system setters and testers now returns corresponding attributes and properties (#1144)

• Remove command line options -c, -U, -i and -X, add --quitonbreak (#1192, #1265, #1421, #1448)

• Remove Itanium support (#1163)

• Adding two strings now shows a more helpful error message (#1314)

• Suppress Unbound global variable warning in IsBound (#1334)

• Increase warning level for Conway polynomial (#1363)

• Performance improvements to maximal and intermediate subgroups, fix of RepresentativeAction (#1390)

• Revise Chapter 52 of the reference manual (fp semigroups and monoids) (#1441)

• Improve the performance of the Info statement (#1464, #1770)

• When printing function bodies, avoid some redundant spaces (#1498)

• Add kernel functions for directly accessing entries of GF2/8bit compressed matrices (#1585)

• Add String method for functions (#1591)

• Check modules were compiled with the same version of GAP when loading them (#1600)

• When printing function, reproduce TryNextMethod() correctly (#1613)

• New "Bitfields" feature providing efficient support for packing multiple data items into a single word for cache and memory efficiency (#1616)

• Improved bin/BuildPackages.sh, in particular added option to abort upon failure (#2022)

• Rewrote integer code (GMP) for better performance of certain large integer operations, and added kernel implementations of various functions, including these:

• Add kernel implementations of AbsInt, SignInt; add new kernel functions ABS_RAT, SIGN_RAT; and speed up mod, RemInt, QuoInt for divisors which are small powers of 2 (#1045)

• Add kernel implementations of Jacobi, PowerModInt, Valuation (for integers), PValuation (for integers) (#1075)

• Add kernel implementation of Factorial (#1969)

• Add kernel implementation of Binomial (#1921)

• Add kernel implementation of LcmInt (#2019)

• Check version of kernel for package versions (#1600)

• Add new AlgebraicExtensionNC operation (#1665)

• Add NumberColumns and NumberRows to MatrixObj interface (#1657)

• MinimalGeneratingSet returns an answer for non-cyclic groups that already have a generating set of size 2 (which hence is minimal) (#1755)

• Add GetWithDefault which returns the n-th element of the list if it is bound, and the default value otherwise (#1762)

• Fast method for ElmsBlist when positions are a range with increment 1 (#1773)

• Make permutations remember their inverses (#1831)

• Add invariant forms for GU(1,q) and SU(1,q) (#1874)

• Implement StandardAssociate and StandardAssociateUnit for ZmodnZ, clarify documentation for IsEuclideanRing (#1990)

• Improve documentation and interface for floats (#2016)

• Add PositionsProperty method for non-dense lists (#2021)

• Add TrivialGroup(IsFpGroup) (#2037)

• Change ObjectifyWithAttributes to return the new objects (#2098)

• Removed a never released undocumented HPC-GAP syntax extension which allowed to use a backtick/backquote as alias for MakeImmutable. (#2202).

• Various changes (#2253):

• Improve performance and memory usage of ImageKernelBlocksHomomorphism"

• Document LowIndexSubgroups

• Correct ClassesSolvableGroup documentation to clarify that it requires, but does not test membership

• fix IsNaturalGL for trivial matrix groups with empty generating set

• Make it possible to interrupt repeat continue; until false; and similar tight loops with "Ctrl-C" (#2259).

• Improved GAP testing infrastructure, extended GAP test suite, and increased code coverage

• Countless other tweaks, improvements, fixes were applied to the GAP library, kernel and manual

### Fixed bugs:

• Fix bugs in NormalSubgroups and PrintCSV (#433)

• Fix nice monomorphism dispatch for HallSubgroup (e.g. fixes HallSubgroup(GL(3,4), [2,3])) (#559)

• Check for permutations whose degree would exceed the internal limit, and document that limit (#581)

• Fix segfault after quitting from the break loop in certain cases (#709 which fixes #397)

• Fix rankings for Socle and MinimalNormalSubgroups (#711)

• Make key and attribute values immutable (#714)

• Make OnTuples([-1], (1,2)) return an error (#718)

• Fix bug in NewmanInfinityCriterion which could corrupt the PCentralSeries attribute (#719)

• The length of the list returned by OnSetsPerm is now properly set (#731)

• Fix Remove misbehaving when last member of list with gaps in it is removed (#766)

• Fix bugs in various methods for Rees (0-)matrix semigroups: IsFinite, IsOne, Enumerator, IsReesMatrixSemigroup and IsReesZeroMatrixSemigroup (#768, #1676)

• Fix IsFullTransformationSemigroup to work correctly for the full transformation semigroup of degree 0 (#769)

• Fix printing very large (> 2^28 points) permutations (#782)

• Fix Intersection([]) (#854)

• Fix crash in IsKernelFunction for some inputs (#876)

• Fix bug in ShortestVectors which could cause OrthogonalEmbeddings to enter a break loop (#941)

• Fix crash in some methods involving partial perms (#948)

• FreeMonoid(0) no longer satisfies IsGroup (#950)

• Fix crash when invoking weak pointer functions on invalid arguments (#1009)

• Fix a bug parsing character constants (#1015)

• Fix several bugs and crashes in Z(p,d) for invalid arguments, e.g. Z(4,5), Z(6,3) (#1029, #1059, #1383, #1573)

• Fix starting GAP on systems with large inodes (#1033)

• Fix NrFixedPoints and FixedPointsOfPartialPerm for a partial perm and a partial perm semigroup (they used to return the moved points rather than the fixed points) (#1034)

• Fix MeetOfPartialPerms when given a collection of 1 or 0 partial perms (#1035)

• The behaviour of AsPartialPerm for a transformation and a list is corrected (#1036)

• IsomorphismReesZeroMatrixSemigroup for a 0-simple semigroup is now defined on the zero of the source and range semigroups (#1038)

• Fix isomorphisms from finitely-presented monoids to finitely-presented semigroups, and allow isomorphisms from semigroups to fp-monoids (#1039)

• Fix One for a partial permutation semigroup without generators (#1040)

• Fix MemoryUsage for positional and component objects (#1044)

• Fix PlainString causing immutable strings to become mutable (#1096)

• Restore support for sparc64 (#1124)

• Fix a problem with < for transformations, which could give incorrect results (#1130)

• Fix crash when comparing recursive data structures such as [~] = [~] (#1151)

• Ensure output of TrivialGroup(IsPermGroup) has zero generators (#1247)

• Fix for applying the InverseGeneralMapping of an IsomorphismFpSemigroup (#1259)

• Collection of improvements and fixes: (#1294)

• A fix for quotient rings of rings by structure constants

• Generic routine for transformation matrix to rational canonical form

• Speed improvements to block homomorphisms

• New routines for conjugates or subgroups with desired containment

• Performance improvement for conjugacy classes in groups with a huge number of classes, giving significant improvements to IntermediateSubgroups (e.g. 7-Sylow subgroup in PSL(7,2)), ascending chain and thus in turn double coset calculations and further routines that rely on it

• Fix EqFloat to return correct results, instead of always returning false (#1370)

• Various changes, including fixes for CallFuncList (#1417)

• Better define the result of MappingPermListList (#1432)

• Check the arguments to IsInjectiveListTrans to prevent crashes (#1435)

• Change BlownUpMat to return fail for certain invalid inputs (#1488)

• Fixes for creating Green's classes of semigroups (#1492, #1771)

• Fix DoImmutableMatrix for finite fields (#1504)

• Make structural copy handle boolean lists properly (#1514)

• Minimal fix for algebraic extensions over finite fields of order > 256 (#1569)

• Fix for computing quotients of certain algebra modules (#1669)

• Fix an error in the default method for PositionNot (#1672)

• Improvements to Rees matrix semigroups code and new tests (#1676)

• Fix CodePcGroup for the trivial polycyclic group (#1679)

• Fix FroidurePinExtendedAlg for partial permutation monoids (#1697)

• Fix computing the radical of a zero dimensional associative algebra (#1701)

• Fix a bug in RadicalOfAlgebra which could cause a break loop for some associative algebras (#1716)

• Fix a recursion depth trap error when repeatedly calling Test (#1753)

• Fix bugs in PrimePGroup for direct products of p-groups (#1754)

• Fix UpEnv (available in break loops) when at the bottom of the backtrace (#1780)

• Fix IsomorphismPartialPermSemigroup and IsomorphismPartialPermMonoid for permutation groups with 0 generators (#1784)

• Fix DisplaySemigroup for transformation semigroups (#1785)

• Fix "no method found" errors in MagmaWithOne and MagmaWithInverses (#1798)

• Fix an error computing kernel of group homomorphism from fp group into permutation group (#1809)

• Fix an error in MTC losing components when copying a new augmented coset table (#1809)

• Fix output of Where in a break loop, which pointed at the wrong code line in some cases (#1814)

• Fix the interaction of signals in GAP and the IO package (#1851)

• Make line editing resilient to LineEditKeyHandler failure (in particular, don't crash) (#1856)

• Omit non-characters from PermChars results (#1867)

• Fix ExteriorPower when exterior power is 0-dimensional (used to return a 1-dimensional result) (#1872)

• Fix recursion depth trap and other improvements for quotients of fp groups (#1884)

• Fix a bug in the computation of a permutation group isomorphic to a group of automorphisms (#1907)

• Fix bug in InstallFlushableValueFromFunction (#1920)

• Fix ONanScottType and introduce RestrictedInverseGeneralMapping (#1937)

• Fix QuotientMod documentation, and the integer implementation. This partially reverts changes made in version 4.7.8 in 2013. The documentation is now correct (resp. consistent again), and several corner cases, e.g. QuotientMod(0,0,m) now work correctly (#1991)

• Fix PositionProperty with from < 1 (#2056)

• Fix inefficiency when dealing with certain algebra modules (#2058)

• Restrict capacity of plain lists to 2^28 in 32-bit and 2^60 in 64-bit builds (#2064)

• Fix crashes with very large heaps (> 2 GB) on 32 bit systems, and work around a bug in memmove in 32-bit glibc versions which could corrupt memory (affects most current Linux distributions) (#2166).

• Fix name of the reversed option in documentation of LoadAllPackages (#2167).

• Fix TriangulizedMat([]) (see TriangulizedMat to return an empty list instead of producing an error (#2260).

• Fix several potential (albeit rare) crashes related to garbage collection (#2321, #2313, #2320).

### Removed or obsolete functionality:

• Make SetUserPreferences obsolete (use SetUserPreference instead) (#512)

• Remove undocumented NameIsomorphismClass (#597)

• Remove unused code for rational classes of permutation groups (#886)

• Remove unused and undocumented Randomizer and CheapRandomizer (#1113)

• Remove install-tools.sh script and documentation mentioning it (#1305)

• Withdraw CallWithTimeout and CallWithTimeoutList (#1324)

• Make RecFields obsolete (use RecNames instead) (#1331)

• Remove undocumented SuPeRfail and READ_COMMAND (#1374)

• Remove unused oldmatint.gi (old methods for functions that compute Hermite and Smith normal forms of integer matrices) (#1765)

• Make TRANSDEGREES obsolete (#1852)

### HPC-GAP

GAP includes experimental code to support multithreaded programming in GAP, dubbed HPC-GAP (where HPC stands for "high performance computing"). GAP and HPC-GAP codebases diverged during the project, and we are currently working on unifying the codebases and incorporating the HPC-GAP code back into the mainstream GAP versions.

This is work in progress, and HPC-GAP as it is included with GAP right now still suffers from various limitations and problems, which we are actively working on to resolve. However, including it with GAP (disabled by default) considerably simplifies development of HPC-GAP. It also means that you can very easily get a (rough!) sneak peak of HPC-GAP. It comes together with the new manual book called "HPC-GAP Reference Manual" and located in the doc/hpc directory.

Users interested in experimenting with shared memory parallel programming in GAP can build HPC-GAP by following the instructions. While it is possible to build HPC-GAP from a release version of GAP you downloaded from the GAP website, due to the ongoing development of HPC-GAP, we recommend that you instead build HPC-GAP from the latest development version available in the GAP repository at GitHub.

### New and updated packages since GAP 4.8.10

There were 132 packages redistributed together with GAP 4.8.10. The GAP 4.9.1 distribution includes 134 packages, including numerous updates of previously redistributed packages, and some major changes outlined below.

The libraries of small, primitive and transitive groups which previously were an integral part of GAP were split into three separate packages PrimgGrp, SmallGrp and TransGrp:

• The PrimGrp package by Alexander Hulpke, Colva M. Roney-Dougal and Christopher Russell provides the library of primitive permutation groups which includes, up to permutation isomorphism (i.e., up to conjugacy in the corresponding symmetric group), all primitive permutation groups of degree < 4096.

• The SmallGrp package by Bettina Eick, Hans Ulrich Besche and Eamonn O’Brien provides the library of groups of certain "small" orders. The groups are sorted by their orders and they are listed up to isomorphism; that is, for each of the available orders a complete and irredundant list of isomorphism type representatives of groups is given.

• The TransGrp package by Alexander Hulpke provides the library of transitive groups, with an optional download of the library of transitive groups of degree 32.

For backwards compatibility, these are required packages in GAP 4.9 (i.e., GAP will not start without them). We plan to change this for GAP 4.10 (see #2434), once all packages which currently implicitly rely on these new packages had time to add explicit dependencies on them (#1650, #1714).

The new ZeroMQInterface package by Markus Pfeiffer and Reimer Behrends has been added for the redistribution. It provides both low-level bindings as well as some higher level interfaces for the ZeroMQ message passing library for GAP and HPC-GAP enabling lightweight distributed computation.

The HAPprime package by Paul Smith is no longer redistributed with GAP. Part of the code has been incorporated into the HAP package. Its source code repository, containing the code of the last distributed version, can still be found at https://github.com/gap-packages/happrime.

Also, the ParGAP package by Gene Cooperman is no longer redistributed with GAP because it no longer can be compiled with GAP 4.9 (see this announcement). Its source code repository, containing the code of the last distributed version, plus some first fixes needed for compatibility for GAP 4.9, can still be found at https://github.com/gap-packages/pargap. If somebody is interested in repairing this package and taking over its maintenance, so that it can be distributed again, please contact the GAP team.

## GAP 4.8.8 (August 2017)

### Fixed bugs that could lead to incorrect results:

• Fixed a bug in RepresentativeAction producing incorrect answers for both symmetric and alternating groups, with both OnTuples and OnSets, by producing elements outside the group. (Reported by Mun See Chang)

### Fixed bugs that could lead to break loops:

• Fixed a bug in RepresentativeAction for S_n and A_n acting on non-standard domains.

### Other fixed bugs:

• Fixed a problem with checking the path to a file when using the default browser as a help viewer on Windows. (Reported by Jack Saunders)

### New and updated packages since GAP 4.8.7

This release contains updated versions of 29 packages from GAP 4.8.7 distribution. Additionally, the Gpd package (author: Chris Wensley) has been renamed to Groupoids.

## GAP 4.8.7 (March 2017)

### Fixed bugs that could lead to incorrect results:

• Fixed a regression from GAP 4.7.6 when reading compressed files after a workspace is loaded. Before the fix, if GAP is started with the -L option (load workspace), using ReadLine on the input stream for a compressed file returned by InputTextFile only returned the first character. (Reported by Bill Allombert)

### Other fixed bugs:

• Fixed compiler warning occurring when GAP is compiled with gcc 6.2.0. (Reported by Bill Allombert)

### New and updated packages since GAP 4.8.6

This release contains updated versions of 19 packages from GAP 4.8.6 distribution. Additionally, the following package has been added for the redistribution with GAP:

• lpres package (author: René Hartung, maintainer: Laurent Bartholdi) to work with L-presented groups, namely groups given by a finite generating set and a possibly infinite set of relations given as iterates of finitely many seed relations by a finite set of endomorphisms. The package implements nilpotent quotient, Todd-Coxeter and Reidemeister-Schreier algorithms for such groups.

## GAP 4.8.6 (November 2016)

### Fixed bugs that could lead to break loops:

• Fixed regression in the GAP kernel code introduced in GAP 4.8.5 and breaking StringFile ability to work with compressed files. (Reported by Bill Allombert)

## GAP 4.8.5 (September 2016)

### Improved and extended functionality:

• The error messages produced when an unexpected fail is returned were made more clear by explicitly telling that the result should not be boolean or fail (before it only said "not a boolean").

• For consistency, both NrTransitiveGroups and TransitiveGroup now disallow the transitive group of degree 1.

### Fixed bugs that could lead to incorrect results:

• A bug in the code for algebraic field extensions over non-prime fields that may cause, for example, a list of all elements of the extension not being a duplicate-free. (Reported by Huta Gana)

• So far, FileString only wrote files of sizes less than 2G and did not indicate an error in case of larger strings. Now strings of any length can be written, and in the case of a failure the corresponding system error is shown.

### Fixed bugs that could lead to break loops:

• NaturalHomomorphismByIdeal was not reducing monomials before forming a quotient ring, causing a break loop on some inputs. (Reported by Dmytro Savchuk)

• A bug in DefaultInfoHandler caused a break loop on startup with the setting SetUserPreference( "InfoPackageLoadingLevel", 4 ). (Reported by Mathieu Dutour)

• The Iterator for permutation groups was broken when the StabChainMutable of the group was not reduced, which can reasonably happen as the result of various algorithms.

## GAP 4.8.4 (June 2016)

### New features:

• The GAP distribution now includes bin/BuildPackages.sh, a script which can be started from the pkg directory via ../bin/BuildPackages.sh and will attempt to build as many packages as possible. It replaces the InstPackages.sh script which was not a part of the GAP distribution and had to be downloaded separately from the GAP website. The new script is more robust and simplifies adding new packages with binaries, as it requires no adjustments if the new package supports the standard ./configure; make build procedure.

