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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)
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)
The computer algebra software CASA (Computer Algebra Software for Algebraic Geometry), which is based on the computer algebra system Maple, is being developed by the computer algebra group at RISC under the direction of F. Winkler. In this report, CASA is analyzed with respect to its current state and possible improvements. Finally, some improvements and… (More)
SIN~ITNDcI~EIA\ONMOV ABSTRACT In order to parametrize an algebraic' curve of genus zero, one usually faces the problem of finding rational points on it. This problem can be reduced to find rational points on a (birationally equivalent) conic. In this paper, we deal with a method of computing such a rational point on a conic from its defining equation (we… (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.
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)