Consider the following two system of linear (in)eqaulities:$S = Ax \leq b;\; Cx = e$$T = Dx \leq d;\; Gx = g$How can I check if $S\cap \neg T=\emptyset$ where $\neg T$ is the complement of the linear system $T$. 
Inclusion of polytopes
ds.algorithms;linear algebra;linear programming;computational geometry