  In this article we suggest a model of computation for the cake cutting
problem. In this model the mediator can ask the same queries as in the
Robertson-Webb model but he or she can only perform algebraic operations as in
the Blum-Shub-Smale model. All existing algorithms described in the
Robertson-Webb model can be described in this new model.We show that in this
model there exist explicit couples of measures for which no algorithm outputs
an equitable fair division with connected parts.We also show that there exist
explicit set of measures for which no algorithm in this model outputs a fair
division which maximizes the utilitarian social welfare function.The main tool
of our approach is Galois theory.