### Improved and extended functionality:

• SimpleGroup now produces more informative error message in the case when AtlasGroup could not load the requested group.

• An info message with the suggestion to use InfoPackageLoading will now be displayed when LoadPackage returns fail (unless GAP is started with -b option).

• The build system will now enable C++ support in GMP only if a working C++ compiler is detected.

• More checks were added when embedding coefficient rings or rational numbers into polynomial rings in order to forbid adding polynomials in different characteristic.

### Fixed bugs that could lead to crashes:

• Fixed the crash in --cover mode when reading files with more than 65,536 lines.

### Fixed bugs that could lead to incorrect results:

• Fixed an error in the code for partial permutations that occurred on big-endian systems. (Reported by Bill Allombert)

• Fixed the kernel method for Remove with one argument, which failed to reduce the length of a list to the position of the last bound entry. (Reported by Peter Schauenburg)

Fixed bugs that could lead to break loops:

• Fixed the break loop while using Factorization on permutation groups by removing some old code that relied on further caching in Factorization. (Reported by Grahame Erskine)

• Fixed a problem with computation of maximal subgroups in an almost simple group. (Reported by Ramon Esteban Romero)

• Added missing methods for Intersection2 when one of the arguments is an empty list. (Reported by Wilf Wilson)

### Other fixed bugs:

• Fixed several bugs in RandomPrimitivePolynomial. (Reported by Nusa Zidaric)

• Fixed several problems with Random on long lists in 64-bit GAP installations.

## GAP 4.8.3 (March 2016)

### New features:

• New function TestPackage to run standard tests (if available) for a single package in the current GAP session (also callable via make testpackage PKGNAME=pkgname to run package tests in the same settings that are used for testing GAP releases).

### Improved and extended functionality:

• TestDirectory now prints a special status message to indicate the outcome of the test (this is convenient for automated testing). If necessary, this message may be suppressed by using the option suppressStatusMessage

• Improved output of tracing methods (which may be invoked, for example, with TraceAllMethods) by displaying filename and line number in some more cases.

### Changed functionality:

• Fixed some inconsistencies in the usage of IsGeneratorsOfSemigroup.

### Fixed bugs that could lead to incorrect results:

• Fallback methods for conjugacy classes, that were never intended for infinite groups, now use IsFinite filter to prevent them being called for infinite groups. (Reported by Gabor Horvath)

### Fixed bugs that could lead to break loops:

• Calculating stabiliser for the alternating group caused a break loop in the case when it defers to the corresponding symmetric group.

• It was not possible to use DotFileLatticeSubgroups for a trivial group. (Reported by Sergio Siccha)

• A break loop while computing AutomorphismGroup for TransitiveGroup(12,269). (Reported by Ignat Soroko)

• A break loop while computing conjugacy classes of PSL(6,4). (Reported by Martin Macaj)

### Other fixed bugs:

• Fix for using Firefox as a default help viewer with SetHelpViewer. (Reported by Tom McDonough)

## GAP 4.8.2 (February 2016)

This is the first public release of GAP 4.8.

The GAP development repository is now hosted on GitHub, and GAP 4.8 is the first major GAP release made from this repository. The public issue tracker for the core GAP system is located here, and you may use appropriate milestones to see all changes that were introduced in corresponding GAP releases. An overview of the most significant ones is provided below.

### New features:

• Added support for profiling which tracks how much time in spent on each line of GAP code. This can be used to show where code is spending a long time and also check which lines of code are even executed. See the documentation for ProfileLineByLine and CoverageLineByLine for details on generating profiles, and the Profiling package for transforming these profiles into a human-readable form.

• Added ability to install (in the library or packages) methods for accessing lists using multiple indices and indexing into lists using indices other than positive small integers. Such methods could allow, for example, to support expressions like

m[1,2];
m[1,2,3] := x;
IsBound(m["a","b",Z(7)]);
Unbind(m[1][2,3])

• Added support for partially variadic functions to allow function expressions like

function( a, b, c, x... ) ... end;


which would require at least three arguments and assign the first three to a, b and c and then a list containing any remaining ones to x.

The former special meaning of the argument arg is still supported and is now equivalent to function( arg... ), so no changes in the existing code are required.

• Introduced CallWithTimeout and CallWithTimeoutList to call a function with a limit on the CPU time it can consume. This functionality may not be available on all systems and you should check GAPInfo.TimeoutsSupported before using this functionality. (These functions were withdrawn in GAP 4.9.)

• GAP now displays the filename and line numbers of statements in backtraces when entering the break loop.

• Introduced TestDirectory function to find (recursively) all .tst files from a given directory or a list of directories and run them using Test.

### Improved and extended functionality:

• Method tracing shows the filename and line of function during tracing.

• TraceAllMethods and UntraceAllMethods to turn on and off tracing all methods in GAP. Also, for the uniform approach UntraceImmediateMethods has been added as an equivalent of TraceImmediateMethods(false).

• The most common cases of AddDictionary on three arguments now bypass method selection, avoiding the cost of determining homogeneity for plain lists of mutable objects.

• Improved methods for symmetric and alternating groups in the "natural" representations and removed some duplicated code.

• Package authors may optionally specify the source code repository, issue tracker and support email address for their package using new components in the PackageInfo.g file, which will be used to create hyperlinks from the package overview page (see PackageInfo.g from the Example package which you may use as a template).

### Changed functionality:

• As a preparation for the future developments to support multithreading, some language extensions from the HPC-GAP project were backported to the GAP library to help to unify the codebase of both GAP 4 and HPC-GAP. The only change which is not backwards compatible is that atomic, readonly and readwrite are now keywords, and thus are no longer valid identifiers. So if you have any variables or functions using that name, you will have to change it in GAP 4.8.

• There was inconsistent use of the following properties of semigroups: IsGroupAsSemigroup, IsMonoidAsSemigroup, and IsSemilatticeAsSemigroup. IsGroupAsSemigroup was true for semigroups that mathematically defined a group, and for semigroups in the category IsGroup; IsMonoidAsSemigroup was only true for semigroups that mathematically defined monoids, but did not belong to the category IsMonoid; and IsSemilatticeAsSemigroup was simply a property of semigroups, as there is no category IsSemilattice.

From version 4.8 onwards, IsSemilatticeAsSemigroup is renamed to IsSemilattice, and IsMonoidAsSemigroup returns true for semigroups in the category IsMonoid.

This way all of the properties of the type IsXAsSemigroup are consistent. It should be noted that the only methods installed for IsMonoidAsSemigroup belong to the Semigroups and Smallsemi packages.

• ReadTest became obsolete and for backwards compatibility is replaced by Test with the option to compare the output up to whitespaces.

• The function ErrorMayQuit, which differs from Error by not allowing execution to continue, has been renamed to ErrorNoReturn.

### Fixed bugs:

• A combination of two bugs could lead to a segfault. First off, NullMat (and various other GAP functions), when asked to produce matrix over a small field, called ConvertToMatrixRep. After this, if the user tried to change one of the entries to a value from a larger extension field, this resulted in an error. (This is now fixed).

Unfortunately, the C code catching this error had a bug and allowed users to type "return" to continue while ignoring the conversion error. This was a bad idea, as the C code would be in an inconsistent state at this point, subsequently leading to a crash.

This, too, has been fixed, by not allowing the user to ignore the error by entering "return".

• The Fitting-free code and code inheriting PCGS is now using IndicesEANormalSteps instead of IndicesNormalSteps, as these indices are neither guaranteed, nor required to be maximally refined when restricting to subgroups.

• A bug that caused a break loop in the computation of the Hall subgroup for groups having a trivial Fitting subgroup.

• Including a break or continue statement in a function body but not in a loop now gives a syntax error instead of failing at run time.

• GroupGeneralMappingByImages now verifies that that image of a mapping is contained in its range.

• Fixed a bug in caching the degree of transformation that could lead to a non-identity transformation accidentally changing its value to the identity transformation.

• Fixed the problem with using Windows default browser as a help viewer using SetHelpViewer("browser");.

### New and updated packages since GAP 4.7.8

At the time of the release of GAP 4.7.8 there were 119 packages redistributed with GAP. New packages that have been added to the redistribution since the release of GAP 4.7.8 are:

• CAP (Categories, Algorithms, Programming) package by Sebastian Gutsche, Sebastian Posur and Øystein Skartsæterhagen, together with three associated packages GeneralizedMorphismsForCAP, LinearAlgebraForCAP and ModulePresentationsForCAP (all three - by Sebastian Gutsche and Sebastian Posur).

• Digraphs package by Jan De Beule, Julius Jonušas, James Mitchell, Michael Torpey and Wilf Wilson, which provides functionality to work with graphs, digraphs, and multidigraphs.

• FinInG package by John Bamberg, Anton Betten, Philippe Cara, Jan De Beule, Michel Lavrauw and Max Neunhöffer for computation in Finite Incidence Geometry.

• HeLP package by Andreas Bächle and Leo Margolis, which computes constraints on partial augmentations of torsion units in integral group rings using a method developed by Luthar, Passi and Hertweck. The package can be employed to verify the Zassenhaus Conjecture and the Prime Graph Question for finite groups, once their characters are known. It uses an interface to the software package 4ti2 to solve integral linear inequalities.

• matgrp package by Alexander Hulpke, which provides an interface to the solvable radical functionality for matrix groups, building on constructive recognition.

• NormalizInterface package by Sebastian Gutsche, Max Horn and Christof Söger, which provides a GAP interface to Normaliz, enabling direct access to the complete functionality of Normaliz, such as computations in affine monoids, vector configurations, lattice polytopes, and rational cones.

• profiling package by Christopher Jefferson for transforming profiles produced by ProfileLineByLine and CoverageLineByLine into a human-readable form.

• Utils package by Sebastian Gutsche, Stefan Kohl and Christopher Wensley, which provides a collection of utility functions gleaned from many packages.

• XModAlg package by Zekeriya Arvasi and Alper Odabas, which provides a collection of functions for computing with crossed modules and Cat1-algebras and morphisms of these structures.

## GAP 4.7.8 (June 2015)

### Fixed bugs which could lead to incorrect results:

• Added two groups of degree 1575 which were missing in the library of first primitive groups. (Reported by Gordon Royle)

• Fixed the error in the code for algebra module elements in packed representation caused by the use of Objectify with the type of the given object instead of ObjByExtRep as recommended in the reference manual. The problem was that after calculating u+v where one of the summands was known to be zero, this knowledge was wrongly passed to the sum via the type. (Reported by Istvan Szollosi)

• Fixed a bug in PowerMod causing wrong results for univariate Laurent polynomials when the two polynomial arguments are stored with the same non-zero shift. (Reported by Max Horn)

### New Packages

• PatternClass by Michael Albert, Ruth Hoffmann and Steve Linton, allowing to explore the permutation pattern classes build by token passing networks. Amongst other things, it can compute the basis of a permutation pattern class, create automata from token passing networks and check if the deterministic automaton is a possible representative of a token passing network.

• QPA by Edward Green and Øyvind Solberg, providing data structures and algorithms for computations with finite dimensional quotients of path algebras, and with finitely generated modules over such algebras. It implements data structures for quivers, quotients of path algebras, and modules, homomorphisms and complexes of modules over quotients of path algebras.

## GAP 4.7.7 (February 2015)

### New features:

• Introduced some arithmetic operations for infinity and negative infinity

• Introduced new property IsGeneratorsOfSemigroup which reflects wheter the list or collection generates a semigroup.

### Fixed bugs which could lead to incorrect results:

• Fixed a bug in Union (actually, in the internal library function JoinRanges) caused by downward running ranges. (Reported by Matt Fayers)

• Fixed a bug where recursive records might be printed with the wrong component name, coming from component names being ordered differently in two different pieces of code. (Reported by Thomas Breuer)

• The usage of abs in src/gmpints.c was replaced by AbsInt. The former is defined to operate on 32-bit integers even if GAP is compiled in 64-bit mode. That lead to truncating GAP integers and caused a crash in RemInt, reported by Willem De Graaf and Heiko Dietrich. Using AbsInt fixes the crash, and ensures the correct behaviour on 32-bit and 64-bit builds.

### Fixed bugs that could lead to break loops:

• A problem with ProbabilityShapes not setting frequencies list for small degrees. (Reported by Daniel Błażewicz and independently by Mathieu Gagne)

• An error when generating a free monoid of rank infinity. (Reported by Nick Loughlin)

• Several bugs with the code for Rees matrix semigroups not handling trivial cases properly.

• A bug in IsomorphismTypeInfoFiniteSimpleGroup affecting one particular group due to a misformatting in a routine that translates between the Chevalley type and the name used in the table (in this case, "T" was used instead of ["T"]). (Reported by Petr Savicky)

### Other fixed bugs:

• The Basis method for full homomorphism spaces of linear mappings did not set basis vectors which could be obtained by GeneratorsOfLeftModule.

• A problem with GaloisType entering an infinite loop in the routine for approximating a root. (Reported by Daniel Błażewicz)

• Fixed the crash when GAP is called when the environment variables HOME or PATH are unset. (Reported by Bill Allombert)

### New packages

• json package by Christopher Jefferson, providing a mapping between the JSON markup language and GAP

• SglPPow package by Bettina Eick and Michael Vaughan-Lee, providing the database of p-groups of order p^7 for p > 11, and of order 3^8.

## GAP 4.7.6 (November 2014)

### Fixed bugs which could lead to incorrect results:

• A bug that may cause ShortestVectors to return an incomplete list. (Reported by Florian Beye)

• A bug that may lead to incorrect results and infinite loops when GAP is compiled without GMP support using gcc 4.9.

• A bug that may cause OrthogonalEmbeddings to return an incomplete result. (Reported by Benjamin Sambale)

### Fixed bugs that could lead to break loops:

• ClosureGroup should be used instead of ClosureSubgroup in case there is no parent group, otherwise some calculations such as e.g. NormalSubgroups may fail. (Reported by Dmitrii Pasechnik)

• Fixed a line in the code that used a hard-coded identity permutation, not a generic identity element of a group. (Reported by Toshio Sumi)

• Fixed a problem in the new code for calculating maximal subgroups that caused a break loop for some groups from the transitive groups library. (Reported by Petr Savicky)

• Fixed a problem in ClosureSubgroup not accepting some groups without Parent. (Reported by Inneke van Gelder)

### Other fixed bugs:

• Eliminated a number of compiler warnings detected with some newer versions of C compilers.

• Some minor bugs in the transformation and partial permutation code and documentation were resolved.

## GAP 4.7.5 (May 2014)

### Fixed bugs which could lead to incorrect results:

• InstallValue cannot handle immediate values, characters or booleans for technical reasons. A check for such values was introduced to trigger an error message and prevent incorrect results caused by this. (Reported by Sebastian Gutsche)

• KnowsDictionary and LookupDictionary methods for IsListLookupDictionary were using PositionFirstComponent; the latter is only valid on sorted lists, but in IsListLookupDictionary the underlying list is NOT sorted in general, leading to bogus results.

### Other fixed bugs:

• A bug in DirectProductElementsFamily which used CanEasilyCompareElements instead of CanEasilySortElements.

• Fixed wrong Infolevel message that caused a break loop for some automorphism group computations.

• Fixed an error that sometimes caused a break loop in HallSubgroup. (Reported by Benjamin Sambale)

• Fixed a rare error in computation of conjugacy classes of a finite group by homomorphic images, providing fallback to a default algorithm.

• Fixed an error in the calculation of Frattini subgroup in the case of the trivial radical.

• Several minor bugs were fixed in the documentation, kernel, and library code for transformations.

• Fixed errors in NumberPerfectGroups and NumberPerfectLibraryGroups not being aware that there are no perfect groups of odd order.

• Restored the ability to build GAP on OS X 10.4 and 10.5 which was accidentally broken in the previous GAP release by using the build option not supported by these versions.

• Fixed some problems for ia64 and sparc architectures. (Reported by Bill Allombert and Volker Braun)

### New packages

• permut package by A.Ballester-Bolinches, E.Cosme-Llópez, and R.Esteban-Romero to deal with permutability in finite groups.

## GAP 4.7.4 (February 2014)

This release was prepared immediately after GAP 4.7.3 to revert the fix of the error handling for the single quote at the end of an input line, contained in GAP 4.7.3. It happened that (only on Windows) the fix caused error messages in one of the packages.

## GAP 4.7.3 (February 2014)

### Fixed bugs which could lead to incorrect results:

• Incorrect result returned by AutomorphismGroup(PSp(4,2^n)). (Reported by Anvita)

• The Order method for group homomorphisms newly introduced in GAP 4.7 had a bug that caused it to sometimes return incorrect results. (Reported by Benjamin Sambale)

### Fixed bugs that could lead to break loops:

• Several bugs were fixed and missing methods were introduced in the new code for transformations, partial permutations and semigroups that was first included in GAP 4.7. Some minor corrections were made in the documentation for transformations.

• Break loop in IsomorphismFpMonoid when prefixes in generators names were longer than one letter. (Reported by Dmytro Savchuk and Yevgen Muntyan)

• Break loop while displaying the result of MagmaWithInversesByMultiplicationTable. (Reported by Grahame Erskine)

### Improved functionality:

• Better detection of UTF-8 terminal encoding on some systems. (Suggested by Andries Brouwer)

## GAP 4.7.2 (December 2013)

This is the first public release of GAP 4.7.

### Improved and extended functionality:

• The methods for computing conjugacy classes of permutation groups have been rewritten from scratch to enable potential use for groups in different representations. As a byproduct the resulting code is (sometimes notably) faster. It also now is possible to calculate canonical conjugacy class representatives in permutation groups, which can be beneficial when calculating character tables.

• The methods for determining (conjugacy classes of) subgroups in non-solvable groups have been substantially improved in speed and scope for groups with multiple nonabelian composition factors.

