A symbolic approach to the computation of the determinant of a matrix from
the solution of an associated linear system of equations, proposed in
1988, was recently revived and made a method of practical choice. In many
geometric applications (e.g. to computation of convex hulls), however, one
needs only a single bit defining the sign of the determinant.  In this
case, there are more effective algorithms, which use some numerical
techniques.
 One approach works for the
computation of one or a few leading bits of the determinant or another
algebraic predicate and relies on numerical version of Chinese remainder
theorem. Another approach works only for the sign of matrix determinant.
It is purely numerical and complements naturally the symbolic  ones.