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6 Overview of updates for GAP 4.4
6.1 GAP 4.4 Bugfix 2 (April 2004)
6.2 GAP 4.4 Bugfix 3 (May 2004)
6.3 GAP 4.4 Bugfix 4 (December 2004)
6.4 GAP 4.4 Update 5 (May 2005)
6.5 GAP 4.4 Update 6 (September 2005)
6.6 GAP 4.4 Update 7 (March 2006)
6.7 GAP 4.4 Update 8 (September 2006)
6.8 GAP 4.4 Update 9 (November 2006)
6.9 GAP 4.4 Update 10 (October 2007)
6.10 GAP 4.4 Update 11 (December 2008)
6.11 GAP 4.4 Update 12 (December 2008)

### 6 Overview of updates for GAP 4.4

This chapter lists changes in the main system (excluding packages) that have been corrected or added in bugfixes and updates for GAP 4.4.

#### 6.1 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).

#### 6.2 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:

- Problems with the online help with some manual sections.

- Problems of the online help on Windows systems.

- 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 \(q = 3\).

#### 6.3 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.

#### 6.4 GAP 4.4 Update 5 (May 2005)

Fixed bugs which could produce wrong results:

- `GroupWithGenerators` (Reference: 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` (Reference: 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` (Reference: Intersection) for pc groups.

- The function `CompareVersionNumbers` (Reference: 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` (Reference: 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 `The PackageInfo.g File` (Reference: The PackageInfo.g File) 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` (Reference: String) for strings not in `IsStringRep` (Reference: IsStringRep) that occur as list entries or record components was erroneously missing the double quotes around the strings.

- A bug which caused `InducedPcgs` (Reference: 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` (Reference: 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` (Reference: DirectProduct) for trivial permutation groups returned a strange object.

- A problem with `PolynomialReduction` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: IsPrimeInt) and `IsProbablyPrimeInt` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: ConwayPolynomial) and `IsPrimitivePolynomial` (Reference: IsPrimitivePolynomial) for p < 256

  - improved documentation of `ConwayPolynomial`

  - added and documented new functions `IsCheapConwayPolynomial` (Reference: IsCheapConwayPolynomial) and `RandomPrimitivePolynomial` (Reference: RandomPrimitivePolynomial)

- Added method for `NormalBase` (Reference: 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` (Reference: 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` (Reference: ContinuedFractionExpansionOfRoot) and `ContinuedFractionApproximationOfRoot` (Reference: 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` (Reference: 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` (Reference: MultiplicationTable) is now an attribute, and the construction of a magma, monoid, etc. from multiplication tables has been unified.

#### 6.5 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` (Reference: 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 `Finite Perfect Groups` (Reference: Finite Perfect Groups) library of perfect groups.

- The functions `EpimorphismSchurCover` (Reference: EpimorphismSchurCover) and `AbelianInvariantsMultiplier` (Reference: 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` (Reference: DerivedSubgroup) and `CommutatorSubgroup` (Reference: CommutatorSubgroup) for permutation groups sometimes returned groups with an incorrect stabilizer chain due to a missing verification step after a random Schreier Sims.

- `NaturalHomomorphismByNormalSubgroup` (Reference: NaturalHomomorphismByNormalSubgroup) for FpGroups did unnecessary rewrites.

- The alternating group \(A_3\) incorrectly claimed to be not simple.

- `ExponentSyllable` (Reference: ExponentSyllable) for straight line program elements gave a wrong result.

- `PrimePGroup` (Reference: 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` (Reference: TestPackageAvailability) and `LoadPackage` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: InstallValue) must not be used for objects in the filter `IsFamily` because these objects are compared via `IsIdenticalObj` (Reference: 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_BAG`s 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` (Reference: 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` (Reference: IsNaturalSymmetricGroup) and `IsNaturalAlternatingGroup` (Reference: IsNaturalAlternatingGroup) are faster and should run much less often into inefficient tests.

