Professor Emeritus

Theory of Equations Book

Permutations and Necklaces

Approximate local Rings (Paper presented at Notre Dame AMS meeting, April 9, 2006)

Numerical Local Rings of Analytic Systems (January 2008)

Talk at SNC 2007
Numerical Local Rings

Talk at Depaul AMS Meeting, October 2007
Multiple Zeros of Analytic Systems

Preprint August 2008
Numerically generic Unions of Lines
Analysis of Bertini Experiments
Data for Bertini Experiments

Preprint January 2011
Algebraic Foundation of Local Multiplicity

Preprint April 2011
Numerical Calculation of H-bases for Positive Dimensional Varieties

SNC 2011 Talk on Numerical Calculation of H-bases... at ACM-FCRC conference, San Jose, CA, June 2011 (PDF slides)

AG11 Talk on Numerical Algebraic Geometry at SIAM AG11 conference, Raleigh NC, October 2011 (PDF slides)

Michigan Computational Algebraic Geometry talk on global duals at MCAG12, Oakland University, May 2012 (PDF slides).

SIAM talk on Numerical Algebraic Geometry via Macaulay at Numerical Methods for Polynomial Systems, AN12, Minneapolis, July 2012 (PDF slides).

Preprint July 2013
Real Quadradic Surface Intersection Curves

Cheshire Cat

The union of the two quadric surfaces, the sphere and the ellipse are the "cat" and the intersection is the "grin". In Lewis Carroll's Alice and Wonderland the Cheshire cat vanished leaving only the grin. Actually the intersection curve of these two quadric surfaces is known as a Quadric Surface Intersection Curve, QSIC, and, as some of the simplest space curves, are part of classical mathematics. But QSIC such as the "grin" here are essentially elliptic curves and there are so many other possibilities that only recently have we had the computing power to adequately deal with them.

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Lines in a cubic Surface

In 1849 Salmon and Caley discovered that there are exactly 27 straight lines contained in a non-singular complex projective cubic in 3-space. Unfortunately it is not easy to show these in Euclidean 3-space, some of these lines may lie in the plane at infinity and most of these lines generally are complex.

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Oakton Adjunct Faculty Assoc.

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Home Page of Barry H Dayton
Professor Emeritus
Northeastern Illinois University
Chicago, IL 60625-4699, USA