A package for semigroups and monoids
Version 3.0.15
Released 2018-03-24
This project is maintained by J. D. Mitchell
This version contains some bugfixes, and some improved functionality:
IsTrivial did not check if the number of generators was non-zero. [J. D. Mitchell]NrCongruenceClasses sometimes returned the wrong result for classes of semigroups not defined in the Semigroups package. [Michael Torpey]EvalString by ValueGlobal. [J. D. Mitchell]This version contains a fix for the following issue, this was resolved by updating the version of libsemigroups to 0.6.3:
This version contains some minor updates for compatibility with GAP 4.9, and some fixes for some minor issues.
This version contains some minor updates for compatibility with GAP 4.9, to fix some bugs, to update the build system, and to update the kernel module for libsemigroups version 0.6.2.
The following improvements have been made:
IsomorphismFpSemigroup for factorisable inverse monoids is added. [Chris Russell]The following issues are resolved:
MinimalFactorization sometimes returned incorrect results. [J. D. Mitchell]ClosureInverseMonoid sometimes returned incorrect results. [J. D. Mitchell]This version contains some minor updates for compatibility GAP 4.9, the build system has been modified slightly, the kernel module has been updated for libsemigroups version 0.6.1.
This version contains some minor updates for compatibility GAP 4.9.
This version contains some minor bugfixes, and updates for compatibility GAP 4.9, IO 4.5.0, and Digraphs 0.11.0.
This version contains some minor bugfixes, and updates for compatibility GAP 4.9 and Orb 4.8.0.
This version contains some minor bugfixes, fixes some issues where some tests
in the main GAP repo returned different output when Semigroups was loaded than
when it was not, and updates the kernel module for version 0.5.2 of
libsemigroups. The
configuration option --enable-debug was added.
The following issues are resolved:
NaturalPartialOrder sometimes returned incorrect results. [Wilf A. Wilson]StructureDescription for finitely presented groups failed with an error when Semigroups was loaded. [J. D. Mitchell]tst/testinstall/semigrp.tst failed because of a missing method for NrEquivalenceClasses for a generic semigroup congruence. [J. D. Mitchell] and [Wilf A. Wilson]This version contains some minor bugfixes, improves the compatibility of Semigroups with other GAP packages, and updates the kernel module for version 0.5.0 of libsemigroups
The following issues are resolved:
GeneratorsOfSemigroup. This meant that the semigroup generated by GeneratorsOfSemigroup(M) was not equal to M in some rare cases. [Wilf A. Wilson]IsInverseSemigroup for non-acting semigroups that sometimes returned a false positive. [Wilf A. Wilson]This version contains some minor tweaks and the following issue is resolved:
RandomMatrix and IsTorsion. [J. D. Mitchell]Some minor issues are fixed in this release:
DirectProduct for transformation semigroups returned the wrong answer when applied to semigroups satisfying IsMonoidAsSemigroup. [J. D. Mitchell]Some documentation and tests were added. [Michael Torpey]
Some minor issues are fixed in this release:
IsEUnitaryInverseSemigroup for non-inverse semigroups, which previously resulted in no method found. [Chris Russell]ReadGenerators and WriteGenerators. [J. D. Mitchell]This is an minor release fixing some minor issues in the last release.
The following issues were resolved:
InversesOfSemigroupElement some times returned an incorrect value, specifically when applied to the identity of a transformation monoid. [J. D. Mitchell]There are improvements to the following:
IdempotentGeneratedSubsemigroup for Rees
(0-)matrix semigroup over a group has a smaller generating set than
previously, and can be found more quickly. [Wilf A. Wilson]IsomorphismSemigroups is extended so that it can be applied to arbitrary
simple, 0-simple, or monogenic semigroups. [Wilf A. Wilson]This is an extremely minor release fixing some minor issues in the last release.
This is a major release that dramatically expands the scope of the package. The package now features a compiled C/C++ module which interfaces with the libsemigroups C++ library to allow high-speed computations for congruences and certain categories of semigroup. There are also several new types of semigroup and a variety of new methods which can be used with them.
This is a minor release to correct the required version of GAP in PackageInfo.g (from GAP 4.9.0 to GAP 4.8.9).
This is a minor release to update the output in some test file and manual examples due to some changes in the GAP library code.
