First presenter Co-presenter(s)
Name :  Dan Bates * Name:   
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Affiliation: Colorado State University Name:   
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09-01  E-mail:    
Session: 9- Symbolic and Numeric Computation Schedule:
Saturday, 11:30
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Title of
Exact ideals from numerical data

Numerical homotopy methods, pioneered largely by Sommese, Verschelde, and Wampler, may be used to construct a numerical irreducible decomposition of an algebraic set. In particular, these methods will produce at least one approximation of a generic point on each irreducible component of the solution set of a set of polynomials. Applying a method such as LLL or PSLQ to certain embeddings of one of these approximate generic points will yield all integer relations (exact defining equations) for the irreducible component on which the point lies. As a result, one may recover at least some of the information contained in the symbolic decomposition of an ideal without relying on symbolic methods such as Groebner basis computations.

This is ongoing work with J. Hauenstein, T. McCoy, C. Peterson, and A. Sommese.