Consider the following parametric polynomial system F.
For different values of u and v, the solution set has a different nature. For example, u=0 and v=0 is a degenerate case: x=0 and y can be any value. To understand more about F, first decompose F into a set of regular chains.
The first regular chain is simple. For all values of u and v, it is well-specialized.
For the last one, its defining set is given by and , and the inequality is to ensure that rc1 specializes well.