Log of updates to the package LOOPS for GAP

In version 3.0.0:

• Fixed a bug in IsotopismLoops (now returns a correct isotopism).
• Added library of RCC loops (provided by Katharina Artic) up to order 27. See RCCLoop( n, m ), LCCLoop( n, m ).
• Extended library of CC loops up to order 27: CCLoop( n, m ).
• Added synonyms IsLeftConjugacyClosedLoop, IsRightConjugacyClosedLoop, IsConjugacyClosedLoop, RightConjugacyClosedLoop( n, m ), ConjugacyClosedLoop( n, m ), LeftConjugacyClosedLoop( n, m ).
• New conversion functions and encoding functions for multiplication tables.
• New structure of global variables to better separate the package from the rest of GAP.
• Added InterestingLoop(92,1), the simple right Bol loop of order 92 and exponent 2.
• Implemented AssociatedRightBruckLoop for Bol loops.
• Changed QuasigroupByRightSection( G, H, T ) to QuasigroupsByRightFolder( G, H, T ), and LoopByRightSection( G, H, T ) to LoopByRightFolder( G, H, T ).
• Added IsExactGroupFactorization( G, H1, H2 ) and RightBolLoopFromExactGroupFactorization( G, H1, H2 ).
• Added support for right Bol loops, including RightBolLoop(n, m).
• New documentation.
• Updated tests.

In version 2.2.0:

• Converted the package so that it is compatible with GAP 4r5.
• Added library of Moufang loops of order 243, based on the classification of Slattery and Zenisek.
• Added library of automorphic loops of order less than 16.
• Added library function AutomorphicLoop.
• Created synomyms to all ALoop attributes. For instance, IsLeftAutomorphicLoop is the synonym of IsLeftALoop.
• Updated the manual.

In version 2.1.3:

• Fixed a bug in Subquasigroup. It now correcly forwards the second argument (generators) to SubquasigroupNC as a set, not just as a list.
• We now allow Subquasigroup(Q,[]) and return [], rather than returning an error. This is useful, for instance, when the user calls Nuc(Q) with a quasigroup Q that has empty nucleus.

In version 2.1.2:

• IsAssociative now works properly for quasigroups.
• Added two missing left Bol loops of order 12 to the library.

In version 2.1.1:

• fixed typo in the definition of left Bol loops in the manual
• fixed methods IsLeftAlternative, IsRightAlternative, IsAlternative; they now work properly for quasigroups, too

In version 2.1.0:

• Added library "nilpotent" of all nonassociative nilpotent loops of order less than 12.
• Added functions RandomLoop, RandomNilpotentLoop, RandomQuasigroup.
• AsGroup, AsLoop, AsQuasigroup replaced with IntoGroup, IntoLoop, IntoQuasigroup to avoid conflict with naming rules of GAP.
• Added functions that, given a permutation group G, search for a loop Q such that the multiplication group of Q is contained in G.
• Major update of test files and documentation, particulary of the index.

In version 2.0.0

• New file structure for the entire package.
• Updated test files.
• Updated documentation.
• Added AssociatedLeftBruckLoop( L ) for left Bol loops L in which squaring is a permutation.
• Improved Discriminator. (It is a bit slower but it can substantially speed up search for isomorphisms.)
• Removed IsomorphismTypeOfMoufangLoop and the data file moufang_discriminators.dat, since the isomorphism problem for Moufang loops of order 64 has been solved.

In version 1.9.0:

• New library "code" of code loops and related functions and filters: IsCodeLoop, CodeLoop.
• DisplayLibraryInfo( name ) now announces the list of correct library names and returns fail when name is not a correct library name. Before, it returned an error.
• Documentation updated, including HTML.
• Added MiddleInnerMappingGroup.
• Added IsLeftALoop, IsMiddleALoop, IsRightALoop, IsALoop, and many filters related to A-loops.
• Changed creation of quasigroups and loops by sections. We now support CayleyTableByPerms( perms ), QuasigroupByLeftSection( section ), LoopByLeftSection( section ), QuasigroupByRightSection( section ), LoopByRightSection( section ), QuasigroupByRightSection( G, H, T ), and LoopByRightSection( G, H, T ). The methods with arguments G, H, T are much faster than in version 1.5.0. Note that we no more support QuasigroupByLeftSection( G, H, T ), and LoopByLeftSection( G, H, T) since actions act by default on the right in GAP.
• Test files updated.

