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\title{Descartes' Rule of Signs}
\author{Manuel Eberl}
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\begin{abstract}
In this work, we formally proved Descartes Rule of Signs, which relates the number of positive real roots of a polynomial with the number of sign changes in its coefficient list.

Our proof follows the simple inductive proof given by Arthan~\cite{arthan}, which was also used by John Harrison in his HOL Light formalisation. We proved most of the lemmas for arbitrary linearly-ordered integrity domains (e.g. integers, rationals, reals); the main result, however, requires the intermediate value theorem and was therefore only proven for real polynomials.
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