The command DiscriminantSet(F, d, R) returns the discriminant set of a polynomial system with respect to a positive integer, which is a constructible set.

d is positive and less than the number of variables in R.

Given a positive integer d, the last d variables will be regarded as parameters.

A point P is in the discriminant set of F if and only if after specializing F at P, the polynomial system F has no solution or an infinite number of solutions.

This command is part of the RegularChains[ParametricSystemTools] package, so it can be used in the form DiscriminantSet(..) only after executing the command with(RegularChains[ParametricSystemTools]). However, it can always be accessed through the long form of the command by using RegularChains[ParametricSystemTools][DiscriminantSet](..).