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Real Plane Curves - A Numerical Approach via Mathematica
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Wolfram Technology Conference 2014
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Champaign, Illinois, USA
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Our objects of study are the real solution sets ofÊ2-variable polynomial equations with floating point Mathematica machine numbers as coefficients. ÊWe work primarily in the affine plane with the addition of infinite points of the curve. Among the various procedures available are point finding, including singular points, isolated points, and infinite points with their asymptotes. Fractional Linear Transformations are supported allowing degree 2 and 3 curves to be transformed to canonical form.ÊInfinite points can be transformed to finite points for inspection. There are plotting and decomposition routines for further analysis. Real plane curves can be decomposed into affine topological components, projective components, algebraic components or ovals. ÊOur analsys of curves is based on the oval decomposition.ÊThe present software works well for nicely scaled polynomials up to degree 6 and adequately for poorly scaled polynomials up to degree four.
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http://www.wolfram.com/events/technology-conference/2014
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| RealNumericalCurves-BarryHDayton.nb (643.6 KB) - Mathematica Notebook |
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