load numberofsolutions;

A:=[
    [ q - 1, 0,        0        ],
    [ 0,     q^3 - 1,  0        ],
    [ 0,     0,        q^3 - 1  ],
    [ 0,     q^2 - 1,  q^2 - 1  ],
    [ -1,    q^2,      q^2      ],
    [ 1,     -q^2 + q, 0        ],
    [ 0,     q - 1,    -q^2 + 1 ],
    [ 0,     -q^2 + 1, q - 1    ],
    [ 1,     0,        q - 1    ]
];

rows:=#A;
cols:=#A[1];
H:=RMatrixSpace(P,rows,cols);
A:=H!A;
load numberofsolutions;
coeff,pol:=NumberOfSolutions(A,cols);
"";
A;
"";
"Coefficient =",coeff;
"Polynomial =",pol;