Isolating the real roots of the piecewise algebraic variety

The piecewise algebraic variety, as a set of the common zeros of multivariate splines, is a kind of generalization of the classical algebraic variety. In this paper, we present an algorithm for isolating the zeros of the zero-dimensional piecewise algebraic variety which is primarily based on the interval zeros of univariate interval polynomials. Numerical example illustrates that the proposed algorithm is flexible.