μ-bases for polynomial systems in one variable

The notion of a μ-basis for an arbitrary number of polynomials in one variable is defined. The basic properties of these μ-bases are derived, and an algorithm is presented based on Gaussian Elimination to calculate a μ-basis for any collection of univariate polynomials. These μ-bases are then applied to solve implicitization, inversion and intersection problems for rational space curves. Systems where base points are present are also discussed.