- The perfect group library, see `Finite Perfect Groups` (Reference: 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` (Reference: IsRat) was not called; instead a more general method was used that called `Conductor` (Reference: Conductor (for a cyclotomic)) 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` (Reference: PermutationCycle) returned `fail` if the cycle was not a contiguous subset of the specified domain. [Reported by Luc Teirlinck]

- Now `Inverse` (Reference: Inverse) correctly returns `fail` for zeros in finite fields (and does no longer enter a break loop).

- Up to now, `CharacterDegrees` (Reference: CharacterDegrees) ignored the attribute `Irr` (Reference: 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` (Reference: IsElementaryAbelian) and `ClassPositionsOfMinimalNormalSubgroups` (Reference: ClassPositionsOfMinimalNormalSubgroups) are available for ordinary character tables. Now the operation `CharacterTableIsoclinic` (Reference: CharacterTableIsoclinic) is an attribute, and there is another new attribute `SourceOfIsoclinicTable` (Reference: 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` (Reference: ClassPositionsOfDerivedSubgroup) avoids calling `Irr` (Reference: Irr), since `LinearCharacters` (Reference: LinearCharacters) is sufficient. Now `ClassPositionsOfElementaryAbelianSeries` (Reference: 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` (Reference: IsPGroup) has rarely been set. Now many basic operations such as `SylowSubgroup` (Reference: 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` (Reference: Lists) with `ShallowCopy` (Reference: 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` (Reference: Remove) and extended functionality of `Add` (Reference: 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` (Reference: IsProbablyPrimeInt) can be used with larger numbers. (Made internal function `TraceModQF` non-recursive.)

- A new operation `PadicValuation` (Reference: PadicValuation) and a corresponding method for rationals.

- A new operation `PartialFactorization` (Reference: 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` (Reference: EpimorphismFromFreeGroup). The code has been written by Alexander Hulpke.

- The functions `Lambda` (Reference: Lambda), `Phi` (Reference: Phi), `Sigma` (Reference: Sigma), and `Tau` (Reference: 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` (Reference: InstallFlushableValue). Now also records are admitted.

- `InstallMethod` (Reference: 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` (Reference: 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.

#### 6.6 GAP 4.4 Update 7 (March 2006)

New or improved functionality:

- The `Display` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: 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` (Reference: 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 `Printing Character Tables` (Reference: Printing Character Tables), 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` (Reference: 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` (Reference: 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` (Reference: InvariantBilinearForm), `InvariantQuadraticForm` (Reference: InvariantQuadraticForm), and `InvariantSesquilinearForm` (Reference: InvariantSesquilinearForm), for matrix groups over finite fields, are now in the (compressed) format returned by `ImmutableMatrix` (Reference: 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` (Reference: 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` (Reference: 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).

#### 6.7 GAP 4.4 Update 8 (September 2006)

New or improved functionality:

- A function `Positions` (Reference: Positions) with underlying operation `PositionsOp`, which returns the list of all positions at which a given object appears in a given list.

- `LogFFE` (Reference: 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` (Reference: 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 distributed at http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html). 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` (Reference: 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` (Reference: 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` (Reference: StabChain (for a group (and a record))) 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` (Reference: 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 (see `More about Boolean Lists` (Reference: More about Boolean Lists)) was computed wrongly: The type previously had `IS_PLIST_REP` instead of `IS_BLIST_REP` in its filter list.

- `Orbits` (Reference: Orbits) did not respect a special `PositionCanonical` (Reference: PositionCanonical) method for right transversals. [Reported by Steve Costenoble]

- Wrong results for `GcdInt` (Reference: 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` (Reference: CompositionMapping2) were not correct, such that composing (and multiplying) certain group homomorphisms did not work. [Reported by Peter Mayr]

- In the definition of `FrobeniusCharacterValue` (Reference: 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` (Reference: 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` (Reference: IsPolycyclicGroup) has been added. Such a method was missing so far.

- Corrected `EpimorphismSchurCover` (Reference: EpimorphismSchurCover) to handle the trivial group correctly. Added new methods that follow immediately from computing the Schur Cover of a group. The attribute `Epicentre` (Reference: Epicentre), the operations `NonabelianExteriorSquare` (Reference: NonabelianExteriorSquare) and `EpimorphismNonabelianExteriorSquare` (Reference: EpimorphismNonabelianExteriorSquare), and the property `IsCentralFactor` (Reference: 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` (Reference: 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.

