Spline Implicitization of Planar Curves

We present two software packages for computing the null space of a matrix with rational function coefficients. We use two approaches based on classical interpolation algorithms. The packages are written in the Mathematica language.In the first package we use polynomial interpolation and Cramer's rule to reconstruct the components of the solutions. This package works under some assumptions on the matrix that, in most cases, are true for systems involved in Zeilberger's algorithm for hypergeometric definite summation.In the second package we use a hybrid method based on heuristic rational function interpolation on some low degree components of the solutions and "symbolic" Gaussian elimination on the other components. The second package works under very general conditions and can be customized for systems related to symbolic summation.

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