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- Erik Hillgarter, Franz Winkler
- Automated Deduction in Geometry
- 1996

A plane algebraic curve is given as the zeros of a bivariate polynomial. However, this implicit representation is badly suited for many applications, for instance in computer aided geometric design. What we want in many of these applications is a rational parametrization of an algebraic curve. There are several approaches to deciding whether an algebraic… (More)

- Günter Landsmann, Josef Schicho, Franz Winkler, Erik Hillgarter
- ISSAC
- 2000

A canal surface <italic>S</italic>, generated by a parametrized curve <italic>m</italic>(<italic>t</italic>), in R<supscrpt>3</supscrpt> is the envelope of the set of spheres with radius <italic>r</italic>(<italic>t</italic>) centered at <italic>m</italic>(<italic>t</italic>). This concept generalizes the classical offsets (for… (More)

Differential problems are ubiquitous in mathematical modeling of physical and scientific problems. Algebraic analysis of differential systems can help in determining qualitative and quantitative properties of solutions of such systems. In this tutorial paper we describe several algebraic methods for investigating differential systems.

- ERIK HILLGARTER
- 2004

I report on a contribution to the point symmetry classification problem for second-order partial differential equations (PDEs) in z(x, y), i.e. to an overview over all possible symmetry groups admitted by this class of equations. The article also contains a concise introduction into classical symmetry analysis. Sophus Lie (1842–1899) determined all… (More)

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