We present methods for the decision, classification and construction
problems of number expansions.
First we consider one of the necessary conditions -
the expansivity of the base - of the number system property.
Next, we present two algorithms for the decision problem:
a randomized algorithm using an enclosing parallelepiped for the set of
fractions and the generalization of Brunotte's canonical number system
algorithm. Then, we extend the results for the classification problems.
Finally, we describe strategies for various number system constructions.