• There is a new method for calculating the maximal subgroups of a permutation group (with chief factors of width less or equal 5) without calculating the whole subgroup lattice.

• If available, information from the table of marks library is used to speed up subgroup calculations in almost simple factor groups.

• The broader availability of maximal subgroups is used to improve the calculation of double cosets.

• To illustrate the improvements listed above, one could try, for example

g:=WreathProduct(MathieuGroup(11),Group((1,2)));
Length(ConjugacyClassesSubgroups(g));


and

g:=SemidirectProduct(GL(3,5),GF(5)^3);
g:=Image(IsomorphismPermGroup(g));
MaximalSubgroupClassReps(g);

• Computing the exponent of a finite group G could be extremely slow. This was due to a slow default method being used, which computed all conjugacy classes of elements in order to compute the exponent. We now instead compute Sylow subgroups P_1, ..., P_k of G and use the easily verified equality exp(G) = exp(P_1) x ... x exp(P_k). This is usually at least as fast and in many cases orders of magnitude faster.

gap> G:=SmallGroup(2^7*9,33);;
gap> H:=DirectProduct(G, ElementaryAbelianGroup(2^10));;
gap> Exponent(H); # should take at most a few milliseconds
72
gap> K := PerfectGroup(2688,3);;
gap> Exponent(K); # should take at most a few seconds
168

• The functionality in GAP for transformations and transformation semigroups has been rewritten and extended. Partial permutations and inverse semigroups have been newly implemented. The documentation for transformations and transformation semigroups has been improved. Transformations and partial permutations are implemented in the GAP kernel. Methods for calculating attributes of transformations and partial permutations, and taking products, and so are also implemented in the kernel. The new implementations are largely backwards compatible; some exceptions are given below.

The degree of a transformation f is usually defined as the largest positive integer where f is defined. In previous versions of GAP, transformations were only defined on positive integers less than their degree, it was only possible to multiply transformations of equal degree, and a transformation did not act on any point exceeding its degree. Starting with GAP 4.7, transformations behave more like permutations, in that they fix unspecified points and it is possible to multiply arbitrary transformations.

• in the display of a transformation, the trailing fixed points are no longer printed. More precisely, in the display of a transformation f if n is the largest value such that n^f<>n or i^f=n for some i<>n, then the values exceeding n are not printed.

• the display for semigroups of transformations now includes more information, for example <transformation semigroup on 10 pts with 10 generators> and <inverse partial perm semigroup on 10 pts with 10 generators>.

• transformations which define a permutation can be inverted, and groups of transformations can be created.

Further information regarding transformations and partial permutations, can be found in the relevant chapters of the reference manual.

The code for Rees matrix semigroups has been completely rewritten to fix the numerous bugs in the previous versions. The display of a Rees matrix semigroup has also been improved to include the numbers of rows and columns, and the underlying semigroup. Again the new implementations should be backwards compatible with the exception that the display is different.

The code for magmas with a zero adjoined has been improved so that it is possible to access more information about the original magma. The display has also been changed to indicate that the created magma is a magma with zero adjoined (incorporating the display of the underlying magma). Elements of a magma with zero are also printed so that it is clear that they belong to a magma with zero.

If a semigroup is created by generators in the category IsMultiplicativeElementWithOneCollection and CanEasilyCompareElements, then it is now checked if the One of the generators is given as a generator. In this case, the semigroup is created as a monoid.

• Added a new operation GrowthFunctionOfGroup that gives sizes of distance spheres in the Cayley graph of a group.

• A new group constructor FreeAbelianGroup for free abelian groups has been added. By default, it creates suitable fp groups. Though free abelian groups groups do not offer much functionality right now, in the future other implementations may be provided, e.g. by the Polycyclic package.

• The message about halving the pool size at startup is only shown when -D command line option is used. (Suggested by Volker Braun)

• An info class called InfoObsolete with the default level 0 is introduced. Setting it to 1 will trigger warnings at runtime if an obsolete variable declared with DeclareObsoleteSynonym is used. This is recommended for testing GAP distribution and packages.

• The GAP help system now recognises some common different spelling patterns (for example, -ise/-ize, -isation/-ization, solvable/soluble) and searches for all possible spelling options even when the synonyms are not declared.

• Added new function Cite which produces citation samples for GAP and packages.

• It is now possible to compile GAP with user-supplied CFLAGS which now will not be overwritten by GAP default settings. (Suggested by Jeroen Demeyer)

### Fixed bugs:

• Union had O(n^3) behaviour when given many ranges (e.g. it could take 10 seconds to find a union of 1000 1-element sets). The new implementation reduces that to O(n log n) (and 4ms for the 10 second example), at the cost of not merging ranges as well as before in some rare cases.

• IsLatticeOrderBinaryRelation only checked the existence of upper bounds but not the uniqueness of the least upper bound (and dually for lower bounds), so in some cases it could return the wrong answer. (Reported by Attila Egri-Nagy)

• LowIndexSubgroupsFpGroup triggered a break loop if the list of generators of the 2nd argument contained the identity element of the group. (Reported by Ignat Soroko)

• Fixed regression in heuristics used by NaturalHomomorphismByNormalSubgroup that could produce a permutation representation of an unreasonably large degree. (Reported by Izumi Miyamoto)

• Fixed inconsistent behaviour of QuotientMod( Integers, r, s, m ) in the case where s and m are not coprime. This fix also corrects the division behaviour of ZmodnZ objects, see QuotientMod and ZmodnZ. (Reported by Mark Dickinson)

• Fixed an oversight in the loading process causing OnQuit not resetting the options stack after exiting the break loop.

• Empty strings were treated slightly differently than other strings in the GAP kernel, for historical reasons. This resulted in various inconsistencies. For example, IsStringRep("") returned true, but a method installed for arguments of type IsStringRep would NOT be invoked when called with an empty string.

We remove this special case in the GAP kernel (which dates back the very early days of GAP 4 in 1996). This uncovered one issue in the kernel function POSITION_SUBSTRING (when calling it with an empty string as second argument), which was also fixed.

• The parser for floating point numbers contained a bug that could cause GAP to crash or to get into a state where the only action left to the user was to exit GAP via Ctrl-D. For example, entering four dots with spaces between them on the GAP prompt and then pressing the return key caused GAP to exit.

The reason was (ironically) an error check in the innards of the float parser code which invoked the GAP Error() function at a point where it should not have.

• Removing the last character in a string was supposed to overwrite the old removed character in memory with a zero byte, but failed to do so due to an off-by-one error. For most GAP operations, this has no visible effect, except for those which directly operate on the underlying memory representation of strings. For example, when trying to use such a string to reference a record entry, a (strange) error could be triggered.

• ViewString and DisplayString are now handling strings, characters and immediate FFEs in a consistent manner.

• Multiple fixes to the build process for less common Debian platforms (arm, ia64, mips, sparc, GNU/Hurd). (Suggested by Bill Allombert)

• Fixes for several regressions in the gac script. (Suggested by Bill Allombert)

### Changed functionality:

• It is not possible now to call WreathProduct with 2nd argument H not being a permutation group, without using the 3rd argument specifying the permutation representation. This is an incompatible change but it will produce an error instead of a wrong result. The former behaviour of WreathProduct may now be achieved by using StandardWreathProduct which returns the wreath product for the (right regular) permutation action of H on its elements.

• The function ViewLength to specify the maximal number of lines that are printed in ViewObj became obsolete, since there was already a user preference ViewLength to specify this. The value of this preference is also accessible in GAPInfo.ViewLength.

### New and updated packages since GAP 4.6.5

At the time of the release of GAP 4.6.5 there were 107 packages redistributed with GAP. The first public release of GAP 4.7 contains 114 packages.

One of essential changes is that the Citrus package by J.Mitchell has been renamed to Semigroups. The package has been completely overhauled, the performance has been improved, and the code has been generalized so that in the future the same code can be used to compute with other types of semigroups.

Furthermore, new packages that have been added to the redistribution since the release of GAP 4.6.5 are:

• 4ti2interface package by Sebastian Gutsche, providing an interface to 4ti2, a software package for algebraic, geometric and combinatorial problems on linear spaces.

• CoReLG by Heiko Dietrich, Paolo Faccin and Willem de Graaf for calculations in real semisimple Lie algebras.

• IntPic package by Manuel Delgado, aimed at providing a simple way of getting a pictorial view of sets of integers. The main goal of the package is producing Tikz code for arrays of integers. The code produced is to be included in a LaTeX file, which can then be processed. Some of the integers are emphasized by using different colors for the cells containing them.

• LieRing by Serena Cicalo and Willem de Graaf for constructing finitely-presented Lie rings and calculating the Lazard correspondence. The package also provides a database of small n-Engel Lie rings.

• LiePRing package by Michael Vaughan-Lee and Bettina Eick, introducing a new datastructure for nilpotent Lie rings of prime-power order. This allows to define such Lie rings for specific primes as well as for symbolic primes and other symbolic parameters. The package also includes a database of nilpotent Lie rings of order at most p^7 for all primes p > 3.

• ModIsom by Bettina Eick, which contains various methods for computing with nilpotent associative algebras. In particular, it contains a method to determine the automorphism group and to test isomorphisms of such algebras over finite fields and of modular group algebras of finite p-groups. Further, it contains a nilpotent quotient algorithm for finitely presented associative algebras and a method to determine Kurosh algebras.

• SLA by Willem de Graaf for computations with simple Lie algebras. The main topics of the package are nilpotent orbits, theta-groups and semisimple subalgebras.

Furthermore, some packages have been upgraded substantially since the GAP 4.6.5 release:

• ANUPQ package by Greg Gamble, Werner Nickel and Eamonn O'Brien has been updated after Max Horn joined it as a maintainer. As a result, it is now much easier to install and use it with the current GAP release.

• Wedderga package by Osnel Broche Cristo, Allen Herman, Alexander Konovalov, Aurora Olivieri, Gabriela Olteanu, Ángel del Río and Inneke Van Gelder has been extended to include functions for calculating local and global Schur indices of ordinary irreducible characters of finite groups, cyclotomic algebras over abelian number fields, and rational quaternion algebras (contribution by Allen Herman).

## GAP 4.6.5 (July 2013)

### Improved functionality:

• TraceMethods and UntraceMethods now better check their arguments and provide a sensible error message if being called without arguments. Also, both variants of calling them are now documented.

• Library methods for Sortex are now replaced by faster ones using the kernel SortParallel functionality instead of making expensive zipped lists.

### Fixed bugs which could lead to incorrect results:

• IntHexString wrongly produced a large integer when there were too many leading zeros. (Reported by Joe Bohanon)

### Fixed bugs that could lead to break loops:

• A bug that may occur in some cases while calling TransitiveIdentification. (Reported by Izumi Miyamoto)

• The new code for semidirect products of permutation groups, introduced in GAP 4.6, had a bug which was causing problems for Projection. (Reported by Graham Ellis)

## GAP 4.6.4 (April 2013)

### New functionality:

• New command line option -O was introduced to disable loading obsolete variables. This option may be used, for example, to check that they are not used in a GAP package or one's own GAP code.

### Fixed bugs which could lead to incorrect results:

• Fixed the bug in NewmanInfinityCriterion which may cause returning true instead of false. (Reported by Lev Glebsky)

### Fixed bugs which could lead to crashes:

• Fixed the kernel method for Remove which did not raise an error in case of empty lists, but corrupted the object. The error message in a library method is also improved. (Reported by Roberto Ràdina)

### Fixed bugs that could lead to break loops:

• Fixed requirements in a method to multiply a list and an algebraic element. (Reported by Sebastian Gutsche)

• Fixed a bug in NaturalCharacter entering a break loop when being called on a homomorphism whose image is not a permutation group. (Reported by Sebastian Gutsche)

• Fixed a bug in ExponentsConjugateLayer which occurred, for example, in some calls of SubgroupsSolvableGroup (Reported by Ramon Esteban-Romero)

• Fixed a problem with displaying function fields, e.g. Field(Indeterminate(Rationals,"x")). (Reported by Jan Willem Knopper)

• Fixed two bugs in the code for NaturalHomomorphismByIdeal for polynomial rings. (Reported by Martin Leuner)

• Added missing method for String for -infinity.

• Fixed the bug with ONanScottType not recognising product action properly in some cases.

• The method for SlotUsagePattern for straight line programs had a bug which triggered an error, if the straight line program contained unnecessary steps.

## GAP 4.6.3 (March 2013)

### Improved functionality:

• Several changes were made to IdentityMat and NullMat. First off, the documentation was changed to properly state that these functions support arbitrary rings, and not just fields. Also, more usage examples were added to the manual.

For NullMat, it is now also always possible to specify a ring element instead of a ring, and this is documented. This matches existing IdentityMat behavior, and partially worked before (undocumented), but in some cases could run into error or infinite recursion.

In the other direction, if a finite field element, IdentityMat now really creates a matrix over the smallest field containing that element. Previously, a matrix over the prime field was created instead, contrary to the documentation.

Furthermore, IdentityMat over small finite fields is now substantially faster when creating matrices of large dimension (say a thousand or so).

Finally, MutableIdentityMat and MutableNullMat were explicitly declared obsolete (and may be removed in GAP 4.7). They actually were deprecated since GAP 4.1, and their use discouraged by the manual. Code using them should switch to IdentityMat respectively NullMat.

• Two new PerfectResiduum methods were added for solvable and perfect groups, handling these cases optimally. Moreover, the existing generic method was improved by changing it to use DerivedSeriesOfGroup. Previously, it would always compute the derived series from scratch and then throw away the result.

• A new MinimalGeneratingSet method for groups handled by a nice monomorphisms was added, similar to the existing SmallGeneratingSet method. This is useful if the nice monomorphism is already mapping into a pc or pcp group.

• Added a special method for DerivedSubgroup if the group is known to be abelian.

### Fixed bugs:

• Fixed a bug in PowerModInt computing r^e mod m in a special case when e=0 and m=0. (Reported by Ignat Soroko)

• CoefficientsQadic now better checks its arguments to avoid an infinite loop when being asked for a q-adic representation for q=1. (Reported by Ignat Soroko)

• Methods for SylowSubgroupOp (see SylowSubgroup) for symmetric and alternating group did not always set IsPGroup and PrimePGroup for the returned Sylow subgroup.

• Display of matrices consisting of Conway field elements (which are displayed as polynomials) did not print constant 1 terms.

• Added an extra check and a better error message in the method to access natural generators of domains using the . operator (see GeneratorsOfDomain).

• Trying to solve the word problem in an fp group where one or more generators has a name of more than one alphabetic character led to a break loop.

• Provided the default method for AbsoluteIrreducibleModules as a temporary workaround for the problem which may cause returning wrong results or producing an error when being called for a non-prime field.

• A bug in the GAP kernel caused RNamObj to error out when called with a string that had the IsSSortedList property set (regardless of whether it was set to true or false). This in turn would lead to strange (and inappropriate) errors when using such a string to access entries of a record.

• GAP can store vectors over small finite fields (size at most 256) in a special internal data representation where each entry of the vector uses exactly one byte. Due to an off-by-one bug, the case of a field with exactly 256 elements was not handled properly. As a result, GAP failed to convert a vector to the special data representation, which in some situations could lead to a crash. The off-by-one error was fixed and now vectors over GF(256) work as expected.

• A bug in the code for accessing sublist via the list{poss} syntax could lead to GAP crashing. Specifically, if the list was a compressed vector over a finite field, and the sublist syntax was nested, as in vec{poss1}{poss2}. This now correctly triggers an error instead of crashing.

### New packages

• SpinSym package by L. Maas, which contains Brauer tables of Schur covers of symmetric and alternating groups and provides some related functionalities.

## GAP 4.6.2 (February 2013)

This is the first public release of GAP 4.6.

### Improved and extended functionality:

• It is now possible to declare a name as an operation with two or more arguments (possibly several times) and THEN declare it as an attribute. Previously this was only possible in the other order. This should make the system more independent of the order in which packages are loaded.

• Words in fp groups are now printed in factorised form if possible and not too time-consuming, i.e. a*b*a*b*a*b will be printed as (a*b)^3.

• Added methods to calculate Hall subgroups in nonsolvable groups.

• Added a generic method for IsPSolvable and a better generic method for IsPNilpotent for groups.

• Improvements to action homomorphisms: image of an element can use existing stabiliser chain of the image group (to reduce the number of images to compute), preimages under linear/projective action homomorphisms use linear algebra to avoid factorisation.

• To improve efficiency, additional code was added to make sure that the HomePcgs of a permutation group is in IsPcgsPermGroupRep representation in more cases.

• Added an operation SortBy with arguments being a function f of one argument and a list l to be sorted in such a way that l(f[i]) <= l(f[i+1]).

• Added a kernel function MEET_BLIST which returns true if the two boolean lists have true in any common position and false otherwise. This is useful for representing subsets of a fixed set by boolean lists.

• When assigning to a position in a compressed FFE vector GAP now checks to see if the value being assigned can be converted into an internal FFE element if it isn't one already. This uses new attribute AsInternalFFE, for which methods are installed for internal FFEs, Conway FFEs and ZmodpZ objects.

• Replaced ViewObj method for fields by ViewString method to improve the way how polynomial rings over algebraic extenstions of fields are displayed.

• Made the info string (optional 2nd argument to InstallImmediateMethod) behave similarly to the info string in InstallMethod. In particular, TraceImmediateMethods now always prints the name of the operation.

• Syntax errors such as Unbind(x,1) had the unhelpful property that x got unbound before the syntax error was reported. A specific check was added to catch this and similar cases a little earlier.

• Allow a GAPARGS parameter to the top-level GAP Makefile to pass extra arguments to the GAP used for manual building.

• Added an attribute UnderlyingRingElement for Lie objects.

