Dennis S. Arnon
Abstract
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].
- {ARN81} Arnon DS: Algorithms for the geometry of semi-algebraic sets, Ph.D. Dissertation, Technical Report #436, Computer Sciences Department, University of Wisconsin - Madison, 1981. Google Scholar
Digital Library
- {COL75} Collins GE: Quantifier elimination for real closed fields by cylindrical algebraic decomposition, in Second GI Conference on Automata Theory and Formal Languages, vol. 33 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1975, pp 134--183. Google ScholarDigital Library
- {COL76} Collins GE: Quantifier elimination for real closed fields by cylindrical algebraic decomposition - a synopsis. SIGSAM Bulletin of the ACM 10, 1 (1976), pp 10--12. Google ScholarDigital Library
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