The package contains an implementation for computing determinant of free graded complexes, called detComplex, with several derived methods: listDetComplex, mapsComplex, and minorsComplex. This provides a method for producing universal formulas for any family of schemes, just by combining the resolution, method with detComplex. In Section 2 determinants of free resolutions are treated, as well as a few examples. We recommend to see [Dem84, Jou95, GKZ94, Bus06] for more details on determinants of complexes in elimination theory.

The package also provides methods for computing matrices and formulas for different resultants applicable on different families of polynomials, such as the Macaulay resultant macRes, for generic homogeneous polynomials; residual resultant (ciRes, cm2Res) for generic polynomials having a non empty base locus scheme; determinantal resultant (detRes) for generic polynomial matrices of a given generic rank. Those resultants and their implementation are reviewed in Section 3 and for the theory behind the author can refer to [Jou91, Cha93, GKZ94, Jou95, Jou97, CLO98, BEM01, Bus01b, Bus06, Bus04].

The goal of this package is to provide universal formulas for elimination. The main advantage of this approach consists in the fact that we can provide formulas for any family of polynomials just by taking determinant to a free resolution. A direct consequence of a universal formula is that it is preserved by base change, this is, in particular, it commutes with specialization. A deep study of universal formulas for the image of a map of schemes can be seen in EH00.