• The function PrimeDivisors now became an attribute. (suggested by Mohamed Barakat)

• Added an operation DistancePerms with a kernel method for internal permutations and a generic method.

• Added a method for Subfields to support large finite fields. (reported by Inneke van Gelder)

### Fixed bugs which could lead to crashes:

• The extremely old DEBUG_DEADSONS_BAGS compile-time option has not worked correctly for many years and indeed crashes GAP. The type of bug it is there to detect has not arisen in many years and we have certainly not used this option, so it has been removed. (Reported by Volker Braun)

### Other fixed bugs:

• Scanning of floating point literals collided with iterated use of integers as record field elements in expressions like r.1.2.

• Fixed two potential problems in NorSerPermPcgs, one corrupting some internal data and one possibly mixing up different pcgs.

• Fixed a performance problem with NiceMonomorphism. (reported by John Bamberg)

• Fixed a bug in ReadCSV that caused some .csv files being parsed incorrectly.

### No longer supported:

• The file lib/consistency.g, which contained three undocumented auxiliary functions, has been removed from the library. In addition, the global record Revision is now deprecated, so there is no need to bind its components in GAP packages.

### New and updated packages since GAP 4.5.4

At the time of the release of GAP 4.5 there were 99 packages redistributed with GAP. The first public release of GAP 4.6 contains 106 packages.

The new packages that have been added to the redistribution since the release of GAP 4.5.4 are:

• AutoDoc package by S. Gutsche, providing tools for automated generation of GAPDoc manuals.

• Congruence package by A. Konovalov, which provides functions to construct various canonical congruence subgroups in SL_2(ℤ), and also intersections of a finite number of such subgroups, implements the algorithm for generating Farey symbols for congruence subgroups and uses it to produce a system of independent generators for these subgroups.

• Convex package by S. Gutsche, which provides structures and algorithms for convex geometry.

• Float package by L. Bartholdi, which extends GAP floating-point capabilities by providing new floating-point handlers for high-precision real, interval and complex arithmetic using MPFR, MPFI, MPC or CXSC external libraries. It also contains a very high-performance implementation of the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library FPLLL.

• PolymakeInterface package by T. Baechler and S. Gutsche, providing a link to the callable library of the polymake system.

• ToolsForHomalg package by M. Barakat, S. Gutsche and M. Lange-Hegermann, which provides some auxiliary functionality for the homalg project.

• ToricVarieties package by S. Gutsche, which provides data structures to handle toric varieties by their commutative algebra structure and by their combinatorics.

Furthermore, some packages have been upgraded substantially since the GAP 4.5.4 release:

• Starting from 2.x.x, the functionality for iterated monodromy groups has been moved from the FR package by L. Bartholdi to a separate package IMG (currently undeposited, available at https://github.com/laurentbartholdi/img). This completely removes the dependency of FR on external library modules, and should make its installation much easier.

## GAP 4.5.7 (December 2012)

### Fixed bugs which could lead to crashes:

• Closing with LogInputTo (or LogOutputTo) a logfile opened with LogTo left the data structures corrupted, resulting in a crash.

• On 32-bit systems we can have long integers n such that Log2Int(n) is not an immediate integer. In such cases Log2Int gave wrong or corrupted results which in turn could crash GAP, e.g., in ViewObj(n).

• Some patterns of use of UpEnv and DownEnv were leading to a segfault.

### Other fixed bugs:

• Viewing of long negative integers was broken, because it went into a break loop.

• Division by zero in ZmodnZ (n not prime) produced invalid objects. (Reported by Mark Dickinson)

• Fixed a bug in determining multiplicative inverse for a zero polynomial.

• Fixed a bug causing infinite recursion in NaturalHomomorphismByNormalSubgroup.

• A workaround was added to deal with a package method creating pcgs for permutation groups for which the entry permpcgsNormalSteps is missing.

• For a semigroup of associative words that is not the full semigroup of all associative words, the methods for Size and IsTrivial called one another causing infinite recursion.

• The 64-bit version of the gac script produced wrong (>= 2^31) CRC values because of an integer conversion problem.

• It was not possible to compile GAP on some systems where HAVE_SELECT detects as false.

• Numbers in memory options on the command line exceeding 2^32 could not be parsed correctly, even on 64-bit systems. (Reported by Volker Braun)

### New packages added for the redistribution with GAP:

• Float package by L. Bartholdi, which extends GAP floating-point capabilities by providing new floating-point handlers for high-precision real, interval and complex arithmetic using MPFR, MPFI, MPC or CXSC external libraries. It also contains a very high-performance implementation of the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library FPLLL.

• ToricVarieties package by S. Gutsche, which provides data structures to handle toric varieties by their commutative algebra structure and by their combinatorics.

## GAP 4.5.6 (September 2012)

### Improved functionality:

• The argument of SaveWorkspace can now start with ~/ which is expanded to the users home directory.

• Added the method for Iterator for PositiveIntegers. (Suggested by Attila Egri-Nagy).

• Changed kernel tables such that list access functionality for T_SINGULAR objects can be installed by methods at the GAP level.

• In case of saved history, "UP" arrow after starting GAP yields last stored line. The user preference HistoryMaxLines is now used when storing and saving history (see SetUserPreference).

### Fixed bugs which could lead to crashes:

• A crash occuring during garbage collection following a call to AClosVec for a GF(2) code. (Reported by Volker Braun)

• A crash when parsing certain syntactically invalid code. (Reported by multiple users)

• Fixed and improved command line editing without readline support. Fixed a segfault which could be triggered by a combination of "UP" and "DOWN" arrows. (Reported by James Mitchell)

• Fixed a bug in the kernel code for floats that caused a crash on SPARC Solaris in 32-bit mode. (Reported by Volker Braun)

### Other fixed bugs:

• Very large (more than 1024 digit) integers were not being coded correctly in function bodies unless the integer limb size was 16 bits. (Reported by Stefan Kohl)

• An old variable was used in assertion, causing errors in a debugging compilation. (Reported by Volker Braun)

• The environment variable PAGER is now correctly interpreted when it contains the full path to the pager program. Furthermore, if the external pager less is found from the environment it is made sure that the option -r is used (same for more -f). (Reported by Benjamin Lorenz)

• Fixed a bug in PermliftSeries. (Reported by Aiichi Yamasaki)

• Fixed discarder function in lattice computation to distinguish general and zuppo discarder. (Reported by Leonard Soicher)

• The GL and SL constructors did not correctly handle GL(filter,dim,ring).

• The names of two primitive groups of degree 64 were incorrect.

• The \in method for groups handled by a nice monomorphism sometimes could produce an error in situations where it should return false. This only happened when using SeedFaithfulAction to influence how NiceMonomorphism builds the nice monomorphims for a matrix groups.

• Wrong PrintObj method was removed to fix delegations accordingly to the reference manual.

• Fixed a method for Coefficients which, after Gaussian elimination, did not check that the coefficients actually lie in the left-acting-domain of the vector space. This could lead to a wrong answer in a vector space membership test. (Reported by Kevin Watkins)

### Improved documentation:

• Removed outdated statements from the documentation of StructureDescription which now non-ambiguosly states that StructureDescription is not an isomorphism invariant: non-isomorphic groups can have the same string value, and two isomorphic groups in different representations can produce different strings.

• GAP now allows overloading of a loaded help book by another one. In this case, only a warning is printed and no error is raised. This makes sense if a book of a not loaded package is loaded in a workspace and then GAP is started with a root path that contains a newer version. (Reported by Sebastian Gutsche)

• Provided a better description of user preferences mechanism and a hint to familiarise with them using WriteGapIniFile function to create a file which contains descriptions of all known user preferences and also sets those user preferences which currently do not have their default value. One can then edit that file to customize (further) the user preferences for future GAP sessions.

### New packages

• AutoDoc package by S. Gutsche, providing tools for automated generation of GAPDoc manuals.

• Convex package by S. Gutsche, which provides structures and algorithms for convex geometry.

• PolymakeInterface package by T. Baechler and S. Gutsche, providing a link to the callable library of the polymake system.

• ToolsForHomalg package by M. Barakat, S. Gutsche and M. Lange-Hegermann, which provides some auxiliary functionality for the homalg project.

## GAP 4.5.5 (July 2012)

### Fixed bugs which could lead to crashes:

• For small primes (compact fields) ZmodnZObj(r,p) now returns the corresponding FFE to avoid crashes when compacting matrices. (Reported by Ignat Soroko)

### Other fixed bugs:

• Fixed a bug in CommutatorSubgroup for fp groups causing infinite recursion, which could, for example, be triggered by computing automorphism groups.

• Previously, the list of factors of a polynomial was mutable, and hence could be accidentally corrupted by callers. Now the list of irreducible factors is stored immutable. To deal with implicit reliance on old code, always a shallow copy is returned. (reported by Jakob Kroeker)

• Computing high powers of matrices ran into an error for matrices in the format of the cvec package. Now the library function also works with these matrices. (reported by Klaus Lux)

• The pseudo tty code which is responsible for spawning subprocesses has been partially rewritten to allow more than 128 subprocesses on certain systems. This mechanism is for example used by ANUPQ and nq packages to compute group quotients via an external program. Previously, on Mac OS X this could be done precisely 128 times, and then an error would occur. That is, one could e.g. compute 128 nilpotent quotients, and then had to restart GAP to compute more. This also affected other systems, such as OpenBSD, where it now also works correctly.

• On Mac OS X, using GAP compiled against GNU readline 6.2, pasting text into the terminal session would result in this text appearing very slowly, with a 0.1 sec delay between each "keystroke". This is not the case with versions 6.1 and older, and has been reported to the GNU readline team. In the meantime, we work around this issue in most situations by setting rl_event_hook only if OnCharReadHookActive is set.

• ShowUserPreferences ran into a break loop in case of several undeclared user preferences. (Reported by James Mitchell)

• GAP did not start correctly if the user preference "InfoPackageLoadingLevel" was set to a number >= 3. The reason is that PrintFormattedString was called before it was installed. The current fix is a temporary solution.

• The "hints" member of TypOutputFile used to contain 3*100 entries, yet addLineBreakHint would write entries with index up to and including 3*99+3=300, leading to a buffer overflow. This would end up overwriting the "stream" member with -1. Fixed by incrementing the size of "hints" to 301. (Reported by Jakob Kroeker)

• The function IsDocumentedWord tested the given word against strings obtained by splitting help matches at non-letter characters. This way, variable names containing underscores or digits were erroneously not regarded as documented, and certain substrings of these names were erroneously regarded as documented.

• On Windows, an error occurred if one tried to use the default Windows browser as a help viewer (see SetHelpViewer). Now the browser opens the top of the correspoding manual chapter. The current fix is a temporary solution since the problem remains with the positioning at the required manual section.

### Improved functionality:

• WriteGapIniFile on Windows now produces the gap.ini file with Windows style line breaks. Also, an info message is now printed if an existing gap.ini file was moved to a backup file gap.ini.bak.

• The CTblLib and TomLib packages are removed from the list of suggested packages of the core part of GAP. Instead they are added to the default list of the user preference "PackagesToLoad". This way it is possible to configure GAP to not load these packages via changing the default value of "PackagesToLoad".

• The conjugacy test in S_n for intransitive subgroups was improved. This deals with inefficiency issue in the case reported by Stefan Kohl.

• Added InstallAndCallPostRestore to lib/system.g and call it in lib/init.g instead of CallAndInstallPostRestore for the function that reads the files listed in GAP command line. This fixes the problem reported by Yevgen Muntyan when SaveWorkspace was used in a file listed in GAP command line (before, according to the documentation, SaveWorkspace was only allowed at the main GAP prompt).

• There is now a new user preference PackagesToIgnore, see SetUserPreference. It contains a list of names of packages that shall be regarded as not available at all in the current session, both for autoloading and for later calls of LoadPackage. This preference is useful for testing purposes if one wants to run some code without loading certain packages.

## GAP 4.5.4 (June 2012)

This is the first public release of GAP 4.5.

This chapter lists most important changes between GAP 4.4.12 and the first public release of GAP 4.5. It also contains information about subsequent update releases for GAP 4.5. It is not meant to serve as a complete account on all improvements; instead, it should be viewed as an introduction to GAP 4.5, accompanying its release announcement.

### Performance improvements:

• The GAP kernel now uses GMP (GNU multiple precision arithmetic library) for faster large integer arithmetic.

• Improved performance for records with large number of components.

• Speedup of hash tables implementation at the GAP library level.

• MemoryUsage is now much more efficient, in particular for large objects.

• Speedups in the computation of low index subgroups, Tietze transformations, calculating high powers of matrices over finite fields, Factorial, etc.

### New and improved kernel functionality:

• By default, the GAP kernel compiles with the GMP and readline libraries. The GMP library is supplied with GAP and we recommend that you use the version we supply. There are some problems with some other versions. It is also possible to compile the GAP kernel with the system GMP if your system has it. The readline library must be installed on your system in advance to be used with GAP.

• Floating point literals are now supported in the GAP language, so that, floating point numbers can be entered in GAP expressions in a natural way. Support for floats is now properly documented. GAP has an interface using which packages may add new floating point implementations and integrate them with the parser. In particular, we expect that there will soon be a package that implements arbitrary precision floating point arithmetic.

• The Mersenne twister random number generator has been made independent of endianness, so that random seeds can now be transferred between architectures.

• Defaults for -m and -o options have been increased. Changes have been made to the way that GAP obtains memory from the Operating System, to make GAP more compatible with C libraries. A new -s option has been introduced to control or turn off the new behaviour.

• The filename and lines from which a function was read can now be recovered using FilenameFunc, StartlineFunc and EndlineFunc. This allows you, for example, to implement a function such as PageSource to show the file containing the source code of a function or a method in a pager, see Pager.

• CallFuncList was made into an operation so that it can be used to define behaviour of a non-function when called as a function.

• Improvements to the cyclotomic number arithmetic for fields with large conductors.

• Better and more flexible viewing of some large objects.

• Opportunity to interrupt some long kernel computations, e.g. multiplication of compressed matrices, intercepting Ctrl-C in designated places in the kernel code by means of a special kernel function for that purpose.

• ELM_LIST now allows you to install methods where the second argument is NOT a positive integer.

• Kernel function DirectoryContents to get the list of names of files and subdirectories in a directory.

• Kernel functions for Kronecker product of compressed matrices, see KroneckerProduct.

### New and improved library functionality:

• Extensions of data libraries:

• Functions and iterators are now available to create and enumerate simple groups by their order up to isomorphism: SimpleGroup, SmallSimpleGroup, SimpleGroupsIterator and AllSmallNonabelianSimpleGroups.

• Many more methods are now available for the built-in floating point numbers.

• The bound for the proper primality test in IsPrimeInt increased up to 10^18.

• Improved code for determining transversal and double coset representatives in large groups.

• Improvements in Normalizer for S_n.

• Smith normal form of a matrix may be computed over arbitrary euclidean rings, see NormalFormIntMat.

• Improved algorithms to determine the subgroup lattice of a group, as well as the function DotFileLatticeSubgroups to save the lattice structure in .dot file to view it e.g. with GraphViz.

• Special teaching mode which simplifies some output and provides more basic functionality.

• Functionality specific for use in undergraduate abstract algebra courses, e.g. checksums; string/integer list conversion; rings of small orders; the function SetNameObject to set display names for objects for more informative examples, e.g. constructing groups from "named" objects, such as, for example, R90 for a 90-degree rotation).

• Functions DirectoryDesktop and DirectoryHome which provide uniform access to default directories under Windows, Mac OS X and Unix.

• Improved methods for hashing when computing orbits.

• Functionality to call external binaries under Windows.

• Symplectic groups over residue class rings, see SymplecticGroup.

• Basic version of the simplex algorithm for matrices.

• New functions, operations and attributes: PrimeDivisors, Shuffle for lists, IteratorOfPartitions, IteratorOfCombinations, EnumeratorOfCombinations and others.

• The behaviour of Info statements can now be configured per info class, this applies to the way the arguments are printed and to the output stream.

• New function Test which is a more flexible and informative substitute of ReadTest operation.

• ConnectGroupAndCharacterTable is replaced by more robust function CharacterTableWithStoredGroup.

### Many problems in GAP have have been fixed, among them the following:

• Polynomial factorisation over rationals could miss factors of degree greater than deg(f)/2 if they have very small coefficients, while the cofactor has large coefficients.

• IntermediateSubgroups called on a group and a normal subgroup did not properly calculate maximal inclusion relationships.

• CentreOfCharacter and ClassPositionsOfCentre called for a group character could return a perhaps too large result.

• Trace called for an element of a finite field that was created with AlgebraicExtension ran into an error.

• IrreducibleRepresentationsDixon did not accept a list with one character as a second argument.

• Composing a homomorphism from a permutation group to a finitely presented group with another homomorphism could give wrong results.

• For certain arguments, the function EU returned wrong results.

• In the table of marks of cyclic groups, NormalizersTom value was wrong.

• The function PermChars returned a perhaps wrong result when the second argument was a positive integer (not a record) and the trivial character of the character table given as the first argument was not the first in the list of irreducibles.

• GAP crashed when the intersection of ranges became empty.

• IsPSL, and in turn StructureDescription, erroneously recognised non-PSL groups of the right order as PSL.

• The semidirect product method for pcgs computable groups sometimes tried to use finite presentations which were not polycyclic. This usually happened when the groups were not pc groups, and there was a very low risk of getting a wrong result.

• The membership test for a group of finite field elements ran into an error if the zero element of the field was given as the first argument.

• Constant polynomials were not recognised as univariate in any variable.

• The kernel recursion depth counter was not reset properly when running into many break loops.

• GAP did not behave well when printing of a (large) object was interrupted with Ctrl-C. Now the object is no longer corrupted and the indentation level is reset.

