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Sturm's Theorem: determining the number of zeroes of polynomials in an open interval.

Spreen, E. (2014) Sturm's Theorem: determining the number of zeroes of polynomials in an open interval. Bachelor's Thesis, Mathematics.

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Abstract

A review of the theory of polynomial rings and extension fields is presented, followed by an introduction on ordered, formally real, and real closed fields. This theory is then used to prove Sturm's Theorem, a classical result that enables one to find the number of zeroes of a polynomial that are contained within an open interval, simply by counting the number of sign changes in two sequences. This result can be extended to decide the existence of a zero of a family of polynomials, by evaluating a set of polynomial equations, inequations and inequalities with integer coefficients.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:58
Last Modified: 15 Feb 2018 07:58
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/11953

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