Solving the implicitization, inversion and reparametrization problems for rational curves through subresultants

From the rational functions defining a rational plane curve it is possible to construct two bivariate polynomials that can be seen as univariate polynomials in the parameter value. In this paper several relevant properties of the subresultant sequence of these two polynomials are introduced which are used to solve simultaneously the implicitization, inversion, properness and reparametrization problems. It is also shown that these methods can be suitably transformed in order to deal with curves in the three-dimensional space presented by a polynomial parametrization.