# A Decision Procedure for Univariate Real Polynomials in Isabelle/HOL

by Manuel Eberl

In: *Proceedings of CPP 2015*

### DOI:

10.1145/2676724.2693166### Abstract:

Sturm sequences are a method for computing the number of real roots of a univariate real polynomial inside a given interval efficiently. In this paper, this fact and a number of methods to construct Sturm sequences efficiently have been formalised with the interactive theorem prover Isabelle/HOL. Building upon this, an Isabelle/HOL proof method was then implemented to prove interesting statements about the number of real roots of a univariate real polynomial and related properties such as non-negativity and monotonicity.

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### BibTeX:

```
@inproceedings{eberl15cpp,
author = "Eberl, Manuel",
title = "A Decision Procedure for Univariate Real Polynomials in {I}sabelle/{HOL}",
booktitle = "Certified Programs and Proofs, {CPP} 2015",
year = "2015",
isbn = "978-1-4503-3296-5",
pages = "75--83",
numpages = "9",
doi = "10.1145/2676724.2693166",
publisher = "ACM"
}
```

(The final publication is available at ACM)