Degree Bounds for Zero-dimensional Gröbner Bases

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Title: Degree Bounds for Zero-dimensional Gröbner Bases
Author: Ritscher, Stephan
Advisors: Hoon Hong, Committee Chair
Agnes Szanto, Committee Member
Michael Singer, Committee Member
Abstract: The theory of Gröbner bases plays a fundamental role in solving and reasoning with polynomial equations (ideals). This thesis will review and prove matching upper and lower degree bounds of Gröbner bases for zero-dimensional ideals and prove that this degree is also obtained in the generic case. For the lexicographic monomial ordering, this degree is d^n, for graded monomial ordering it is n (d - 1) + 1.
Date: 2009-04-27
Degree: MS
Discipline: Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/281


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