In this release there are some new features and some bug fixes. In this version, we welcome Nick Ham to the contributors to the package.
The new features in this release are contributed by Nick Ham:
ApsisMonoidCrossedApsisMonoidModularPartitionMonoidPlanarModularPartitionMonoidPlanarPartitionMonoidPlanarUniformBlockBijectionMonoidSingularApsisMonoidSingularCrossedApsisMonoidSingularModularPartitionMonoidSingularPlanarModularPartitionMonoidSingularPlanarPartitionMonoidSingularPlanarUniformBlockBijectionMonoidSingularUniformBlockBijectionMonoidUniformBlockBijectionMonoidIrreundantGeneratingSubset behaved incorrectly when given a
semigroup whose generating set consisted of a single repeated
element. [Wilf A. Wilson]MatrixEntries
gave an error for Rees 0-matrix semigroups whose
matrices contain 0. [Wilf A. Wilson]This is a very minor release changing the name of the README (to README.md) in
the PackageInfo.g file.
This is a minor release to fix Issue
151, and to make
some changes for future compatibility with GAP. In Issue
151 when the
method IsomorphismPermGroup was applied to a semigroups of non-permutation
transformations the returned mapping was not an isomorphism.
This is a minor release to fix Issue 150, and to correct the required version of GAP (from 4.8.2 to 4.8.3). In Issue 150 the function IsZeroSimpleSemigroup entered an infinite loop for some examples of semigroups of partial permutations.
This is a minor release to fix some manual examples, to correct the package url
in the PackageInfo.g file, and to fix some issues with semigroups of
bipartitions. It was formerly possible to create semigroups of bipartitions
where the generators had different degrees, but the created semigroups were
invalid; this is fixed in version 2.7.3.
This is a minor release to fix to remove ErrorMayQuit which was renamed
ErrorNoReturn in GAP 4.8.2. This change was made by Max Horn.
This is a minor release to fix Issue
144.
This issue resulted in IsInverseSemigroup sometimes returning true for
semigroups which were not inverse. This occurred when the \(\mathscr{D}\)-classes of the semigroup were computed before the method for IsInverseSemigroup was first
run.
This is a minor release including some changes for compatibility with GAP 4.8, and some bug fixes.
IsomorphismReesZeroMatrixSemigroup is introduced, and it is no longer possible to apply IsomorphismReesMatrixSemigroup to a 0-simple semigroup. This change was made for the sake of consistency, so that the Range of an IsomorphismReesMatrixSemigroup is always a Rees matrix semigroup and not sometimes a Rees 0-matrix semigroup as was formerly the case.ViewString methods for semigroups and their elements were moved from the Semigroups package to the GAP library. Some minor changes were made in the method for ViewString for semigroups, and the tests, and manual examples were updated accordingly.IsMonoidAsSemigroup was changed to be consistent with the meaning of IsGroupAsSemigroup. In earlier versions, IsMonoidAsSemigroup was false for semigroups in the category IsMonoid. From Version 2.7, IsMonoidAsSemigroup is true for monoids in the category IsMonoid and for some further semigroups.CyclesOfPartialPermSemigroup sometimes resulted in an error due to using DegreeOfPartialPermSemigroup instead of the maximum of the degree and the codegree. [James Mitchell]PartialOrderOfDClasses sometimes resulted in an error. This bug was
introduced in Semigroups 2.6 and did not effect any previous versions.
[James Mitchell]This release includes some bugfixes, some minor new features, and one major new feature (efficient methods for semigroups of matrices over a finite field).
extensive new features for computing with semigroups, monoids, and ideals, of matrices with entries in a finite field. See Chapter 7 of the manual for more details. [Markus Pfeiffer]
The functions RectangularBand, MonogenicSemigroup, and ZeroSemigroup
now have an optional first argument to specify the category of the result;
the functions LeftZeroSemigroup and RightZeroSemigroup are introduced
in a similar sense.
[Wilf A. Wilson]
The new property IsSemigroupWithAdjoinedZero and attribute
UnderlyingSemigroupOfSemigroupWithAdjoinedZero are introduced.
[Wilf A. Wilson]
The operations MotzkinMonoid and PartialJonesMonoid were introduced.
