Implement SmallAntimagmasInformation function similar to SmallGroupInformation

[Copilot]

This PR implements a SmallAntimagmasInformation function similar to the SmallGroupInformation function from the smallgrp package, addressing issue #112.

New Functions

SmallAntimagmasInformation(n)

Returns a record with comprehensive information about antiassociative magmas of order n:

• total: Total number of antiassociative magmas (including isomorphic copies)
• upToIsomorphism: Number of antiassociative magmas up to isomorphism
• upToIsomorphismAndAntiisomorphism: Number of antiassociative magmas up to isomorphism and anti-isomorphism

NrSmallAntimagmasUpToAntiisomorphism(n)

Returns the count of antiassociative magmas of order n up to isomorphism and anti-isomorphism.

Usage Example

gap> SmallAntimagmasInformation(3);
rec( total := 52, upToIsomorphism := 10, upToIsomorphismAndAntiisomorphism := 7 )

gap> NrSmallAntimagmasUpToAntiisomorphism(2);
1

Implementation Details

The implementation leverages existing anti-isomorphism functionality (IsMagmaAntiisomorphic) to identify equivalence classes under both isomorphism and anti-isomorphism. The algorithm:

1. Starts with all magmas up to isomorphism (using AllSmallAntimagmas)
2. Iteratively checks if each magma is anti-isomorphic to any previously processed magma
3. Only counts magmas that form new equivalence classes
4. Maintains the mathematical relationship: upToIsomorphismAndAntiisomorphism ≤ upToIsomorphism ≤ total

Files Changed

• lib/smallantimagmas.gd: Added function declarations with documentation
• lib/smallantimagmas.gi: Added function implementations
• tst/test_smallantimagmas_information.tst: Added comprehensive tests verifying mathematical properties

The implementation follows existing code patterns and maintains compatibility with all existing functionality.

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