### Potentially incompatible changes:

• The zero polynomial now has degree -infinity, see DegreeOfLaurentPolynomial.

• Multiple unary + or - signs are no longer allowed (to avoid confusion with increment/decrement operators from other programming languages).

• Due to changes to improve the performance of records with large number of components, the ordering of record components in View'ed records has changed.

• Due to improvements for vectors over finite fields, certain objects have more limitations on changing their base field. For example, one cannot create a compressed matrix over GF(2) and then assign an element of GF(4) to one of its entries.

### No longer supported:

• Completion files mechanism.

• GAP 3 compatibility mode.

In addition, we no longer recommend using the GAP compiler gac to compile GAP code to C, and may withdraw it in future releases. Compiling GAP code only ever gave a substantial speedup for rather specific types of calculation, and much more benefit can usually be achieved quite easily by writing a small number of key functions in C and loading them into the kernel as described in LoadDynamicModule. The gac script will remain available as a convenient way of compiling such kernel modules from C.

Also, the following functions and operations were made obsolete: AffineOperation, AffineOperationLayer, FactorCosetOperation, DisplayRevision, ProductPol, TeXObj, LaTeXObj.

### Changes in distribution formats

The GAP 4.5 source distribution has the form of a single archive containing the core system and the most recent "stable" versions of all currently redistributed packages. There are no optional archives to download: the TomLib package now contains all its tables of marks in one archive; we do not provide separate versions of manuals for Internet Explorer, and the former tools archive is now included as an archive in the etc directory. To unpack and install the archive, user the script etc/install-tools.sh.

We no longer distribute separate bugfix archives when the core GAP system changes, or updated packages archives when a redistributed package is updated. Instead, the single GAP source distribution archive will be labelled by the version of the core GAP system and also by a timestamp. This archive contains the core system and the stable versions of the relevant packages on that date. To upgrade, you simply replace the whole directory containing the GAP installation, and rebuild binaries for the GAP kernel and packages. For new versions of packages, we will also continue to redistribute individual package archives so it will be possible to update a single package without changing the rest of the GAP installation.

Furthermore, by default GAP will now automatically read a user-specific GAP root directory (unless GAP is called with the -r option). All user settings can be made in that directory, so there will be no risk of them being lost during an update. Private packages can also be installed in this directory for the same reason.

There are some changes in archive formats used for the distribution: we continue to provide .tar.gz, .tar.bz2 and -win.zip archives. We have added .zip, and stopped providing .zoo archives. We no longer provide GAP binaries for Mac OS 9 (Classic) any more. For installations from source on Mac OS X one may follow the instructions for UNIX.

With the release of GAP 4.5, we also encourage more users to take advantage of the increasingly mature binary distributions which are now available. These include:

• The binary rsync distribution for GAP on Linux PCs with i686 or x86_64 compatible processors provided by Frank Lübeck.

• BOB, a tool for Linux and Mac OS X to download and build GAP and its packages from source provided by M. Neunhöffer.

• The GAP installer for Windows, provided by Alexander Konovalov.

In the near future, we also hope to have a binary distribution for Mac OS X.

Internally, we now have infrastructure to support more robust and frequent releases, and an improved system to fetch and test new versions of the increasingly large number of packages. The Example package documents technical requirements for packages, many of which are checked automatically by our systems. This will allow us to check the compatibility of packages with the system and with other packages more thoroughly before publishing them on the GAP website.

### Improvements to the user interface

By default, GAP now uses the readline library for command line editing. It provides such advantages as working with unicode terminals, nicer handling of long input lines, improved TAB-completion and flexible configuration. For further details, see Reference: Editing using the readline library.

We have extended facilities for user interface customisation. By default GAP automatically scans a user specific GAP root directory (unless GAP is called with the -r option). The name of this user specific directory depends on the operating system and is contained in GAPInfo.UserGapRoot. This directory can be used to tell GAP about personal preferences, to load some additional code, to install additional packages, or to overwrite some GAP files, see Reference: GAP Root Directories. Instead of a single .gaprc file we now use more flexible setup based on two files: gap.ini which is read early in the startup process, and gaprc which is read after the startup process, but before the first input file given on the command line. These files may be located in the user specific GAP root directory GAPInfo.UserGapRoot which by default is the first GAP root directory, see Reference: The gap.ini and gaprc files. For compatibility, the .gaprc file is still read if the directory GAPInfo.UserGapRoot does not exist. See Reference: The former .gaprc file for the instructions how to migrate your old setup.

Furthermore, there are functions to deal with user preferences, for example, to specify how GAP's online help is shown or whether the coloured prompt should be used. Calls to set user preferences may appear in the user's gap.ini file, as explained in Reference: Configuring User preferences.

In the Windows version, we include a new shell which uses the mintty terminal in addition to the two previously used shells (Windows command line and RXVT). The mintty shell is now recommended. It supports Unicode encoding and has flexible configurations options. Also, GAP under Windows now starts in the %HOMEDRIVE%%HOMEPATH% directory, which is the user's home directory. Besides this, a larger workspace is now permitted without a need to modify the Windows registry.

Other changes in the user interface include:

• the command line history is now implemented at the GAP level, it can be stored on quitting a GAP session and reread when starting a new session, see Reference: The command line history.

• SetPrintFormattingStatus("stdout",false); may be used to switch off the automatic line breaking in terminal output, see SetPrintFormattingStatus.

• GAP supports terminals with up to 4096 columns (extendable at compile time).

• Directories in -l command-line option can now be specified starting with ~/.

• Large integers are now displayed by a short string showing the first and last few digits, and the threshold to trigger this behaviour is user configurable (call UserPreference("MaxBitsIntView") to see the default value).

• The GAP banner has been made more compact and informative.

• SetHelpViewer now supports the Google Chrome browser.

• Multiple matches in the GAP online help are displayed via a function from the Browse package, which is loaded in the default configuration. This feature can be replaced by the known pager using the command


SetUserPreference( "browse", "SelectHelpMatches", false );


### Better documentation

The main GAP manuals have been converted to the GAPDoc format provided by the GAPDoc package by Frank Lübeck and Max Neunhöffer. This documentation format is already used by many packages and is now recommended for all GAP documentation.

Besides improvements to the documentation layout in all formats (text, PDF and HTML), the new GAP manuals incorporate a large number of corrections, clarifications, additions and updated examples.

We now provide two HTML versions of the manual, one of them with MathJax support for better display of mathematical symbols. Also, there are two PDF versions of the manual - a coloured and a monochrome one.

Several separate manuals now became parts of the GAP Reference manual. Thus, now there are three main GAP manual books:

• GAP Tutorial

• GAP Reference manual

• GAP - Changes from Earlier Versions

Note that there is no index file combining these three manuals. Instead of that, please use the GAP help system which will search all of these and about 100 package manuals.

### Packages in GAP 4.5

Here we list most important changes affecting packages and present new or essentially changed packages.

### Interface between the core system and packages

The package loading mechanism has been improved. The most important new feature is that all dependencies are evaluated in advance and then used to determine the order in which package files are read. This allows GAP to handle cyclic dependencies as well as situations where package A requires package B to be loaded completely before any file of package A is read. To avoid distortions of the order in which packages will be loaded, package authors are strongly discouraged from calling LoadPackage and TestPackageAvailability in a package code in order to determine whether some other package will be loaded before or together with the current package - instead, one should use IsPackageMarkedForLoading. In addition, there is now a better error management if package loading fails for packages that use the new functionality to log package loading messages (see DisplayPackageLoadingLog and the rest of the Chapter "Using and Developing GAP Packages" in the reference manual which documents how to use GAP packages), and package authors are very much encouraged to use these logging facilities.

In GAP 4.4 certain packages were marked as autoloaded and would be loaded, if present, when GAP started up. In GAP 4.5, this notion is divided into three. Certain packages are recorded as needed by the GAP system and others as suggested, in the same way that packages may need or suggest other packages. If a needed package is not loadable, GAP will not start. Currently only GAPDoc is needed. If a suggested package is loadable, it will be loaded. Typically these are packages which install better methods for Operations and Objects already present in GAP. Finally, the user preferences mechanism can be used to specify additional packages that should be loaded if possible. By default this includes most packages that were autoloaded in GAP 4.4.12, see ShowUserPreferences.

GAP packages may now use local namespaces to avoid name clashes for global variables introduced in other packages or in the GAP library, see Reference: Namespaces for GAP packages.

All guidance on how to develop a GAP package has been consolidated in the Example package which also contains a checklist for upgrading a GAP package to GAP 4.5 (the guidance has been transferred to Reference: Using and Developing GAP Packages in GAP 4.9).

### New and updated packages since GAP 4.4.12

At the time of the release of GAP 4.4.12 there were 75 packages redistributed with GAP (including the TomLib which was distributed in the core GAP archive). The first public release of GAP 4.5 contains precisely 99 packages.

The new packages that have been added to the redistribution since the release of GAP 4.4.12 are:

• Citrus package by J.D. Mitchell for computations with transformation semigroups and monoids (this package is a replacement of the Monoid package).

• cvec package by M. Neunhöffer, providing an implementation of compact vectors over finite fields.

• fwtree package by B. Eick and T. Rossmann for computing trees related to some pro-p-groups of finite width.

• GBNP package by A.M. Cohen and J.W. Knopper, providing algorithms for computing Grobner bases of noncommutative polynomials over fields with respect to the "total degree first then lexicographical" ordering.

• genss package by M. Neunhöffer and F. Noeske, implementing the randomised Schreier-Sims algorithm to compute a stabiliser chain and a base and a strong generating set for arbitrary finite groups.

• HAPprime package by P. Smith, extending the HAP package with an implementation of memory-efficient algorithms for the calculation of resolutions of small prime-power groups.

• hecke package by D. Traytel, providing functions for calculating decomposition matrices of Hecke algebras of the symmetric groups and q-Schur algebras (this package is a port of the GAP 3 package Specht 2.4 to GAP 4).

• Homalg project by M. Barakat, S. Gutsche, M. Lange-Hegermann et al., containing the following packages for the homological algebra: homalg, ExamplesForHomalg, Gauss, GaussForHomalg, GradedModules, GradedRingForHomalg, HomalgToCAS, IO_ForHomalg, LocalizeRingForHomalg, MatricesForHomalg, Modules, RingsForHomalg and SCO.

• MapClass package by A. James, K. Magaard and S. Shpectorov to calculate the mapping class group orbits for a given finite group.

• recogbase package by M. Neunhöffer and A. Seress, providing a framework to implement group recognition methods in a generic way (suitable, in particular, for permutation groups, matrix groups, projective groups and black box groups).

• recog package by M. Neunhöffer, A. Seress, N. Ankaralioglu, P. Brooksbank, F. Celler, S. Howe, M. Law, S. Linton, G. Malle, A. Niemeyer, E. O'Brien and C.M. Roney-Dougal, extending the recogbase package and provides a collection of methods for the constructive recognition of groups (mostly intended for permutation groups, matrix groups and projective groups).

• SCSCP package by A. Konovalov and S. Linton, implementing the Symbolic Computation Software Composability Protocol SCSCP for GAP, which provides interfaces to link a GAP instance with another copy of GAP or other SCSCP-compliant system running locally or remotely.

• simpcomp package by F. Effenberger and J. Spreer for working with simplicial complexes.

• Smallsemi package by A. Distler and J.D. Mitchell, containing the data library of all semigroups with at most 8 elements as well as various information about them.

• SymbCompCC package by D. Feichtenschlager for computations with parametrised presentations for finite p-groups of fixed coclass.

Furthermore, some packages have been upgraded substantially since the GAP 4.4.12 release:

• Alnuth package by B. Assmann, A. Distler and B. Eick uses an interface to PARI/GP system instead of the interface to KANT (thanks to B. Allombert for the GP code for the new interface and help with the transition) and now also works under Windows.

• CTblLib package (the GAP Character Table Library) by T. Breuer has been extended by many new character tables, a few bugs have been fixed, and new features have been added, for example concerning the relation to GAP's group libraries, better search facilities, and interactive overviews. For details, see the package manual.

• DESIGN package by L.H. Soicher:

• The functions PointBlockIncidenceMatrix, ConcurrenceMatrix, and InformationMatrix compute matrices associated with block designs.

• The function BlockDesignEfficiency computes certain statistical efficiency measures of a 1-(v,k,r) design, using exact algebraic computation.

• Example package by W. Nickel, G. Gamble and A. Konovalov has a more detailed and up-to-date guidance on developing a GAP package.

• FR package by L. Bartholdi now uses floating-point numbers to compute approximations of rational maps given by their group-theoretical description.

• The GAPDoc package by F. Lübeck and M. Neunhöffer provides various improvements, for example:

• The layout of the text version of the manuals can be configured quite freely, several standard "themes" are provided. The display is now adjusted to the current screen width.

• Some details of the layout of the HTML version of the manuals can now be configured by the user. All manuals are available with and without MathJax support for display of mathematical formulae.

• The text and HTML versions of manuals make more use of unicode characters (but the text version is also still reasonably good on terminals with latin1 or ASCII encoding).

• Of course, there are various improvements for authors of manuals as well, for example new functions ExtractExamples and RunExamples for automatic testing and correcting of manual examples.

• Gpd package by E.J. Moore and C.D. Wensley has been substantially rewritten. The main extensions provide functions for:

• Subgroupoids of a direct product with complete graph groupoid, specified by a root group and choice of rays.

• Automorphisms of finite groupoids - by object permutations; by root group automorphisms; and by ray images.

• The automorphism group of a finite groupoid together with an isomorphism to a quotient of permutation groups.

• Homogeneous groupoids (unions of isomorphic groupoids) and their morphisms, in particular homogeneous discrete groupoids: the latter are used in constructing crossed modules of groupoids in the XMod package.

• GRAPE package by L.H. Soicher:

• With much help from A. Hulpke, the interface between GRAPE and dreadnaut is now done entirely in GAP code.

• A 32-bit nauty/dreadnaut binary for Windows (XP and later) is included with GRAPE, so now GRAPE provides full functionality under Windows, with no installation necessary.

• Graphs with ordered partitions of their vertices into "colour-classes" are now handled by the graph automorphism group and isomorphism testing functions. An automorphism of a graph with colour-classes is an automorphism of the graph which additionally preserves the list of colour-classes (classwise), and an isomorphism from one graph with colour-classes to a second is a graph isomorphism from the first graph to the second which additionally maps the first list of colour-classes to the second (classwise).

• The GAP code and old standalone programs for the undocumented functions Enum and EnumColadj have been removed as their functionality can now largely be handled by current documented GAP and GRAPE functions.

• IO package by M. Neunhöffer:

• New build system to allow for more flexibility regarding the use of compiler options and adjusting to GAP 4.5.

• New functions to access time like IO_gettimeofday, IO_gmtime and IO_localtime.

• Some parallel skeletons built on fork like: ParListByFork, ParMapReduceByFork, ParTakeFirstResultByFork and ParWorkerFarmByFork.

• IOHub objects for automatic I/O multiplexing.

• New functions IO_gethostbyname and IO_getsockname.

• IRREDSOL package by B. Höfling now covers all irreducible soluble subgroups of GL(n,q) for q^n < 1000000 and primitive soluble permutation groups of degree < 1000000 (previously, the bound was 65536). It also has faster group recognition and adds a few omissions for GL(3,8) and GL(6,5).

• ParGAP package by G. Cooperman is now compiled using a system-wide MPI implementation by default to facilitate running it on proper clusters. There is also an option to build it with the MPINU library which is still supplied with the package (thanks to P. Smith for upgrading ParGAP build process).

• OpenMath package by M. Costantini, A. Konovalov, M. Nicosia and A. Solomon now supports much more OpenMath symbols to facilitate communication by the remote procedure call protocol implemented in the SCSCP package. Also, a third-party external library to support binary OpenMath encoding has been replaced by a proper implementation made entirely in GAP.

• Orb package by J. Müller, M. Neunhöffer and F. Noeske:

There have been numerous improvements to this package:

• A new fast implementation of AVL trees (balanced binary trees) in C.

• New interface to hash table functionality and implementation in C for speedup.

• Some new hash functions for various object types like transformations.

• New function ORB_EstimateOrbitSize using the birthday paradox.

• Improved functionality for product replacer objects.

• New "tree hash tables".

• New functionality to compute weak and strong orbits for semigroups and monoids.

• OrbitGraph for Orb orbits.

• Fast C kernel methods for the following functions:

PermLeftQuoTransformationNC, MappingPermSetSet, MappingPermListList, ImageSetOfTransformation, and KernelOfTransformation.

• New build system to allow for more flexibility regarding the use of compiler options and to adjust to GAP 4.5.

• RCWA package by S. Kohl among the new features and other improvements has the following:

• A database of all 52394 groups generated by 3 class transpositions of ℤ which interchange residue classes with modulus less than or equal to 6. This database contains the orders and the moduli of all of these groups. Also it provides information on what is known about which of these groups are equal and how their finite and infinite orbits on ℤ look like.

• More routines for investigating the action of an rcwa group on ℤ. Examples are a routine which attempts to find out whether a given rcwa group acts transitively on the set of nonnegative integers in its support and a routine which looks for finite orbits on the set of all residue classes of ℤ.

• Ability to deal with rcwa permutations of ℤ^2.

• Important methods have been made more efficient in terms of runtime and memory consumption.

• The output has been improved. For example, rcwa permutations are now Display'ed in ASCII text resembling LaTeX output.

• The XGAP package by F. Celler and M. Neunhöffer can now be used on 64-bit architectures (thanks to N. Eldredge and M. Horn for sending patches). Furthermore, there is now an export to XFig option (thanks to Russ Woodroofe for this patch). The help system in XGAP has been adjusted to GAP 4.5.

