Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Algorithmic algebra
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Solving systems of algebraic equations by using Gröbner bases
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Extracting Cylinders in Full 3D Data Using a Random Sampling Method and the Gaussian Image
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Solving parametric polynomial systems
Journal of Symbolic Computation
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It is known that five points in R3 generically determine a finite number of cylinders containing those points. We discuss ways in which it can be shown that the generic (complex) number of solutions, with multiplicity, is six, of which an even number will be real valued and hence correspond to actual cylinders in R3. We partially classify the case of no real solutions in terms of the geometry of the five given points. We also investigate the special case where the five given points are coplanar, as it differs from the generic case for both complex and real valued solution cardinalities.