  In this paper we show how to split the Root Locus plot for an irreducible
rational transfer function into several individual algebraic plane curves, like
lines, circles, conics, etc. To achieve this goal we use results of a previous
paper of the author to represent the Root Locus as an algebraic variety
generated by an ideal over a polynomial ring, and whose primary decomposion
allow us to isolate the planes curves that composes the Root Locus. As a
by-product, using the concept of duality in projective algebraic geometry, we
show how to obtain the dual curve of each plane curve that composes the Root
Locus and unite them to obtain what we denominate the "Algebraic Dual Root
Locus".
