Description
The package gauss doesn't seem to always properly store matrices that are constructed over an explicitly specified ring. For example, I thought that the following would be a valid way of constructing a matrix over GF(3):
LoadPackage("gauss");
SN := SparseMatrix( 2, 3, [ [ 2 ], [ 1, 3 ] ], [ [ 1 ], [ 3, 2 ] ], GF(3) );
The documentation doesn't specify that this is incorrect, so I assumed that this call would automatically convert the integer entries to elements of GF(3). However, when recovering the matrix from gauss, it becomes clear that no conversion has taken place:
gap> N := ConvertSparseMatrixToMatrix(SN);
[ [ 0*Z(3), 1, 0*Z(3) ], [ 3, 0*Z(3), 2 ] ]
On rare occasions, this could lead to problems when doing further computations with these sparse matrices. For instance, I have had a case where computing the rank (using the Rank function from gauss) failed because the algorithm ended up trying to compute -1/3 mod 3, presumably because earlier steps in the Gaussian elimination algorithm had set that pivot to some rational number (like 3 or -1/3) instead of an element of GF(3). However, I have not been able to produce a small example that exhibits this behaviour, and I am currently not at liberty to share the code that led to a failed rank computation.