#### 6.8 GAP 4.4 Update 9 (November 2006)

Fixed bugs which could produce wrong results:

- The methods of `ReadByte` (Reference: 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` (Reference: PseudoRandom) did not succeed.

- A fix for `Orbits` with a set of points as a seed.

- Added a generic method such that `Positions` (Reference: 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]

#### 6.9 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` (Reference: CharacterTableRegular) is documented now.

- The function `ScalarProduct` (Reference: ScalarProduct (for characters)) now accepts also Brauer characters as arguments.

- The function `QuaternionAlgebra` (Reference: 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` (Reference: 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` (Reference: Lists) only occupy the memory they really need. For more details see the documentation of the new function `EmptyPlist` (Reference: 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` (Reference: GeneratorsOfRing) and `GeneratorsOfRingWithOne` (Reference: 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` (Reference: Primitive Permutation Groups) 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` (Reference: DirectoryContents) ran into an error for immutable strings without trailing slash as argument. [Reported by Thomas Breuer]

- The functions `IsInjective` (Reference: IsInjective) and `IsSingleValued` (Reference: 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` (Reference: 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>`.

- Avoid warnings about pointer types by newer gcc compilers.

- `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.

#### 6.10 GAP 4.4 Update 11 (December 2008)

Fixed bugs which could produce wrong results:

- `MemoryUsage` (Reference: 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` (Reference: Irr) might be missing characters. [Reported by Angel del Rio]

- Up to now, it was allowed to call the function `FullMatrixAlgebraCentralizer` (Reference: 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` (Reference: AsField)), the function `DefiningPolynomial` (Reference: 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` (Reference: QuaternionAlgebra) were not consistent w.r.t. the attribute `GeneratorsOfAlgebra` (Reference: GeneratorsOfAlgebra); the returned list could have length four or five. Now always the list of elements of the canonical basis is returned.

- `MonomialGrevlexOrdering` (Reference: MonomialGrevlexOrdering) calculated a wrong ordering in certain cases. [Reported by Paul Smith]

- The (GAP kernel) method for the operation `IntersectSet` (Reference: 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` (Reference: 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` (Reference: LogFFE) code. [Reported by Jia Huang]

- In rare cases `SmithNormalFormIntegerMatTransforms` (Reference: 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` (Reference: StraightLineProgram (for a list of lines (and the number of generators))) 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` (Reference: 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` (Reference: 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` (Reference: Intersection2) which have implicitly assumed that finiteness of a collection can always be decided. Now, these methods check for `IsFinite` (Reference: IsFinite) and `CanComputeSize` (Reference: CanComputeSize) prior to calling `IsFinite` (Reference: 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` (Reference: NewOperation), `DeclareOperation` (Reference: DeclareOperation), and `InstallMethod` (Reference: 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` (Reference: 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` (Reference: Basis), `Iterator` (Reference: Iterator) etc. with the return value of the function `AlgebraicExtension` (Reference: AlgebraicExtension).

- The function `FrobeniusCharacterValue` (Reference: 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` (Reference: FrobeniusCharacterValue) returns `fail`.)

- Methods for testing membership in general linear groups and special linear groups over the integers have been added.

- Methods for `String` (Reference: String) and `ViewString` for full row modules have been added. Further, a default method for `IsRowModule` (Reference: 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` (Reference: View) for polynomial rings has been improved, and methods for `String` (Reference: String) and `ViewString` for polynomial rings have been added.

- `Binomial` (Reference: Binomial) now works with huge `n`.

- The function `InducedClassFunctionsByFusionMap` (Reference: InducedClassFunctionsByFusionMap) is now documented.

- The return values of the function `QuaternionAlgebra` (Reference: QuaternionAlgebra) now store that they are division rings (if optional parameters are given then of course ths depends on these parameters).

#### 6.11 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.

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