I have a $30\times 20$ matrix $A$ with entries of the form $x+y\zeta$ where $\zeta$ is a third root of unity and $x,y$ are rational. I want to solve an equation of the form $AX=B$ where $B$ is a specified column vector (this is a very overdetermined system but I know there is a unique solution). I tried LinearSolve, but it was too slow. I think the expressions involving roots of unity are getting very large in the middle of the computation and Mathematica doesn't simplify the intermediate expressions (any intermediate expression will of course have the form $x+y\zeta$). Is there a way to make Mathematica simplify intermediate expressions in the computation? If so, will this solve the problem?