Details:
Title  Gröbner Basis Structure of Finite Sets of Points  Author(s)  Shuhong Gao, Virginia M. Rodrigues, Jeffrey Stroomer  Type  Technical Report, Misc  Abstract  We study the relationship between certain Gröbner bases for zerodimensional radical ideals, and the varieties defined by the ideals. Such a variety is a finite set of points in an affine ndimensional space. We are interested in monomial orders that "eliminate" one variable, say z. Eliminating z corresponds to projecting points in nspace to (n1)space by discarding the zcoordinate. We show that knowing a minimal Gröbner basis under an elimination order immediately reveals some of the geometric structure of the corresponding variety, and knowing the variety makes available information concerning the basis. These relationships can be used to decompose polynomial systems into smaller systems.  Length  16 
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 Language  English  Year  2003  Translation 
No  Refereed 
No 