[James Mitchell]
Issue 131: testing membership in a Rees 0-matrix semigroup that knows it is inverse sometimes resulted in an error. [Michael Torpey]
Issue 132: this was a feature request to introduce the operations MotzkinMonoid and PartialJonesMonoid.
[James Mitchell]
Issue 134: the operation PartialBrauerMonoid returned the wrong answer when the argument was 1. The returned semigroup was not the partial brauer monoid of degree 1.
[James Mitchell]
This is a minor release including several bugfixes, lots of minor improvements in the documentation, some improvements in performance, and some new features.
Semigroups of partial permutations now have a polynomial time (quadratic in the degree) algorithm for computing the minimal ideal [Wilf A. Wilson]
A more efficient IsInverseSemigroup method for Rees 0-matrix semigroups
is introduced, along with new methods for Idempotents and
NrIdempotents for inverse Rees 0-matrix semigroups
[Wilf A. Wilson]
The documentation for congruences has been improved and new tests have been added. [Michael Torpey]
A UniversalSemigroupCongruence now returns a much smaller set
of generating pairs. [Michael Torpey]
Issue numbers refer to the issues on the tracker.
Issue 126: testing membership in a Rees 0-matrix semigroup that knows it is inverse sometimes resulted in an error. [James Mitchell]
Issue 127: the main algorithm for computing with ideals of acting semigroups which know they are regular contained a bug that resulted in incorrect results. In some cases, some \(\mathscr{D}\)-classes were counted more than once, and the returned value of Size was higher than the actual size of the ideal. [James Mitchell]
Issue 128: in some special cases UnderlyingSemigroup, ViewObj, Size, and related methods, for Rees 0-matrix semigroups over non-groups returned an error. [James Mitchell]
The universal congruence specified by generating pairs on a (0-)simple semigroup no longer causes an error. [Michael Torpey]
This is a extremely minor release to change 1 character in the PackageInfo.g file (wrong package archive URL).
This is a minor release including several bugfixes, and improvements in performance, and some new features.
The function RepresentativeOfMinimalIdeal is introduced. [Wilf
Wilson]
Transformation semigroups now have a polynomial time (cubic in the degree) algorithm for computing the minimal ideal [Wilf A. Wilson]
The functions RectangularBand, ZeroSemigroup, and
MonogenicSemigroup are introduced. [Wilf A. Wilson]
A method for choosing a random element of a semigroup has been introduced in the case that the semigroup knows its set of elements. This new method choose elements at random with uniform probability. [Wilf A. Wilson]
The documentation and tests for congruences has been improved. [Michael Torpey and Wilf A. Wilson]
The functionality for Rees congruences has been rewritten and improved. [Michael Torpey]
There is a new Enumerator method for congruence classes of a
semigroup congruence. [Michael Torpey]
Issue numbers refer to the issues on the tracker.
Issue 88: an inefficiency in JoinIrreducibleDClasses of an
inverse semigroup ideal resulted in a call to
GeneratorsOfSemigroup.
Issue 94: EquivalenceClasses of the trivial congruence (generated
by 0 pairs of elements) returned an error.
Issue 95: The class containing the zero element of a Rees
0-matrix semigroup was not returned by EquivalenceClasses of a
congruence over a Rees 0-matrix semigroup.
Issue 108: IsRegularSemigroup with argument a Rees 0-matrix
semigroup returned an error.
Issue 119: NrCongruencesClasses and related methods did not work for
Rees congruences.
Issue 121: MultiplicativeZero and IsMultiplicativeZero sometimes
returned incorrect results when applied to a non-acting semigroup
(i.e. a semigroup not of transformations, partial permutations,
partitions, or subsemigroups of a Rees 0-matrix semigroup).
Issue 122: A bug in the creation of Green’s classes of ideals of semigroups, which resulted in an error.
Issue 123: IsZeroSemigroup sometimes returned a false positive when applied to a non-acting semigroup.
This is a minor release including some internal refactoring, and subsequent bugfixes, and stability improvements.
This is a minor release including some bug fixes, performance improvements, and additional functionality.
The functions SmallestElementSemigroup, LargestElementSemigroup,
and GeneratorsSmallest.
Free bands are introduced.
Error messages are more uniform.
