Computing the Topology of an Arrangement of Quartics

Improving the topology computation of an arrangement of cubics

“…Since f yy = 6y + 2a 1,2 x + 2a 0,2 (remember that a 0,3 = 1) intersects f in the infinity line, we get that the slope − a 1,2 3 is a root of f 3 (1, y). In order to compute c we now consider the remainder r(x, c) of the division of f by f yy + c considered as polynomials in y.…”

“…The proposed improvement comes from using deeper the well-known geometry of the reducible cubics instead of relying on general algebraic tools. This idea has also been used in [3] to extend the algorithm in [6] for analyzing arrangements of cubic curves to study in a similar way the topology of an arrangement of quartic curves.…”