Add IsSquareMat and IsAntisymmetricMat

[limakzi]

Add IsSquareMatrix/IsSquareMat to check whether a matrix is square.
Add IsAntisymmetricMatrix/IsAntisymmetricMat to check whether mat[i,j] = -mat[j,i] for all entries.

Both symmetric and antisymmetric matrices imply IsSquareMatrix via InstallTrueMethod. IsSymmetricMatrix is simplified to use IsSquareMatrix instead of an inline dimension check.

Fixes #6264.

[Copilot]

Pull request overview

This PR adds new matrix properties to the matrix subsystem, improving reuse and consistency across related predicates.

Changes:

• Introduces IsSquareMatrix / IsSquareMat and adds test coverage for square vs. non-square matrices.
• Introduces IsAntisymmetricMatrix / IsAntisymmetricMat (with documentation and tests).
• Refactors IsSymmetricMatrix to use IsSquareMatrix, and installs implications that symmetric/antisymmetric matrices are square.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated no comments.

File	Description
tst/testinstall/matrix.tst	Adds tests for IsSquareMat and IsAntisymmetricMat.
lib/matrix.gi	Implements IsSquareMatrix and IsAntisymmetricMatrix; simplifies IsSymmetricMatrix square-check.
lib/matrix.gd	Declares new properties/synonyms, adds GAPDoc entries, and installs implications to IsSquareMatrix.
doc/ref/matrix.xml	Includes the new GAPDoc sections in the reference manual.

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[fingolfin]

This should also go, and tests be added.

Luckily, it doesn't actually work for e.g. IsPlistMatrixRep (not sure why, but I also did not try to investigate).

But the following could also be basis for a test.

gap> a := NewZeroMatrix(IsPlistMatrixRep, Integers, 0, 2);
<0x2-matrix over Integers>
gap> b := NewZeroMatrix(IsPlistMatrixRep, Integers, 2, 0);
<2x0-matrix over Integers>
gap> c := NewZeroMatrix(IsPlistMatrixRep, Integers, 0, 0);
<0x0-matrix over Integers>
gap>
gap> IsEmptyMatrix(a);
true
gap> IsEmptyMatrix(b);
true
gap> IsEmptyMatrix(c);
true
gap>
gap> IsSymmetricMatrix(a);
false
gap> IsSymmetricMatrix(b);
false
gap> IsSymmetricMatrix(c);
true

[fingolfin]

I've applied my suggestions and added a bunch of test with "empty" matrices / MatrixObj

[fingolfin]

Fails because the HAPcryst package also defines DeclareProperty("IsSquareMat",IsMatrix); (which is fine) with a really bad method:

InstallMethod(IsSquareMat,"for matrices",[IsMatrix],
        function(mat)
        return Size(Set(mat,Size))=1;
end);

[fingolfin]

See gap-packages/hapcryst#12