• Additionally, some packages with kernel modules or external binaries are now available in Windows. The -win.zip archive and the GAP installer for Windows include working versions of the following packages: Browse, cvec, EDIM, GRAPE, IO and orb, which were previously unavailable for Windows users.

Finally, the following packages are withdrawn:

• IF package by M. Costantini is unmaintained and no longer usable. More advanced functionality for interfaces to other computer algebra systems is now available in the SCSCP package by A. Konovalov and S. Linton.

• Monoid package by J. Mitchell is superseded by the Citrus package by the same author.

• NQL package by R. Hartung has been withdrawn by the author.

## GAP 4.4 Update 12 (December 2008)

### Fixed bugs which could lead to crashes:

• A bug whereby leaving an incomplete statement on a line (for instance typing while and then return) when prompt colouring was in use could lead to GAP crashing.

### Other fixed bugs:

• A bug which made the command-line editor unusable in a 64-bit version of GAP on Mac OS X.

## GAP 4.4 Update 11 (December 2008)

### Fixed bugs which could produce wrong results:

• MemoryUsage on objects with no subobjects left them in the cache and thus reported 0 in subsequent calls to MemoryUsage for the same object. (Reported by Stefan Kohl)

• Irr might be missing characters. (Reported by Angel del Rio)

• Up to now, it was allowed to call the function FullMatrixAlgebraCentralizer with a field and a list of matrices such that the entries of the matrices were not contained in the field; in this situation, the result did not fit to the documentation. Now the entries of the matrices are required to lie in the field, if not then an error is signaled.

• For those finite fields that are regarded as field extensions over non-prime fields (one can construct such fields with AsField), the function DefiningPolynomial erroneously returned a polynomial w.r.t. the extension of the prime field. (Reported by Stefan Kohl)

• Since the release of GAP 4.4.10, the return values of the function QuaternionAlgebra were not consistent w.r.t. the attribute GeneratorsOfAlgebra; the returned list could have length four or five. Now always the list of elements of the canonical basis is returned.

• MonomialGrevlexOrdering calculated a wrong ordering in certain cases. (Reported by Paul Smith)

• The (GAP kernel) method for the operation IntersectSet for ranges had two bugs, which could yield a result range with either too few or too many elements. As a consequence, for example the Intersection results for ranges could be wrong. (Reported by Matthew Fayers)

• Fixed a bug in the short-form display of elements of larger finite fields, a bug in some cross-field conversions and some inefficiencies and a missing method in the LogFFE code. (Reported by Jia Huang)

• In rare cases SmithNormalFormIntegerMatTransforms returned a wrong normal form (the version without transforming matrices did not have this problem). This is fixed. (Reported by Alexander Hulpke)

• The variant of the function StraightLineProgram that takes a string as its first argument returned wrong results if the last character of this string was a closing bracket.

• The code for central series in a permutation group used too tight a bound and thus falsely return a nilpotent permutation group as non-nilpotent.

### Fixed bugs which could lead to crashes:

• Under certain circumstances the kernel code for position in blists would access a memory location just after the end of the blist. If this location was not accessible, a crash could result. This was corrected and the code was cleaned up. (Reported by Alexander Hulpke)

### Other fixed bugs:

• The function IsomorphismTypeInfoFiniteSimpleGroup can be called with a positive integer instead of a group, and then returns information about the simple group(s) of this order. (This feature is currently undocumented.) For the argument 1, however, it ran into an infinite loop.

• A lookup in an empty dictionary entered a break loop. Now returns fail. (Reported by Laurent Bartholdi)

• The c++ keyword and can no longer be used as a macro parameter in the kernel. (Reported by Paul Smith)

• The operation KernelOfMultiplicativeGeneralMapping has methods designed to handle maps between permutation groups in a two-step approach, but did not reliably trigger the second step. This has now been fixed, preventing a slow infinite loop repeating the first step. This was normally only seen as part of a larger calculation.

• There were two methods for the operation Intersection2 which have implicitly assumed that finiteness of a collection can always be decided. Now, these methods check for IsFinite and CanComputeSize prior to calling IsFinite.

• Made error message in case of corrupted help book information (manual.six file) shorter and more informative. (Reported by Alexander Hulpke)

• GAP cannot call methods with more than six arguments. Now the functions NewOperation, DeclareOperation, and InstallMethod signal an error if one attempts to declare an operation or to install a method with more than six arguments.

• Up to now, IsOne had a special method for general mappings, which was much worse than the generic method; this special method has now been removed.

• When printing elements of an algebraic extension parentheses around coefficients were missing. (Reported by Maxim Hendriks)

### New or improved functionality:

• Make dynamic loading of modules possible on CYGWIN using a DLL based approach. Also move to using autoconf version 2.61.

• One can now call Basis, Iterator etc. with the return value of the function AlgebraicExtension.

• The function FrobeniusCharacterValue returned fail for results that require a finite field with more than 65536 elements. Meanwhile GAP can handle larger finite fields, so this restriction was removed. (It is still possible that FrobeniusCharacterValue returns fail.)

• Methods for testing membership in general linear groups and special linear groups over the integers have been added.

• Methods for String and ViewString for full row modules have been added. Further, a default method for IsRowModule has been added, which returns false for objects which are not free left modules.

• A ViewString method for objects with name has been added.

• The method for View for polynomial rings has been improved, and methods for String and ViewString for polynomial rings have been added.

• Binomial now works with huge n.

• The function InducedClassFunctionsByFusionMap is now documented.

• The return values of the function QuaternionAlgebra now store that they are division rings (if optional parameters are given then of course ths depends on these parameters).

## GAP 4.4 Update 10 (October 2007)

### New or improved functionality:

• Files in the cnf directory of the GAP distribution are now archived as binary files. Now GAP can be installed with UNIX or with WINDOWS style line breaks on any system and should work without problems.

• Since large finite fields are available, some restrictions in the code for computing irreducible modules over finite fields are no longer necessary. (They had been introduced in order to give better error messages.)

• Made PositionSublist faster in case the search string does not contain repetitive patterns.

• The function MakeImmutable now returns its argument.

• Dynamically loaded modules now work on Mac OS X. As a consequence, this allows to work with the Browse, EDIM and IO packages on Mac OS X.

• Introduced ViewObj and PrintObj methods for algebraic number fields. Made them applicable to AlgebraicExtension by adding the property IsNumberField in the infinite field case.

• The function CharacterTableRegular is documented now.

• The function ScalarProduct now accepts also Brauer characters as arguments.

• The function QuaternionAlgebra now accepts also a list of field elements instead of a field. Also, now the comparison of return values (w.r.t. equality, containment) yields true if the parameters coincide and the ground fields fit.

• The function RemoveCharacters is now documented.

• Lists in GAP sometimes occupy memory for possible additional entries. Now plain lists and strings read by GAP and the lists returned by List only occupy the memory they really need. For more details see the documentation of the new function EmptyPlist.

• There are some new Conway polynomials in characteristic 2 and 3 provided by Kate Minola.

• A new operation MemoryUsage determines the memory usage in bytes of an object and all its subobjects. It does not consider families and types but handles arbitrary self-referential structures of objects.

### Fixed bugs which could produce wrong results:

• When forming the semidirect product of a matrix group with a vector space over a non-prime field the embedding of the vector space gave a wrong result. (Reported by anvita21)

• DefaultRing failed for constant polynomials over nonprime fields. (Reported by Stefan Kohl)

• The method in ffeconway.gi that gets coefficients WRT to the canonical basis of the field from the representation is only correct if the basis is over the prime field. Added a TryNextMethod if this is not the case. (Reported by Alla Detinko)

• Creating a large (>2^16) field over a non-prime subfield went completely wrong. (Reported by Jack Schmidt, from Alla Detinko)

• A method for Coefficients for Conway polynomial FFEs didn't check that the basis provided was the canonical basis of the RIGHT field. (Reported by Bettina Eick)

• An elementary abelian series was calculated wrongly. (Reported by N. Sieben)

• Orbits on sets of transformations failed.

• Wrong methods for GeneratorsOfRing and GeneratorsOfRingWithOne have been removed. These methods were based on the assumption that one can obtain a set of ring generators by taking the union of a known set of field generators, the set of the inverses of these field generators and {1}.

• The name of a group of order 117600 and degree 50 was incorrect in the Primitive Permutation Groups library. In particular, a group was wrongly labelled as PGL(2, 49).

• There was a possible error in SubgroupsSolvableGroup when computing subgroups within a subgroup.

• An error in 2-Cohomology computation for pc groups was fixed.

• IsConjugate used normality in a wrong supergroup

### Fixed bugs which could lead to crashes:

• GAP crashed when the PATH environment variable was not set. (Reported by Robert F. Morse)

• GAP could crash when started with option -x 1. Now the number of columns is initialized with at least 2. (Reported by Robert F. Morse)

• After loading a saved workspace GAP crashed when one tried to slice a compressed vector over a field with 2 < q <= 256 elements, which had already existed in the saved workspace. (Reported by Laurent Bartholdi)

• FFECONWAY.WriteOverSmallestCommonField tripped up when the common field is smaller than the field over which some of the vector elements are written, because it did a test based on the degree of the element, not the field it is written over. (Reported by Thomas Breuer)

• Fixed the following error: When an FFE in the Conway polynomial representation actually lied in a field that is handled in the internal representation (eg GF(3)) and you tried to write it over a bigger field that is ALSO handled internally (eg GF(9)) you got an element written over the larger field, but in the Conway polynomial representation, which is forbidden. (Reported by Jack Schmidt)

• Attempting to compress a vector containing elements of a small finite field represented as elements of a bigger (external) field caused a segfault. (Reported by Edmund Robertson)

• GAP crashed when BlistList was called with a range and a list containing large integers or non-integers. (Reported by Laurent Bartholdi)

• GAP no longer crashes when OnTuples is called with a list that contains holes. (Reported by Thomas Breuer)

### Other fixed bugs:

• Socle for the trivial group could produce an error message.

• DirectoryContents ran into an error for immutable strings without trailing slash as argument. (Reported by Thomas Breuer)

• The functions IsInjective and IsSingleValued did not work for general linear mappings with trivial (pre)image. (Reported by Alper Odabas)

• Creating an enumerator for a prime field with more than 65536 elements ran into an infinite recursion. (Reported by Akos Seress)

• The performance of List, Filtered, Number, ForAll and ForAny if applied to non-internally represented lists was improved. Also the performance of iterators for lists was slightly improved.

• Finite field elements now know that they can be sorted easily which improves performance in certain lookups.

• A method for IsSubset was missing for the case that exactly one argument is an inhomogeneous list. (Reported by Laurent Bartholdi)

• Long integers in expressions are now printed (was not yet implemented). (Reported by Thomas Breuer)

• Fixed kernel function for printing records.

• New C library interfaces (e.g., to ncurses in the Browse package) need some more memory to be allocated with malloc. The default value of GAP -a option is now 2m>.

• IsBound(l[pos]) was failing for a large integer pos only when coded (e.g. in a loop or function body).

• ZmodpZObj is now a synonym for ZmodnZObj such that from now on such objects print in a way that can be read back into GAP.

• The outdated note that binary streams are not yet implemented has been removed.

## GAP 4.4 Update 9 (November 2006)

### Fixed bugs which could produce wrong results:

• The methods of ReadByte for reading from files or terminals returned wrong results for characters in the range [128..255]. (Reported by Yevgen Muntyan)

### Other fixed bugs:

• A method for the operation PseudoRandom did not succeed.

• A fix for Orbits with a set of points as a seed.

• Added a generic method such that Positions works with all types of lists.

• Fixed a problem in choosing the prime in the Dixon-Schneider algorithm. (Reported by Toshio Sumi)

### New or improved functionality:

• ReducedOrdinary was used in the manual, but was not documented, being a synonym for the documented ReducedCharacters. Changed manual examples to use the latter form. (Reported by Vahid Dabbaghian)

## GAP 4.4 Update 8 (September 2006)

### New or improved functionality:

• A function Positions with underlying operation PositionsOp, which returns the list of all positions at which a given object appears in a given list.

• LogFFE now returns fail when the element is not a power of the base.

• It is now allowed to continue long integers, strings or identifiers by ending a line with a backslash or with a backslash and carriage return character. So, files with GAP code and DOS/Windows-style line breaks are now valid input on all architectures.

• The command line for starting the session and the system environment are now available in GAPInfo.SystemCommandLine and GAPInfo.SystemEnvironment.

• Names of all bound global variables and all component names are available on GAP level.

• Added a few new Conway polynomials computed by Kate Minola and John Bray.

• There is a new concept of random sources, see IsRandomSource, which provides random number generators which are independent of each other. There is kernel code for the Mersenne twister random number generator (based on the code by Makoto Matsumoto available here). It provides fast 32-bit pseudorandom integers with a period of length 2^19937-1 and a 623-dimensional equidistribution. The library methods for random elements of lists and for random (long) integers are using the Mersenne twister now.

• In line editing mode (usual input mode without -n option) in lines starting with gap> , >  or brk>  this beginning part is immediately removed. This is a convenient feature that allows one to cut and paste input lines from other sessions or from manual examples into the current session.

### Fixed bugs which could produce wrong results:

• The function Decomposition returned coefficient vectors also in certain situations where in fact no decomposition exists. This happened only if the matrix entered as the first argument contained irrational values and a row in the matrix entered as the second argument did not respect the algebraic conjugacy relations between the columns of the first argument. So there was no problem for the usual cases that the two matrices are integral or that they are lists of Brauer characters. (Reported by Jürgen Müller)

• PC group homomorphisms can claim a wrong kernel after composition. (Reported by Serge Bouc)

• The return value of OctaveAlgebra had an inconsistent defining structure constants table for the case of coefficients fields not containing the integer zero. (Reported by Gábor Nagy)

• The manual guarantees that a conjugator automorphism has a conjugating element in the group if possible. This was not guaranteed.

• StabChain for symmetric groups gave a wrong result if fixed points were prescribed for base.

• Contrary to what is documented the function POW_OBJ_INT returned an immutable result for POW_OBJ_INT(m,1) for a mutable object m. This is triggered by the code m^1.

• PseudoRandom for a group had a problem if the group had lots of equal generators. The produced elements were extremely poorly distributed in that case. This is now fixed for the case that elements of the group can easily be sorted.

• Fixed the bug that the type of a boolean list was computed wrongly: The type previously had IS_PLIST_REP instead of IS_BLIST_REP in its filter list.

• Orbits did not respect a special PositionCanonical method for right transversals. (Reported by Steve Costenoble)

• Wrong results for GcdInt for some arguments on 64 bit systems only. (Reported by Robert Morse)

• When prescribing a subgroup to be included, the low index algorithm for fp groups sometimes returned subgroups which are in fact conjugate. (No subgroups are missing.) (Reported by Ignaz Soroko)

### Fixed bugs which could lead to crashes:

• The command line option -x allowed arguments > 256 which can then result in internal buffers overflowing. Now bigger numbers in the argument are equivalent to -x 256. (Reported by Michael Hartley)

### Other fixed bugs:

• Two special methods for the operation CompositionMapping2 were not correct, such that composing (and multiplying) certain group homomorphisms did not work. (Reported by Peter Mayr)

• In the definition of FrobeniusCharacterValue, it had been stated erroneously that the value must lie in the field of p^n-th roots of unity; the correct condition is that the value must lie in the field of (p^n-1)-th roots of unity. (Reported by Jack Schmidt)

• The function DirectProduct failed when one of the factors was known to be infinite.

• For a linear action homomorphism PreImageElm was very slow because there was no good method to check for injectivity, which is needed for nearly all good methods for PreImageElm. This change adds such a new method for IsInjective. (Reported by Akos Seress)

• Rare errors in the complement routine for permutation groups.

• Blocks code now uses jellyfish-style random elements to avoid bad Schreier trees.

• A method for IsPolycyclicGroup has been added. Such a method was missing so far.

• Corrected EpimorphismSchurCover to handle the trivial group correctly. Added new methods that follow immediately from computing the Schur Cover of a group. The attribute Epicentre, the operations NonabelianExteriorSquare and EpimorphismNonabelianExteriorSquare, and the property IsCentralFactor are added to the library with documentation and references.

• Display the correct expression in a call stack trace if an operation was called somewhere up due to the evaluation of a unary or binary operation.

• Made StripMemory an operation rather than a global function. Added ForgetMemory operation.

• Adjust things slightly to make later conversion to new vectors/matrices easier. Nothing of this should be visible.

• Corrected some details in the documentation of the GAP language. (Reported by Alexander Konovalov)

• Now PositionSorted is much faster on long mutable plain lists. (The former operation is substituted by a function and a new operation PositionSortedOp.) (Reported by Silviu Radu)

• Now it is possible to switch repeated warnings off when working with iterative polynomial rings.

## GAP 4.4 Update 7 (March 2006)

### New or improved functionality:

• The Display functionality for character tables has been extended by addition of an option to show power maps and centralizer orders in a format similar to that used in the ATLAS. Furthermore the options handling is now hierarchical, in order to admit more flexible overloading.

• For the function LowIndexSubgroupsFpGroup, there is now an iterator variant LowIndexSubgroupsFpGroupIterator. (Suggested (and based on code contributed) by Michael Hartley)

• Semigroup functionality in GAP has been improved and extended. Green's relations are now stored differently, making the system more amenable to new methods for computing these relations in special cases. It is now possible to calculate Green's classes etc. without computing the entire semigroup or necessarily loading the package MONOID. Furthermore, the Froidure-Pin algorithm has now been implemented in GAP.

• Functionality for creating free products of any list of groups for which a finite presentation can be determined had been added. This function returns a finitely presented group. This functionality includes the Embedding operation. As an application of this new code a specialized direct product operation has been added for finitely presented groups which returns a finitely presented group. This application includes Embedding and Projection functionality.