In version 1.5.0:

• New chapter "Creating quasigroups and loops" in the documentation.
• Documentation and bibliography updated.
• Test files updated.
• Added LoopByLeftSection and QuasigroupByLeftSection.
• Added NuclearExtension and LoopByExtension.
• Faster method for IsAssociative (it is much faster for associative loops (factor 10), and slower for nonassociative loops (factor 2)).

In version 1.4.0:

• We now support all nonassociative left Bol loops of order less than 17.
• Updated documentation.
• Updated bibliography.
• Placed all html documentation into a separate "htm" folder.

In version 1.3.0:

• Added IsotopismLoops and LoopsUpToIsotopism.
• Added libraries "small" (of all nonassociative loops of order less than 7 up to isomorphism), and "itp small" (of all nonassociative loops of order less than 7 up to isotopism).
• Streamlined code for PrincipalLoopIsotope and AsLoop.
• Fixed a bug in Subloop (it did not return the correct subloop in some very special circumstances).
• Updated documentation (.dvi, .ps, .pdf).
• Updated all test files, and deleted test file mouflib.tst.
• Changed LOOPS banner to include e-mail addresses of authors.

In version 1.2.2:

• Added RightCosets( L, S ) and RightTransversal( L, S ).
• Added IsomorphicCopyByPerm( L, p ) and IsomorphicCopyByNormalSubloop( L, S )
• dvi, pdf and ps versions of the manual were updated.

In version 1.2.1:

• Added LoopsUpToIsomorphism, a function that filters a list of loops up to isomorphism.
• We now know that the library "Moufang" contains all nonassociative Moufang loops of order 64 up to isomorphism.
• Library "Moufang" extended by all (5) nonassociative Moufang loops of order 81.
• dvi, pdf and ps versions of the manual were updated.

In version 1.2.0:

• Typo fixed in AutomorphismGroup. Because of the typo, the command did not work properly for loops of order less than 8.
• Bug in DirectProduct fixed so that it now works properly when the loops are proper subloops.
• LeftBolLoop(8,2) and LeftBolLoop(8,3) were the same in older versions; the problem is fixed now. Thanks, Ken!
• New operation AllSubloops(L) was added. It returns a list of all subloops of a loop L.
• dvi, pdf and ps versions of the manual were updated.

In version 1.1.0:

• Typo fixed in HasAntiautomorphicInverseProperty.
• IsomorphismLoops still did not work properly in version 1.0.0. for some (rare) non power-associative loops. It should be OK now.
• There was a conflict between our package and package RCWA. We fixed it by declaring RightInverse and LeftInverse as attributes instead of operations.
• Added functions IsLeftPowerAlternative, IsRightPowerAlternative, IsPowerAlternative. Thanks, Michael!
• To improve support for operations of left and right division, we have added functions LeftDivisionCayleyTable and RightDivisionCayleyTable.
• Pdf, ps and div versions of documentation updated. (Html and inline documentation not updated.)
• Many improvements made to filters. They are now much more powerful and layed out in a more logical way.
• AssociatorSubloop is now much faster (at least 100 times).

In version 1.0.0:

• Subquasigroups and subloops are now more tightly linked to their parents. For instance, when L is a loop with elements l1, ..., l6 and S is a subloop consisting of l1, l3, l5, the multiplication table of S, multiplication group of S, etc., are all based on {1,3,5}, not on {1,2,3}, as was the case in the previous versions of LOOPS. This fixes problems with subquasigroups of subquasigroups in previous versions. Please see the documentation for details.
• We have broadened the definition of a Cayley table, to accommodate quasigroups with elements as described above.
• When L is a loop, Subloop( L, S ) now also allows S to be a list of positions of elements in the parent of L, not only a list of elements of L.
• Many methods that were previously declared as global functions are now operations.
• Many methods, notably FactorLoop and tests for nilpotency and solvability are much faster.
• Test files updated.
• Documentation is now written in accordance with GAP specifications, using the style gapmacro.tex.

In version 0.9995:

• RelativeLeftMultiplicationGroup and RelativeRightMultiplicationGroup now work correctly
• IsomorphismLoops and AutomorphismGroup now work for all loops, not just for power associative loops
• small bug in IsLoopTable fixed
• Center of a loop now automatically sets properties IsAssociative and IsCommutative to true
• HasAutomorphicInverseProperty and HasAntiautomorphicInverseProperty have been generalized (we now use one-sided inverses instead of two-sided inverses)
• HasWeakInverseProperty and related filters added
• all nonassociative conjugacy closed loops of order p² and 2p for odd prime p are now available in the library CC