Algorithmic Algebraic Geometry

Duration

May 1988 - April 1991

Director

Franz Winkler.

Sponsored by

Austrian Science Foundation, Austrian Ministery of Science and Research.

Goals

Mathematical research on improved versions of known algorithms and new algorithms for solving some of the fundamental problems of complex and real algebraic geometry as, for example, solution of systems of algebraic equations, primary decomposition, implicit and parameter representation of algebraic manifolds, structure of polynomial ideals. Among others, the method of Gröbner bases, Collin's method of cylindrical algebraic decomposition, Wu's method of triangularization, and Grigoriev's method are studied. The algorithms are implemented in existing computer algebra software systems and their performance is studied. At the same time, the feasibility of an algebraic library in Common LISP, with object-oriented programming features, is investigated.

This research project continues the traditional research emphasis of RISC-Linz during the past ten years, in particular, research on the method of Gröbner bases developed at RISC-Linz.

Selected Publications

Franz Winkler: Automated theorem proving in nonlinear geomtry; Issues in Nonlinear Geometry and Robotics, JAI press, Ch. Hoffmann (ed.). To appear.

Rafael Sendra, Franz Winkler: Symbolic parametrization of curves; Journal of Symbolic Computation; vol. 12, no. 6, pp. 607-631.

Bernd Sturmfels: Gröbner bases and Stanley decomposition of determinantal ideals; Mathematische Zeitschrift, vol. 205, pp. 137-144, 1990.

R. Gebauer, M. Kalkbrener, B. Wall, F. Winkler: CASA: a computer algebra package for constructive algebraic geometry; Proc. ISSAC'91, Bonn, Germany, St.M. Watt (ed.), ACM Press.

Maintained by: The System Administration
Last Modification: March 7, 1997

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