The function RegularDClasses was introduced to resolve Issue 102.
The documentation and code for semigroup congruences has been improved, and is better integrated with the core GAP system.
The functions ReadGenerators and WriteGenerators were improved.
Some minor corrections were made to the methods for creating the
ideals of some semigroups in standard examples semigroups, such as
SingularTransformationSemigroup.
Issue 102: we introduced RegularDClasses.
Issue 104: the performance of MaximalSubsemigroups when applied to
an inverse semigroup has been improved.
Issue 105: CyclesOfPartialPerm is now documented and does not
return nonsense.
Issue 106: MaximalSubsemigroups sometimes failed when the
ResClasses package was loaded. We refactored the code so that the
method from ResClasses is no longer applied.
Issue 107: A bug in the creation of Green’s classes of an ideal of
a semigroup, which sometimes caused an error, has been resolved.
This issue often caused MaximalSubsemigroups to stop in an error.
Issue 110: MaximalSubsemigroups can be applied to any class of
semigroup where it is possible to find an isomorphism to a
transformation semigroup.
Issue 111: POPI(1) returned the wrong semigroup. Similar issues
existed in other corner cases, and these have been resolved too.
This is a very minor release to fix an issue caused by only loading the packages needed (but not required) by Semigroups.
This is a minor release including some bug fixes and performance improvements.
The functions:
AsTransformationSemigroup,AsPartialPermSemigroup,AsBipartitionSemigroup,AsBlockBijectionSemigroupwhich are shortcuts to Range(IsomorphismXSemigroup(S)).
A method for IsTransitive for a transformation semigroup and,
optionally, a positive integer or list of positive integers. This
method is based on Gabow’s algorithm for determining the strongly
connected components of a directed graph.
The functions MeetSemigroupCongruence and JoinSemigroupCongruences
for finding the meet and join of a pair of congruences of a
semigroup.
There is a new method for IsSynchronizingSemigroup, suggested by
Peter Cameron, with better complexity than the previous method.
Issue numbers refer to the issues on the tracker.
There was a bug in ReadGeneratorsFile, which meant it sometimes
returned fail. The mode argument for IO_FilteredFile was not given.
There was a bug in the \in method for a congruence of a Rees
0-matrix semigroup, which sometimes returned the wrong answer for
the zero of the semigroup.
There was a bug in IteratorFromGeneratorsFile that caused it to
read only every other line in the given file, and to crash if there
were an odd number of lines.
There was no hash function for bipartitions.
The documentation for InverseSubsemigroupByProperty did not
specify the arguments of the function.
Issue 82: it is now possible to take the quotient of a semigroup
by an ideal using the / operator.
Issue 96: IsIsomorphicSemigroup sometimes returned a false
negative by incorrectly comparing the output of
PartialOrderOfDClasses (up to isomorphism) rather than the
transitive reflexive closure of PartialOrderOfDClasses.
Issue 97: there was a bug in the Normalizer method, which
caused GAP to crash when the argument was a monoid with 0
generators.
Issue 98: PartitionMonoid(1) returned the wrong answer, it was
missing the non-identity element.
Issue 99: the documentation for PartialOrderOfDClasses was
incorrect.
Issue 103: under certain circumstances an error was given when trying to compute with an ideal of an inverse semigroup.
This is a major release including many new features and several bug fixes.
