Solving the ARE Symbolically

Methods from computer algebra, mostly so called Grr obner bases from commutative algebra, are used to solve the algebraic Riccati equation (ARE) symbolically. The methods suggested allow us to track the innuence of parameters in the system or penalty matrices on the solution. Some non-trivial aspects arise when addressing the problem from the point of view commutative algebra, for example the original equations are rational, not polynomial. We explain how this can be dealt with rather easily. Some methods for lowering the computational complexity are suggested and diierent methods are compared regarding eeciency. Preprocessing of the equations before applying Grr obner bases can make computations more eecient.