Hello, I'm having trouble understanding the computation involved in the resultants from algebraic geometry. I've checked out the textbook Using Algebraic Geometry by Cox et al, so I'll be using terminologies from that text. For systems of 2 polynomials I can compute the resultant the "long way" by taking the determinate of the Sylvester matrix; or when the polynomials are linear, simply take the determinate of the coefficient matrix. The problem I'm having is understanding the multiplication map mf that is introduced in the text. This multiplication map is used for computing the resultant of 2 polynomials (page 74 in the textbook) and for n polynomials (page 90). I'm quite lost in how to compute this multiplication map and the examples in the text don't seem to help me. If anybody can give some insights it would be greatly appreciated!