extensive new features for computing with elements and subsemigroups of the partition monoid. It is now possible to compute with semigroups, monoids, inverse semigroups, inverse monoids, and ideals consisting of elements of the partition monoid. Examples of subsemigroups of this type are the Brauer monoids, Temperley-Lieb monoids, and the dual symmetric inverse monoid. See Chapter 5 of the manual for more details;
support for ideals of transformation, partial permutation, and bipartition semigroups, and subsemigroups of Rees 0-matrix semigroups. It is now possible to compute anything about one of these ideals that could formerly only be computed about a semigroup defined by a generating set. Such ideals now use a data structure similar to that used by semigroups defined by a generating set;
the new operations IsomorphismSemigroups, IsIsomorphicSemigroup,
and SmallestMultiplicationTable. Some of the methods for this
operation require the Grape package to be fully installed;
the new operation MaximalSubsemigroups, which returns the maximal
subsemigroups of an arbitrary semigroup. Some of the methods for
this operation require the Grape package to be fully installed;
the operation IsMaximalSubsemigroup;
the new operation Normalizer for computing a subgroup of a
permutation group consisting of those permutations that stabilise,
under conjugation, a transformation, partial perm, or bipartition
semigroup. The genss package is required for this operation in some
cases;
the new operation CharacterTableOfInverseSemigroup for finding the
character table of an inverse semigroup of partial permutations;
methods for defining and manipulating the congruences of a Rees 0-matrix semigroup;
the properties IsCongruenceFreeSemigroup, IsEUnitaryInverseSemigroup;
the attributes:
ComponentRepsOfTransformationSemigroupComponentsOfTransformationSemigroupCyclesOfTransformationSemigroupComponentRepsOfPartialPermSemigroupComponentsOfPartialPermSemigroupCyclesOfPartialPermSemigroup.the new function IteratorFromGeneratorsFile that returns an
iterator which reads semigroup elements from a file created using
WriteGenerators. This function is a convenient way of, for example,
looping over a collection of generators in a file without loading
every object in the file into memory. This might be useful if
the file contains more information than there is available memory;
the operation EndomorphismsPartition that returns the monoid
of endomorphisms preserving a partition. This monoid is defined
using the minimum possible number of generators;
a version of the function Splash that attempts to convert a string
containing a dot or tikz document into a pdf and opens this pdf.
Other file formats are also supported;
the function DotSemilatticeOfIdempotents that produces a string
containing a dot document of the semilattice of idempotents of an
inverse semigroup grouped by \(\mathscr{D}\)-class;
the operation NaturalLeqInverseSemigroup, which is an umbrella
operation for NaturalLeqPartialPerm, and other such functions.
Issue numbers refer to the issues on the tracker.
the main algorithm underlying many of the methods in Semigroups has been revised to avoid computing the same information more than once. Some further internal rearranging and cleaning up was done.
MinimalIdeal and SingularTransformationSemigroup now returns an ideal rather than a semigroup defined by a generating set;
to reduce the size of the package archive, the examples directory has been removed. The content of the examples directory is available on this webpage.
several bugs in the setup for subsemigroups of Rees 0-matrix semigroups were resolved. These issues would have caused GAP to give an error in certain circumstances.
Issue 33: an error was returned when trying to calculate the size, or multiply elements in the quotient of a semigroup by an ideal.
Issue 36,Issue 64: the function SmallGeneratingSet was ambiguous, in
the sense that it was sometimes unclear how to recreate a semigroup
from its small generating set. For example, SmallGeneratingSet of a
monoid could return an empty list, but this empty list could not be
used to recreate the monoid in GAP. This was resolved by introducing
the functions SmallSemigroupGeneratingSet, SmallMonoidGeneratingSet,
SmallInverseSemigroupGeneratingSet, SmallInverseMonoidGeneratingSet.
These functions can also now be applied to collections of elements,
i.e. not only to semigroups.
Issue 47: ClosureSemigroup had several bugs that could, in some
cases, result in incorrect results, or semigroups with invalid data
structures.
Issue 50 and Issue 59: WriteGenerators wrote nothing to a file in the case
that it was not piping through xz or gzip.
Issue 55: DotDClasses did not work when the argument was a Rees
0-matrix semigroup (it worked as intended when the argument was a
subsemigroup of such a semigroup defined by a generating set).
Issue 56: the functions Monoid and InverseMonoid sometimes
did not contain their identity element.
Issue 57: under certain circumstances a bug in the GAP kernel
function INV_KER_TRANS, that didn’t handle kernels and
transformations with different length and degree properly, caused
GAP to give an error.
Issue 63: there was an error in the GAP library functions Monoid
and InverseMonoid, when they were passed a monoid as an argument.
Issue 63 (and Issue 4 in the Orb package): a bug in the Orb package meant that the log of an Orb was not properly updated if the enumeration stopped early because we found something we were looking for. This caused Semigroups to return incorrect results in some rare cases.
Issue 72: the method for IsomorphismTransformationSemigroup applied to a binary relation monoid returned an isomorphism to a transformation semigroup which was missing the image of the identity.
