# ciResidual -- Strategy for eliminationMatrix.

## Synopsis

• Usage:
eliminationMatrix(..., Strategy => ciResidual)
• Consequences:
• This function basically computes the matrix of the first application in the resolution of (I:J) given in the article of Bruns, Kustin and Miller: 'The resolution of the generic residual intersection of a complete intersection', Journal of Algebra 128.

## Description

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 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

## For the programmer

The object ciResidual is .