Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Algorithms for the geometry of semi-algebraic sets
Algorithms for the geometry of semi-algebraic sets
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Topologically reliable display of algebraic curves
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
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We describe a computer program for the automatic analysis of a real plane affine algebraic curve. The input to the program is a bivariate integral polynomial F (x, y); the outputs are a report on the real curve defined by F(x, y) = 0, and a picture of the curve. The report contains the following information: whether the curve is irreducible, whether singular, and whether bounded; the number of its connected components and the dimension of each; the number of singular, turning, and level points of the curve. Approximations to these special points can be obtained to any desired precision; the more precision, the more time required. The exact form of the picture is controlled by the user; a topologically correct but "linearized" picture can be produced relatively quickly, while a more accurate drawing can be generated but requires more time. The program makes essential use of the clustering cylindrical algebraic decomposition algorithm [Arnon DS: Algorithms for the geometry of semi-algebraic sets (Dissertation). Technical Report #436, Computer Science Department, University of Wisconsin-Madison, 1981].