Issue 89: there was a bug in TRANS_IMG_CONJ which failed to handle
transformations of unequal degrees correctly. This causes incorrect
results to be returned when considering semigroups generated by
transformations of unequal degrees.
This is a minor release containing some bug fixes. Specifically: the functionality of ReadGenerators and WriteGenerators has been improved to allow the argument to be an IO file object, and support is added to read and write directly to files compressed using xz. A minor bug relating to the creation of idempotents in transformation semigroups which was triggered by the identity transformation has been resolved. The functions IsomorphismReesMatrixSemigroup, InjectionPrincipalFactor, and IsZeroSimpleSemigroup have been revised. IsZeroSimpleSemigroup formerly returned true for the 2 element zero semigroup, which is not 0-simple. IsomorphismReesMatrixSemigroup could have returned an error if called for a semigroup which was not a semigroup of partial perms or transformations. The use of AsPermutation was changed to PermutationOfImage where appropriate following a change to the library methods for AsPermutation. The declarations of IsomorphismPermGroup and ClosureSemigroup were moved/changed to avoid warnings that their methods matched more than one declaration. These warnings were exposed by doing LoadAllPackages, but were not present when loading Semigroups by itself.
Version 1.3 contains many bug fixes, extensions and improvements in the documentation, and several new methods and functions. Most notably are (in no particular order):
the methods in Semigroups have been extended to apply to arbitrary subsemigroups of regular Rees 0-matrix semigroups over groups;
a new method for MaximalSubsemigroups of Rees matrix semigroup has been implemented;
the function Read/WriteSemigroups have been renamed Read/WriteGenerators and their performance has been improved. It is now possible to use WriteGenerators to write to a gzipped file;
the operation SingularSemigroup has been renamed SingularTransformationSemigroup;
the following attributes have been introduced: MinimalDClass, MaximalDClasses, StructureDescriptionMaximalSubgroups, StructureDescriptionSchutzenbergerGroups, and IsGreensDLeq.
the attribute/operation DotDClasses has been introduced. This
allows the \(\mathscr{D}\)-class diagram of a semigroup to be viewed.
ComponentRepsOfTransformationSemigroup is reintroduced.
This release includes several new methods for inverse semigroups of partial permutations and for free inverse semigroups. Most notably among the new methods for inverse semigroups of partial permutations are:
for changing the representation of an inverse semigroup of partial permutations. The changes in this release were the result of the University of St Andrews Research for Undergraduates Summer School in 2012, and were largely written by Wilf A. Wilson and Robert Hancock.
Free inverse semigroups, and their elements, are also introduced, this part of the package was written by Julius Jonusas (who wishes to acknowledge the support of the Carnegie Trust).
A minor release to fix some technical issues in PackageInfo.g, the
declarations of IsGreens.Class, and a minor change in the output in
one test in everyfunction.tst which was consequence of the
declarations of IsGreens.Class.
The package has been renamed from Citrus 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.
This is the final release of Citrus (the package will be renamed Citrus in the next release since the scope of the package has expanded to include more types of semigroups than just those of transformations and partial permutations).
A minor release fixing several bugs relating to inverse semigroups of partial permutations pointed out by partcipants at the University of St Andrews Research for Undergraduates Summer School in July 2012. Most notably by Demi Allen, Casey Donoven, Rhiannon Dougall, Robert Hancock, and Wilf A. Wilson. More specifically, SymmetricInverseSemigroup(n) returned an incorrect answer when n=1 or n=2, \in for the empty mapping and an inverse semigroup of partial perms sometimes incorrectly returned false, some harmless compiler warnings were displayed when using more recent versions of gcc, NaturalLeqPP sometimes returned the incorrect value, there was no method for IsInverseSemigroup or IsInverseMonoid for a semigroup of partial perms.
