I am interested in **computational approaches** to problems involving systems of polynomial equations and inequalities, e.g., to the general problem of polynomial optimization. This is why I implement algorithms in computer algebra systems such as Maple or Macaulay2.

# SPECTRA

**S**emidefinite **P**rogramming solved **E**xactly with **C**omputational **T**ools of **R**eal **A**lgebra

*Image 1: a spectrahedron* *Image 2: sample points on a quartic curve*

### Description

SPECTRA is a Maple library for solving linear matrix inequalities (LMI) in exact arithmetic.
An example of solution set of a LMI is the red convex region of *Image 1*, or the interior of
the inner oval of *Image 2*.

### Webpage

Please visit the Spectra permanent webpage for further information.

### Documentation

D. Henrion, S. Naldi, M. Safey El Din. *Spectra: a Maple library for solving linear matrix inequalities in exact arithmetic*. Software documentation, November 2016 [LINK].

An example of quintic spectrahedron of type (12,0) computed by Spectra : quintic.

# HYPER

#### Optimization with hyperbolic polynomials

*Image 3: Hyperbolic quartic* *Image 4: Hyperbolic quintic*

This is a *beta-version* of a library for exact computing with hyperbolic polynomials.

Binary file : HYPER

This library implements algorithms presented in:

- S. Naldi, D. Plaumann.
*Symbolic computation in hyperbolic programming*. Accepted for oral presentation at MEGA 2017, Nice, Juin 2017. Submitted for publication (2016). [arxiv]