• Some new Straight Line Program (SLP) functionality has been added. The new functions take given SLPs and create new ones by restricting to a subset of the results, or to an intermediate result or by calculating the product of the results of two SLPs.

• New code has been added to allow group elements with memory; that is, they store automatically how they were derived from some given set of generators. Note that there is not yet documentation for this functionality, but some packages already use it.

• New code has been added to handle matrices and vectors in such a way that they do not change their representation in a generic manner.

• The Irr method for p-solvable p-modular Brauer tables now keeps the order of the irreducibles in the ordinary table.

• GAP can now handle any finite field for which the Conway polynomial is known or can be computed.

• New Conway polynomials provided by John Bray and Kate Minola have been added.

• The ReadTest methods for strings (filenames) and streams now automatically set the screen width (see SizeScreen) to 80 before the tests, and reset it afterwards.

• Now a few more checks are done during the configure phase of compiling for future use of some I/O functions of the C-library in a package. Also the path to the GAP binaries for the GAP compiler is now handled via autoconf. Finally, now autoconf version 2.59 is used.

### Fixed bugs which could produce wrong results:

• Some technical errors in the functions for compressed vectors and matrices which could lead to corruption of internal data structures and so to crashes or conceivably to wrong results. (Reported by Roman Schmied)

• A potential problem in the generic method for the undocumented operation DirectFactorsOfGroup: It was silently assumed that NormalSubgroups delivers the trivial subgroup as first and the whole group as last entry of the resulting list.

• The code for sublists of compressed vectors created by vec{range} may write one byte beyond the space allocated for the new vector, overwriting part of the next object in the workspace. Thanks to Jack Schmidt for narrowing down the problem.

• Given a class function object of value zero, an Arithmetic Operations for Class Functions method for a class function erroneously did not return fail. (Reported by Jack Schmidt)

• The Arithmetic Operations for Class Functions method for a class function erroneously returned a finite number if one of the values was nonreal, not a cyclotomic integer, and had norm 1.

• Two missing perfect groups were added, and the permutation degree lowered on the perfect groups with the largest degrees. (Reported by Jack Schmidt)

• When a character table was displayed with Display, the centralizer order displayed for the first class shown was not correct if it did not involve all prime divisors of the group. (Reported by Jack Schmidt)

• The first argument of the function VectorSpace must be a field. This is checked from now on. (Reported by Laurent Bartholdi)

• Up to now, it was possible to create a group object from a semigroup of cyclotomics using AsGroup, although groups of cyclotomics are not admissible. (Reported by Alexander Konovalov)

• The documentation of CharacteristicPolynomial(F,mat) was ambiguous if FieldOfMatrix(mat) <= F < DefaultFieldOfMatrix(mat). In particular, the result was representation dependent. This was fixed by introducing a second field which specifies the vector space which mat acts upon. (Reported by Jack Schmidt)

• AssociatedReesMatrixSemigroupOfDClass produced an incorrect sandwich matrix for the semigroup created. This matrix is an attribute set when creating the Rees matrix semigroup but is not used for creating the semigroup. The incorrect result was returned when SandwichMatrix was called. (Reported by Nelson Silva and Joao Araujo)

• The literal "compiled" was given an incorrect length. The kernel was then unable to find compiled library code as the search path was incorrect. Also the documentation example had an error in the path used to invoke the gac compiler.

• The twisting group in a generic wreath product might have had intransitive action. (Reported by Laurent Bartholdi)

• There was an arithmetic bug in the polynomial reduction code.

### Fixed bugs which could lead to crashes:

• Bug 1 in the list of fixed bugs which could lead to wrong results could also potentially lead to crashes.

### Other fixed bugs:

• The matrices of invariant forms stored as values of the attributes InvariantBilinearForm, InvariantQuadraticForm, and InvariantSesquilinearForm, for matrix groups over finite fields, are now in the (compressed) format returned by ImmutableMatrix.

• String now returns an immutable string, by making a copy before changing the argument.

• permutation^0 and permutation^1 were not handled with special code in the kernel, hence were very slow for big permutations. (Reported by Max Neunhöffer)

• Added code to cache the induced pcgs for an arbitrary parent pcgs. (This code was formerly part of the CRISP package.)

• This fix consists of numerous changes to improve support for direct products, including: - new methods for PcgsElementaryAbelianSeries, PcgsChiefSeries, ExponentsOfPcElement, DepthOfPcElement for direct products - fixed EnumeratorOfPcgs to test for membership first - new methods for membership test in groups which have an induced pcgs - added GroupOfPcgs attribute to pcgs in various methods - fixed declarations of PcgsElementaryAbelianSeries, PcgsChiefSeries (the declared argument was a pcgs, not a group) (Reported by Roman Schmied)

• Corrected a term ordering problem encountered by the basis construction code for finite dimensional vector spaces of multivariate rational functions. (Reported by Jan Draisma)

• When the factor of a finite dimensional group ring by an ideal was formed, a method intended for free algebras modulo relations was used, and the returned factor algebra could be used for (almost) nothing. (Reported by Heiko Dietrich)

• Up to now, PowerMap ran into an error when one asked for the n-th power map where n was not a small integer. This happened in some GAP library functions if the exponent of the character table in question was not a small integer.

• Up to now, the test whether a finite field element was contained in a group of finite field elements ran into an error if the element was not in the field generated by the group elements. (Reported by Heiko Dietrich)

• Conjugacy classes of natural (special) linear groups are now always returned with trivial class first.

• Up to now, it could happen that CheckFixedPoints reduced an entry in its second argument to a list containing only one integer but did not replace the list by that integer; according to the conventions, this replacement should be done.

• The functions PrintTo and AppendTo did not work correctly for streams. (Reported by Marco Costantini)

• The function Basis did not return a value when it was called with the argument Rationals. (Reported by Klaus Lux)

• For certain matrix groups, the function StructureDescription raised an error message. The reason for this was that a trivial method for IsGeneralLinearGroup for matrix groups in lib/grpmat.gi which is ranked higher than the nontrivial method for generic groups in lib/grpnames.gi called the operation IsNaturalGL, for which there was no nontrivial method available. (Reported by Nilo de Roock)

• Action on sets of length 1 was not correctly handled. (Reported by Mathieu Dutour)

• Now WriteByte admits writing zero characters to all streams. (Reported by Marco Costantini)

• The conjugacy test for subgroups tests for elementary abelian regular normal subgroup (EARNS) conjugacy. The fix will catch this in the case that the second group has no EARNS. (Reported by Andrew Johnson)

• So far, the UNIX installation didn't result in a correct gap.sh if the installation path contained space characters. Now it should handle this case correctly, as well as other unusual characters in path names (except for double quotes).

## GAP 4.4 Update 6 (September 2005)

Attribution of bugfixes and improved functionalities to those who reported or provided these, respectively, is still fairly incomplete and inconsistent with this update. We apologise for this fact and will discuss until the next update how to improve this feature.

### Fixed bugs which could produce wrong results:

• The perfect group library does not contain any information on the trivial group, so the trivial group must be handled specially. PerfectGroup and NrPerfectLibraryGroups were changed to indicate that the trivial group is not part of the library.

• The descriptions of PerfectGroup(734832,3) and PerfectGroup(864000,3) were corrected in the library of perfect groups.

• The functions EpimorphismSchurCover and AbelianInvariantsMultiplier may have produced wrong results without warning (Reported by Colin Ingalls). These problems are fixed. However, the methods currently used can be expected to be slower than the ones used before; we hope to fix this in the next version of GAP.

• DerivedSubgroup and CommutatorSubgroup for permutation groups sometimes returned groups with an incorrect stabilizer chain due to a missing verification step after a random Schreier Sims.

• NaturalHomomorphismByNormalSubgroup for FpGroups did unnecessary rewrites.

• The alternating group A_3 incorrectly claimed to be not simple.

• ExponentSyllable for straight line program elements gave a wrong result.

• PrimePGroup is defined to return fail for trivial groups, but if the group was constructed as a factor or subgroup of a known p-group, the value of p was retained.

• The functions TestPackageAvailability and LoadPackage did not work correctly when one asked for a particular version of the package, via a version number starting with the character =, in the sense that a version with a larger version number was loaded if it was available. (Reported by Burkhard Höfling)

• The generator names constructed by AlgebraByStructureConstants were nonsense.

• The undocumented function (but recently advertised on gap-dev) COPY_LIST_ENTRIES did not handle overlapping source and destination areas correctly in some cases.

• The elements in a free magma ring have the filter IsAssociativeElement set whenever the elements in the underlying magma and in the coefficients ring have this filter set. (Reported by Randy Cone)

• The function InstallValue must not be used for objects in the filter IsFamily because these objects are compared via IsIdenticalObj. (Reported by Max Neunhöffer)

### Fixed bugs which could lead to crashes:

• Problem in composition series for permutation groups for non-Frobenius groups with regular point stabilizer.

• After lots of computations with compressed GF(2) vectors GAP occasionally crashed. The reason were three missing CHANGED_BAGs in SemiEchelonPListGF2Vecs. They were missing, because a garbage collection could be triggered during the computation such that newly created bags could become "old". It is not possible to provide test code because the error condition cannot easily be reproduced. (Reported by Klaus Lux)

• Minor bug that crashed GAP: The type of IMPLICATIONS could not be determined in a fresh session. (Reported by Marco Costantini)

• Assert caused an infinite loop if called as the first line of a function called from another function.

### Other fixed bugs:

• Wrong choice of prime in Dixon-Schneider if prime is bigger than group order (if group has large exponent).

• Groebner basis code ran into problems when comparing monomial orderings.

• When testing for conjugacy of a primitive group to an imprimitive group,GAP runs into an error in EARNS calculation. (Reported by John Jones)

• The centre of a magma is commonly defined to be the set of elements that commute and associate with all elements. The previous definition left out "associate" and caused problems with extending the functionality to nonassociative loops. (Reported by Petr Vojtechovsky)

• New kernel methods for taking the intersection and difference between sets of substantially different sizes give a big performance increase.

• The commands IsNaturalSymmetricGroup and IsNaturalAlternatingGroup are faster and should run much less often into inefficient tests.

• The perfect group library, see Finite Perfect Groups, is split into several files which are loaded and unloaded to keep memory usage down. The global variable PERFSELECT is a blist which indicates which orders are currently loaded. An off-by-one error wrongly added the last order of the previous file into the list of valid orders when a new file was loaded. A subsequent access to this order raises an error.

• Up to now, the method installed for testing the membership of rationals in the field of rationals via IsRat was not called; instead a more general method was used that called Conductor and thus was much slower. Now the special method has been ranked up by changing the requirements in the method installation.

• Fixed a bug in APPEND_VEC8BIT, which was triggered in the following situation: Let e be the number of field elements stored in one byte. If a compressed 8bit-vector v had length not divisible by e and another compressed 8-bit vector w was appended, such that the sum of the lengths became divisible by e, then one 0 byte too much was written, which destroyed the TNUM of the next GAP object in memory. (Reported by Klaus Lux)

• PermutationCycle returned fail if the cycle was not a contiguous subset of the specified domain. (Reported by Luc Teirlinck)

• Now Inverse correctly returns fail for zeros in finite fields (and does no longer enter a break loop).

• Up to now, CharacterDegrees ignored the attribute Irr if the argument was a group that knew that it was solvable.

• The function Debug now prints a meaningful message if the user tries to debug an operation. Also, the help file for vi is now available in the case of several GAP root directories.

• It is no longer possible to create corrupt objects via ranges of length >2^28, resp. >2^60 (depending on the architecture). The limitation concerning the arguments of ranges is documented. (Reported by Stefan Kohl)

• Now IsElementaryAbelian and ClassPositionsOfMinimalNormalSubgroups are available for ordinary character tables. Now the operation CharacterTableIsoclinic is an attribute, and there is another new attribute SourceOfIsoclinicTable that points back to the original table; this is used for computing the Brauer tables of those tables in the character table library that are computed using CharacterTableIsoclinic. Now ClassPositionsOfDerivedSubgroup avoids calling Irr, since LinearCharacters is sufficient. Now ClassPositionsOfElementaryAbelianSeries works also for the table of the trivial group. Restrictions of character objects know that they are characters.

A few formulations in the documentation concerning character tables have been improved slightly.

• Up to now, IsPGroup has rarely been set. Now many basic operations such as SylowSubgroup set this attribute on the returned result.

• Computing an enumerator for a semigroup required too much time because it used all elements instead of the given generators. (Reported by Manuel Delgado)

• Avoid potential error message when working with automorphism groups.

• Fixed wrong page references in manual indices.

• Make MutableCopyMat an operation and install the former function which does call List with ShallowCopy the default method for lists. Also use this in a few appropriate places.

• An old DEC compiler doesn't like C preprocessor directives that are preceded by whitespace. Removed such whitespace. (Reported by Chris Wensley)

### New or improved functionality:

• The primitive groups library has been extended to degree 2499.

• New operation Remove and extended functionality of Add with an optional argument giving the position of the insertion. They are based on an efficient kernel function COPY_LIST_ENTRIES.

• Added fast kernel implementation of Tarjan's algorithm for strongly connected components of a directed graph.

• Now IsProbablyPrimeInt can be used with larger numbers. (Made internal function TraceModQF non-recursive.)

• A new operation PadicValuation and a corresponding method for rationals.

• A new operation PartialFactorization has been added, and a corresponding method for integers has been installed. This method allows one to specify the amount of work to be spent on looking for factors.

• The generators of full s. c. algebras can now be accessed with the dot operator. (Reported by Marcus Bishop)

• New Conway polynomials computed by Kate Minola, John Bray, Richard Parker.

• A new attribute EpimorphismFromFreeGroup. The code has been written by Alexander Hulpke.

• The functions Lambda, Phi, Sigma, and Tau have been turned into operations, to admit the installation of methods for arguments other than integers.

• Up to now, one could assign only lists with InstallFlushableValue. Now also records are admitted.

• InstallMethod now admits entering a list of strings instead of a list of required filters. Each such string must evaluate to a filter when used as the argument of EvalString. The advantage of this variant is that these strings are used to compose an info string (which is shown by ApplicableMethod) that reflects exactly the required filters.

• In test files that are read with ReadTest, the assertion level is set to 2 between START_TEST and STOP_TEST. This may result in runtimes for the tests that are substantially longer than the usual runtimes with default assertion level 0. In particular this is the reason why some of the standard test files require more time in GAP 4.4.6 than in GAP 4.4.5.

• Some very basic functionality for floats.

## GAP 4.4 Update 5 (May 2005)

### Fixed bugs which could produce wrong results:

• GroupWithGenerators returned a meaningless group object instead of signaling an error when it was called with an empty list of generators.

• When computing preimages under an embedding into a direct product of permutation groups, if the element was not in the image of the embedding then a permutation had been returned instead of fail.

• Two problems with PowerMod for polynomials. (Reported by Jack Schmidt)

• Some methods for computing the sum of ideals returned the first summand instead of the sum. (Reported by Alexander Konovalov)

• Wrong result in Intersection for pc groups.

• The function CompareVersionNumbers erroneously ignored leading non-digit characters.

A new feature in the corrected version is an optional third argument "equal", which causes the function to return true only if the first two arguments describe equal version numbers; documentation is available in the ext-manual. This new feature is used in LoadPackage, now one can require a specific version of a package.

The library code still contained parts of the handling of completion files for packages, which does not work and therefore had already been removed from the documentation. This code has now been removed.

Now a new component PreloadFile is supported in PackageInfo.g files; if it is bound then the file in question is read immediately before the package or its documentation is loaded.

• The result of String for strings not in IsStringRep that occur as list entries or record components was erroneously missing the double quotes around the strings.

• A bug which caused InducedPcgs to return a pcgs which is not induced wrt. the parent pcgs of pcgs. This may cause unpredictable behaviour, e. g. when SiftedPcElement is used subsequently. (Reported by Alexander Konovalov)

• Fixed a bug in SmallGroupsInformation(512).

• PowerModCoeffs with exponent 1 for compressed vectors did not reduce (a copy of) the input vector before returning it. (Reported by Frank Lübeck)

• Sorting a mutable non-plain list (e.g., a compressed matrix over fields of order < 257) could potentially destroy that object. (Reported by Alexander Hulpke)

• Under rare circumstances computing the closure of a permutation group by a normalizing element could produce a corrupted stabilizer chain. (The underlying algorithm uses random elements, probability of failure was below 1 percent). (Reported by Thomas Breuer)

### Fixed bugs which could lead to crashes:

• Some code and comments in the GAP kernel assumed that there is no garbage collection during the core printing function Pr, which is not correct. This could cause GAP in rare cases to crash during printing permutations, cyclotomics or strings with zero bytes. (Reported by Warwick Harvey)

### Other fixed bugs:

• A rare problem with the choice of prime in the Dixon-Schneider algorithm for computing the character table of a group. (Reported by Jack Schmidt)

• DirectProduct for trivial permutation groups returned a strange object.

• A problem with PolynomialReduction running into an infinite loop.

• Adding linear mappings with different image domains was not possible. (Reported by Pasha Zusmanovich)

• Multiplying group ring elements with rationals was not possible. (Reported by Laurent Bartholdi)

• Random now works for finite fields of size larger than 2^28. (Reported by Jack Schmidt)

• Univariate polynomial creators did modify the coefficient list passed. (Reported by Jürgen Müller)

• Fixed IntHexString to accept arguments not in IsStringRep; the argument is now first converted if necessary. (Reported by Kenn Heinrich)

• The library code for stabilizer chains contained quite some explicit references to the identity (). This is unfortunate if one works with permutation groups, the elements of which are not plain permutations but objects which carry additional information like a memory, how they were obtained from the group generators. For such cases it is much cleaner to use the One(...) operation instead of (), such that the library code can be used for a richer class of group objects. This fix contains only rather trivial changes () to One(...) which were carefully checked by me. The tests for permutation groups all run without a problem. However, it is relatively difficult to provide test code for this particular change, since the "improvement" only shows up when one generates new group objects. This is for example done in the package recog which is in preparation. (Reported by Akos Seress and Max Neunhöffer)

• Using {} to select elements of a known inhomogenous dense list produced a list that might falsely claim to be known inhomogenous, which could lead to a segfault if the list typing code tried to mark it homogenous, since the code intended to catch such errors also had a bug. (Reported by Steve Linton)

• The record for the generic iterator construction of subspaces domains of non-row spaces was not complete.