A minor release fixing several bugs relating to partial permutations and monoids thereof, pointed out by Jack Schmidt. More specifically, MultiplicativeZero sometimes incorrectly returned fail for an inverse semigroup of partial permutations, sometimes PartialPerm incorrectly returned fail when given a dense range as an argument, sometimes the size of an inverse monoid was 1 more than the correct value, and RestrictedPP sometimes failed when it should not have.
another minor release. Specific changes were: removed the declaration of SmallGeneratingSet for IsSemigroup since it appears not to be used and caused a warning to be shown when rcwa was loaded after Citrus. Added a new abstract to the PackageInfo.g file, and the documentation, and updated the webpages, in particular so that the html version of the manual is linked to that on the GAP webpage and the links to other manuals work.
renamed the function for creating the semigroup of order-preserving transformations on an n-chain from O to OrderEndomorphisms after it was pointed out that it is not sensible to have function names with one character. Also made some minor adjustments to the manual.
minor changes due to incompatibility with Smallsemi 0.6.4 which caused some test files to fail when Nilmat was loaded after Citrus. The clashes and the failed test were caused by various properties being declared for IsTransformationSemigroup rather than IsSemigroup.
the most major change is the introduction of special methods for
partial permutations and inverse semigroups. So that these methods
are efficient, a GAP kernel component (in C) has also been
introduced for various low-level computations with partial
permutations. Essentially all functions previously available for
transformation semigroups are now available for inverse semigroups
of partial permutations. The manual has been expanded and
reorganised, some standard examples have been included (semigroups
of order preserving transformations or partial permutations, the
symmetric inverse semigroup, the full matrix semigroup over a
finite field), the endomorphism monoids of the non-abelian groups
with at most 64 elements have been included in the catalogues of
examples, the functions InjectionPrincipalFactor,
IsomorphismReesMatrixSemigroup, and PrincipalFactor, and some
specific properties and attributes of inverse semigroups have been
introduced (such as IsFactorisableSemigroup and
PrimitiveIdempotents).
fixed a bug relating to the creation of transformation semigroups
using MagmaByGenerators. Also added the global variable
CitrusOptionsRec containing the default values of the options
used by Citrus when creating a semigroup.
major changes are: the documentation has been further revised,
functions for creating semigroups and monoids with certain
options have been introduced, several functions have had the word
Greens' removed from their names to reduce the length, the
operation ClosureSemigroup has been introduced, the functions
ReadCitrus and WriteCitrus` for reading and writing
transformations to a file have been introduced, several catalogues
of examples of transformation semigroups are now included in the
examples directory, methods for creating a Green’s class inside
another Green’s class have been included (such as an \(\mathscr{R}\)-class of a
\(\mathscr{D}\)-class or an \(\mathscr{H}\)-class of an \(\mathscr{L}\)-class), the hash functions used for
transformations etc have been improved.
Some minor bugs have been fixed, and new methods or functions with the following names have also been introduced:
AntiIsomorphismTransformationSemigroup (for a trans. semigroup),
IdempotentGeneratedSubsemigp, IsomorphismTransformationSemigroup
(for a perm. gp), IsomorphismTransformationMonoid (for a perm. gp),
NrElementsOfRank.
major changes are: the documentation has been updated, some changes
to core functions for \(\mathscr{R}\)-classes/image orbits have resulted in a
performance improvement, there is a method for the operation
Factorization allowing an arbitrary element of a transformation
semigroup to be expressed as a product of the generators.
Some minor bugs have been fixed, and new methods or functions with the following names have also been introduced:
OrbSCC, OrbSCCLookup, OrbSCCTruthTable,
ReverseSchreierTreeOfSCC, SchreierTreeOfSCC,
IsomorphismTransformationSemigroup (for a perm. gp).
fixed a critical (but rare) bug in AddToOrbitsOfKernels that caused computations relating to \(\mathscr{D}\)-classes, \(\mathscr{H}\)-classes, or \(\mathscr{L}\)-classes to return incorrect answers in some cases.
updated the method for \^ for a transformation and perm so that it
is more efficient than the library method, same for * for a perm
and transformation. New method for StructureDescription of a
Brandt semigroup, and IsSubset for a trans. semigroup and trans.
coll.
fixed bugs in IndexPeriodOfTransformation (it returned incorrect
results) and AsPermutation. Also reduce hash table lengths so that
Citrus uses less memory. Fixed bug that triggered an infinite
loop when trying to find elements of a trivial trans. semigroup.
added the functions CitrusDefaultMem, CitrusHiMem,
CitrusLoMem, CitrusVeryLoMem, IsBrandtSemigroup,
IsLeftSimple, IsMonogenicSemigroup, IsRightSimple,
IsZeroRectangularBand, IsZeroSimpleSemigroup.