The option
Algorithm determines which algorithm will be used to compute the Resultant. There are currently two algorithms implemented:
[
Algorithm => Poisson] (default) the resultant is computed, recursively, through the Poisson Formula (see [1, Theorem 3.4]);
[
Algorithm => Macaulay] the resultant is computed as a Macaulay resultant, i.e. as a ratio of two determinants (see [1, Theorem 4.9]).
[1] David A. Cox, John Little, Donal O'shea -
Using Algebraic Geometry, Graduate Texts in Mathematics, Volume 185 (2005).