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Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to… (More)

- Peter Lebmeir, Jürgen Richter-Gebert
- Computer Aided Geometric Design
- 2008

A plane algebraic curve can be represented as the zero-set of a polynomial in two or if one takes homogenous coordinates: three variables. The coefficients of the polynomial determine the curve… (More)

Let P ⊂ R be a d-dimensional polytope. The realization space of P is the space of all polytopes P ′ ⊂ R that are combinatorially equivalent to P , modulo affine transformations. We report on work by… (More)

- Alexander Below, U. Brehm, Jesús A. De Loera, Jürgen Richter-Gebert
- Discrete & Computational Geometry
- 2000

This paper addresses three questions related to minimal triangulations of a 3-dimensional convex polytope P . • Can the minimal number of tetrahedra in a triangulation be decreased if one allows the… (More)

Dynamic or interactive Geometry software (DGS) is the mathematical version of vector based drawing software: the objects (points, lines, circles, conics, polygons, etc.) are both graphical and… (More)

- Ulrich Kortenkamp, Jürgen Richter-Gebert, Sarang Aravamuthan, Günter M. Ziegler
- Discrete & Computational Geometry
- 1997

We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a 2-dimensional projection (“shadow”) of… (More)

This article deals with the intrinsic complexity of tracing and reachability questions in the context of elementary geometric constructions. We consider constructions from elementary geometry as… (More)

- Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler
- Handbook of Discrete and Computational Geometry…
- 2004

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical… (More)

- Jürgen Richter-Gebert
- Annals of Mathematics and Artificial Intelligence
- 1995

We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an… (More)