The shape of the solution set for systems of interval linear equations with dependent coefficients

A standard system of interval linear equations is defined by Ax = b, where A is an m x n coefficient matrix with (compact) intervals as entries, and b is an m-dimensional vector whose components are compact intervals. It is known that for systems of interval linear equations the solution set, i.e., the set of all vectors a for which Ax = b for some A is an element of A and b is an element of b, is a polyhedron. In some cases, it makes sense to consider not all possible A is an element of A and b is an element of b, but only those A and b that satisfy certain linear conditions describing dependencies between the coefficients. For example, if we allow only symmetric matrices A (a(ij) = a(ji)), then the corresponding solution set becomes (in general) piecewise-quadratic. In this paper, we show that for general dependencies, we can have arbitrary (semi)algebraic sets as projections of solution sets.