• When a workspace has been created without packages(-A option) and is loaded into a GAP session without packages (same option) then an error message is printed.

• So far the functions IsPrimeInt and IsProbablyPrimeInt are essentially the same except that IsPrimeInt issues an additional warning when (non-proven) probable primes are considered as primes.

These warnings now print the probable primes in question as well; if a probable prime is used several times then the warning is also printed several times; there is no longer a warning for some known large primes; the warnings can be switched off. See IsPrimeInt for more details.

If we get a reasonable primality test in GAP we will change the definition of IsPrimeInt to do a proper test.

• Corrected some names of primitive groups in degree 26. (Reported by Robert F. Bailey)

### New or improved functionality:

• Several changes for ConwayPolynomial:

• many new pre-computed polynomials

• put data in several separate files (only read when needed)

• added info on origins of pre-computed polynomials

• improved performance of ConwayPolynomial and IsPrimitivePolynomial for p < 256

• improved documentation of ConwayPolynomial

• added and documented new functions IsCheapConwayPolynomial and RandomPrimitivePolynomial

• Added method for NormalBase for extensions of finite fields.

• Added more help viewers for the HTML version of the documentation (firefox, mozilla, konqueror, w3m, safari).

• New function ColorPrompt. (Users of former versions of a colorprompt.g file: Now you just need a ColorPrompt(true); in your .gaprc file.)

• Specialised kernel functions to support GUAVA 2.0. GAP will only load GUAVA in version at least 2.002 after this update.

• Now there is a kernel function CYC_LIST for converting a list of rationals into a cyclotomic, without arithmetics overhead.

• New functions ContinuedFractionExpansionOfRoot and ContinuedFractionApproximationOfRoot for computing continued fraction expansions and continued fraction approximations of real roots of polynomials with integer coefficients.

• A method for computing structure descriptions for finite groups, available via StructureDescription.

• This change contains the new, extended version of the SmallGroups package. For example, the groups of orders p^4, p^5, p^6 for arbitrary primes p, the groups of square-free order and the groups of cube-free order at most 50000 are included now. For more detailed information see the announcement of the extended package.

• The function ShowPackageVariables gives an overview of the global variables in a package. It is thought as a utility for package authors and referees. (It uses the new function IsDocumentedVariable.)

• The mechanisms for testing GAP has been improved:

• The information whether a test file belongs to the list in tst/testall.g is now stored in the test file itself.

• Some targets for testing have been added to the Makefile in the GAP root directory, the output of the tests goes to the new directory dev/log.

• Utility functions for testing are in the new file tst/testutil.g. Now the loops over (some or all) files tst/*.tst can be performed with a function call, and the file tst/testall.g can be created automatically; the file tst/testfull.g is now obsolete. The remormalization of the scaling factors can now be done using a GAP function, so the file tst/renorm.g is obsolete.

• Now the functions START_TEST and STOP_TEST use components in GAPInfo instead of own globals, and the random number generator is always reset in START_TEST.

• GAPInfo.SystemInformation now takes two arguments, now one can use it easier in the tests.

• MultiplicationTable is now an attribute, and the construction of a magma, monoid, etc. from multiplication tables has been unified.

## GAP 4.4 Bugfix 4 (December 2004)

### Fixed bugs which could produce wrong results:

• An error in the Order method for matrices over cyclotomic fields which caused this method to return infinity for matrices of finite order in certain cases.

• Representations computed by IrreducibleRepresentations in characteristic 0 erraneously claimed to be faithful.

• A primitive representation of degree 574 for PSL(2,41) has been missing in the classification on which the GAP library was built.

• A bug in Append for compressed vectors over GF(2): if the length of the result is 1 mod 32 (or 64) the last entry was forgotten to copy.

• A problem with the Ree group Ree(3) of size 1512 claiming to be simple.

• An error in the membership test for groups GU(n,q) and SU(n,q) for non-prime q.

• An error in the kernel code for ranges which caused e.g. -1 in [1..2] to return true.

• An error recording boolean lists in saved workspaces.

• A problem in the selection function for primitive and transitive groups if no degree is given.

• ReducedConfluentRewritingSystem returning a cached result that might not conform to the ordering specified.

### Other fixed bugs:

• A problem with the function SuggestUpdates to check for the most recent version of packages available.

• A problem that caused MatrixOfAction to produce an error when the algebra module was constructed as a direct sum.

• Problems with computing n-th power maps of character tables, where n is negative and the table does not yet store its irreducible characters.

• Element conjugacy in large-base permutation groups sometimes was unnecessarily inefficient.

• A missing method for getting the letter representation of an associate word in straight line program representation.

• A problem with the construction of vector space bases where the given list of basis vectors is itself an object that was returned by Basis.

• A problem of AbelianInvariantsMultiplier insisting that a result of IsomorphismFpGroup is known to be surjective.

• An error in the routine for Resultant if one of the polynomials has degree zero.

## GAP 4.4 Bugfix 3 (May 2004)

### Fixed bugs which could produce wrong results:

• Incorrect setting of system variables (e.g., home directory and command line options) after loading a workspace.

• Wrong handling of integer literals within functions or loops on 64-bit architectures (only integers in the range from 2^28 to 2^60).

### Fixed bugs which could lead to crashes:

• A problem in the installation of the multiplication routine for matrices that claimed to be applicable for more general list multiplications.

• A problem when computing weight distributions of codes with weights

2^28.

### Other fixed bugs:

• A problem in GQuotients when mapping from a finitely presented group which has a free direct factor.

• A bug in the function DisplayRevision.

• The trivial finitely presented group on no generators was not recognized as finitely presented.

• A problem with Process.

• A problem when intersecting subgroups of finitely presented groups that are represented in "quotient representation" with the quotient not apermutation group.

• A bug in the generic Intersection2 method for vector spaces, in the case that both spaces are trivial.

• Enable ReeGroup(q) for q = 3.

## GAP 4.4 Bugfix 2 (April 2004)

### Fixed bugs which could lead to crashes:

• A crash when incorrect types of arguments are passed to FileString.

### Other fixed bugs:

• A bug in DerivedSubgroupTom and DerivedSubgroupsTom.

• An error in the inversion of certain ZmodnZObj elements.

• A wrong display string of the numerator in rational functions returned by MolienSeriesWithGivenDenominator (in the case that the constant term of this numerator is zero).

## Changes between GAP 4.3 and GAP 4.4

This chapter contains an overview of most important changes introduced in GAP 4.4. It also contains information about subsequent update releases of GAP 4.4.

### Potentially Incompatible Changes

• The mechanism for the loading of Packages has changed to allow easier updates independent of main GAP releases. Packages require a file PackageInfo.g now. The new PackageInfo.g files are available for all packages with the new version of GAP.

• IsSimpleGroup returns false now for the trivial group.

• PrimeBlocks: The output format has changed.

• Division rings (see IsDivisionRing) are now implemented as IsRingWithOne.

• DirectSumOfAlgebras: p-th power maps are compatible with the input now.

• The print order for polynomials has been changed.

These changes are, in some respects, departures from our policy of maintaining upward compatibility of documented functions between releases. In the first case, we felt that the old behavior was sufficiently inconsistent, illogical, and impossible to document that we had no alternative but to change it. In the case of the package interface, the change was necessary to introduce new functionality. The planned and phased removal of a few unnecessary functions or synonyms is needed to avoid becoming buried in "legacy" interfaces, but we remain committed to our policy of maintaining upward compatibility whenever sensibly possible.

• Groebner Bases:

Buchberger's algorithm to compute Groebner Bases has been implemented in GAP. (A. Hulpke)

• For large scale Groebner Basis computations there also is an interface to the Singular system available in the Singular package. (M. Costantini and W. de Graaf)

• New methods for factorizing polynomials over algebraic extensions of the rationals have been implemented in GAP. (A. Hulpke)

• For more functionality to compute with algebraic number fields there is an interface to the Kant system available in the Alnuth package. (B. Assmann and B. Eick)

• A new functionality to compute the minimal normal subgroups of a finite group, as well as its socle, has been installed. (B. Höfling)

• A fast method for recognizing whether a permutation group is symmetric or alternating is available now (A. Seress)

• A method for computing the Galois group of a rational polynomial is available again. (A. Hulpke)

• The algorithm for BrauerCharacterValue has been extended to the case where the splitting field is not supported in GAP. (T. Breuer)

• Brauer tables of direct products can now be constructed from the known Brauer tables of the direct factors. (T. Breuer)

• Basic support for vector spaces of rational functions and of uea elements is available now in GAP. (T. Breuer and W. de Graaf)

• Various new functions for computations with integer matrices are available, such as methods for computing normal forms of integer matrices as well as nullspaces or solutions systems of equations. (W. Nickel and F. Gähler)

### New Packages

The following new Packages have been accepted.

### Performance Enhancements

• The computation of irreducible representations and irreducible characters using the Baum-Clausen algorithm and the implementation of the Dixon-Schneider algorithm have been speeded up.

• The algorithm for PossibleClassFusions has been changed: the efficiency is improved and a new criterion is used. The algorithm for PossibleFusionsCharTableTom has been speeded up. The method for PrimeBlocks has been improved following a suggestion of H. Pahlings.

• New improved methods for normalizer and subgroup conjugation in S_n have been installed and new improved methods for IsNaturalSymmetricGroup and IsNaturalAlternatingGroup have been implemented. These improve the available methods when groups of large degrees are given.

• The partition split method used in the permutation backtrack is now in the kernel. Transversal computations in large permutation groups are improved. Homomorphisms from free groups into permutation groups now give substantially shorter words for preimages.

• The membership test in SP and SU groups has been improved using the invariant forms underlying these groups.

• An improvement for the cyclic extension method for the computation of subgroup lattices has been implemented.

• A better method for MinimalPolynomial for finite field matrices has been implemented.

• The display has changed and the arithmetic of multivariate polynomials has been improved.

• The LogMod function now uses Pollard's rho method combined with the Pohlig/Hellmann approach.

• Various functions for sets and lists have been improved following suggestions of L. Teirlinck. These include: Sort, Sortex, SortParallel, SortingPerm, NrArrangements.

• The methods for StructureConstantsTable and GapInputSCTable have been improved in the case of a known (anti-) symmetry following a suggestion of M. Costantini.

The improvements listed in this Section have been implemented by T. Breuer and A. Hulpke.

### New Programming and User Features

• The 2GB limit for workspace size has been removed and version numbers for saved workspaces have been introduced. (S. Linton and B. Höfling)

• The limit on the total number of types created in a session has been removed. (S. Linton)

• There is a new mechanism for loading packages available. Packages need a file PackageInfo.g now. (T. Breuer and F. Lübeck).

Finally, as always, a number of bugs have been fixed. This release thus incorporates the contents of all the bug fixes which were released for GAP 4.3. It also fixes a number of bugs discovered since the last bug fix.

Below we list changes in the main system (excluding packages) that have been corrected or added in bugfixes and updates for GAP 4.4.

## GAP 4.3 Bugfix 5

### Fixed bugs which could lead to wrong results:

• A wrong return format for IsomorphicSubgroups applied to cyclic groups.

• A wrong true result of IsSubset for certain algebras.

• A bug in the subgroup conjugation test for permutation groups that are not subgroups.

• A strange behaviour of Intersection for the case that a strictly sorted list is the unique entry of the list that is given as the argument; in this situation, this entry itself was returned instead of a shallow copy.

• Possibly wrong result of Centre for pc groups.

• Possibly wrong result of DirectSumDecomposition for matrix Lie algebras.

### Fixed bugs which could lead to crashes:

• Segmentation faults and other strange behaviour when assigning finite field elements of different characteristics into compressed vectors.

### Other fixed bugs:

• A missing method for BaseOrthogonalSpaceMat.

• A missing Set call in the construction of the global variable AUTOLOAD_PACKAGES.

• A wrong display string of the numerator in rational functions returned by MolienSeries (in the case that the constant term of this numerator is zero).

• An error in the basis of a product space of algebras.

• An error in LieNormalizer, LieCentralizer for zero subspaces.

• An error in the computation of matrices of adjoint modules.

• A strange error message when constructing the simple Lie algebra of type B1.

• An error in ModuleByRestriction.

• An error in IrrBaumClausen for the trivial group.

• An error with vector space bases of row spaces over fields which neither are prime fields nor contain all entries of the vectors.

• An error with IsMonomial, when it uses the function TestMonomialFromLattice (i.e., in hard cases, likely for characters of nonsolvable groups).

## GAP 4.3 Bugfix 4

### Fixed bugs which could lead to wrong results:

• A problem with composing a homomorphism from an fp group with another homomorphism (images may be wrong).

• An error in the comparison routine for univariate rational functions.

• A problem when calculating representations of a group in which class arrangement in group and character table are not identical.

• Three missing primitive groups of degree 441 were addded.

### Other fixed bugs:

• A problem with a homomorphism from a free group in the trivial permutation group.

• A problem with the multiplication of rationals and elements in large prime fields.

• A problem with attempting to create univariate polynomials of very high degree.

• A problem with output going to errout incorrectly after a syntax error.

• An error in the function ReducedSCTable.

• An error in computing the Rees Matrix semigroup.

• A compatibility problem with earlier versions of gap in semigroup and monoid rewriting systems.

• The behaviour of PQuotient when an attempt is made to compute a p-quotient with more generators than the underlying data structure was initialised with.

• A problem with computing BasisVectors for a basis of an algebraic field extension.

• A problem with the definition of IsRowVector (which previously returned true also for matrices).

• A problem with BaumClausenInfo.

• A problem with IsRowModule for infinite dimensional vector spaces (which are not row spaces).

• A problem with Difference with first argument a list that is not a set and second argument an empty list.

• The failure of Elements() to compute the elements of a pc group with non-prime relative orders.

• A wrong computation of single character values of Weyl groups of type B and character tables of Weyl groups of type D. Furthermore, a much more efficient function for computing all character values is provided.

• Packages accidentally overwriting the setting of InfoWarning.

• A missing method for IsPolynomial for univariate rational functions.

• A problem in the on-line help which sometimes returned a blank entry for a topic even though the topic was documented.

• A problem in the help system where a tilde in a filename was replaced by a blank.

• A problem that prevented the documentation of some packages from autoloading.

## GAP 4.3 Bugfix 3

### Fixed bugs which could lead to wrong results:

• An error in IdGroup that mistakenly was not corrected in Bugfix 2.

• An inconsistent setting of IndicesNormalSteps.

• A problem with the inversion routine for quaternions.

## GAP 4.3 Bugfix 2

### Fixed bugs which could lead to wrong results:

• The result of ProjectiveSymplecticGroup(n,q);.

### Fixed bugs which could lead to crashes:

• A segmentation fault when appending to a length 0 compressed vector over GF2.

### Other fixed bugs:

• An error in the computation of inverses in quaternion algebras with non-standard parameters.

• GeneratorOfCyclicGroup for a trivial pc group.

• A problem in backtrack routines using Suborbits if the group has fixed points in the range [1..max(Omega)].

• A problem with CharacterTableDirectProduct if exactly one argument is a Brauer table.

• Problems with IntScalarProduct and NonnegIntScalarProducts if the third argument is not a plain list (this situation does not occur in GAP library functions).

• A problem with GQuotient.

• A problem with the linear algebra methods for Lie algebra cohomology.

• A Problem with requesting transitive groups of degree including 1.

• A Problem with inverting lists of compressed vectors over fields of order greater than 2.

• An error in computing whether an element is in a Green's D equivalence class or not.

• A missing method for MovedPoints(perm).

• The method IsGreensLessThanOrEqual should work for Green's D classes for finite groups.

• The method GroupHClassOfGreensDClass was not implemented and is required for the Rees Matrix methods.

• The methods AssociatedReesMatrixSemigroupOfDClass, IsZeroSimpleSemigroup, IsomorphismReesMatrixSemigroup, and SandwichMatrixOfReesZeroMatrixSemigroup all create Greens classes using obsolete methods which for some semigroups leads to infinite recursion or causes GAP to stop with an error message.

• A problem with CentralizerModulo for permutation groups.

• A wrong name for PGL(2,49) in the primitive groups library of degree 50.

• Missing Representative methods for certain trivial groups and trivial spaces.

• A missing setting of IndicesNormalSteps.

## GAP 4.3 Bugfix 1

### Fixed bugs which could lead to crashes:

• A segmentation fault when converting length 0 compressed vectors to larger fields.

### Other fixed bugs:

• A bug in the handling of Processes with empty input or output streams.

• An error in the function for computing quotients of algebra modules.

• An error in computing the strongly connected components of a binary relation in which incorrect results can be returned.

• A "no method found" error in OrbitStabilizerAlgorithm for infinite groups.

• Calculation of iterated automorphism groups might stop with an error message.

• The output of the internal pager (see Pager) is no longer copied to log files.

• Some memory is not freed up as soon as it could be, resulting in over-use of memory and over-large saved workspaces.

• Saving and loading a workspace using a kernel containing a statically loaded user module (most likely a compiled GAP file) did not work.

• Problems with EulerianFunction for certain types of groups.

## Changes from Earlier Versions

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` 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 here.

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.

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.