eliminationMatrix(..., Strategy => ciResidual)
The first argument is a list of homogeneous polynomials $J=(g_1,..,g_m)$ forming a complete intersection with respect to the variables 'varList'. Given a system of homogeneous $I=(f_1,..,f_n)$, such that I is included in J and (I:J) is a residual intersection, one wants to compute a sort of resultant of (I:J). The second argument is the matrix M such that I=J.M. The output is a generically (with respect to the other variables than 'varList') surjective matrix such that the determinant of a maximal minor is a multiple of the resultant of I on the closure of the complementary of V(J) in V(I). Such a minor can be obtain withmaxMinor
The object ciResidual is a symbol.