Preprints and in preparation

1. Gröbner bases, syzygies and polynomial matrix multiplication
   (S. Naldi and V. Neiger). In preparation, 2024.
   
   
2. Certifying moment semidefinite representations of convex semialgebraic sets
   (D. Henrion and S. Naldi). In preparation, 2024.
   
   
3. Algebraic certificates for the truncated moment problem
   (D. Henrion, S. Naldi and M. Safey El Din) — January 2023, arXiv/2302.06927.
   
   

Peer-reviewed publications    (full list on arXiv, see also Hal, orcid.org or scopus)

1. Taylor polynomials of rational functions
   (A. Conca, S. Naldi, G. Ottaviani and B. Sturmfels) — Acta Math. Vietn. (2023) [full-text view-only]
   
   
2. Patient identification and tumor identification management: quality program in a cancer multicentric clinical data warehouse
   (K. Pallier, O. Prot, S. Naldi, F. Silva, T. Denis, O. Giry, S. Leobon, E. Deluche, N. Tubiana-Mathieu). Cancer Inform. 2023 May 19;22:11769351231172609
   
   
3. A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension
   (S. Naldi and V. Neiger). Proc. 2020 ACM Int. Symp. Symb. Alg. Comput., pp 380-387, 2020
   
   
4. Conic programming: infeasibility certificates and projective geometry
   (S. Naldi and R. Sinn). J. Pure Appl. Algebra 225(7), 2021 - Special Issue of the Arctic Applied Algebra
   
   
5. Spectrahedral representations of plane hyperbolic curves
   (M. Kummer, S. Naldi and D. Plaumann). Pac. J. Math. 303(1):243--263 (2019)
   
   
6. Real root finding for low rank linear matrices
   (D. Henrion, S. Naldi and M. Safey El Din). Appl. Algebr. Eng. Comm. Comp. 31(2), 101-133 (2020) [full-text view-only]
   
   
7. Exact algorithms for semidefinite programs with degenerate feasible set
   (D. Henrion, S. Naldi and M. Safey El Din). J. Symb. Comp. (104) 942--959, 2021 — Proc. 2018 ACM Int. Symp. Symb. Alg. Comput., pp 191-198, 2018
   
   
8. Symbolic computation in hyperbolic programming
   (S. Naldi and D. Plaumann). J. Algebra Appl. 17:10 (2018) (included in the Proceedings of MEGA 2017)
   
   
9. SPECTRA - A Maple library for solving linear matrix inequalities in exact arithmetic
   (D. Henrion, S. Naldi and M. Safey El Din). Optim. Method. Softw. 34(1):62--78 (2019)
   
   
10. Exact algorithms for linear matrix inequalities
    (D. Henrion, S. Naldi and M. Safey El Din) SIAM J. Optimiz. 26(4):2512--2539 (2016)
    
    
11. Solving rank-constrained semidefinite programs in exact arithmetic
    (S. Naldi). J. Symb. Comput. 85C:206--223 (2018) — Proc. 2016 ACM Int. Symp. Symb. Alg. Comput., pp 357-364, 2016
    
    
12. Real root finding for determinants of linear matrices
    (D. Henrion, S. Naldi and M. Safey El Din). J. Symb. Comput. 74:205--238 (2016)
    
    
13. Real root finding for rank defects in linear Hankel matrices
    (D. Henrion, S. Naldi and M. Safey El Din). Proc. 2015 ACM Int. Symp. Symb. Alg. Comput., pp 221-228, 2015
    
    
14. Nonnegative polynomials and their Carathéodory number
    (S. Naldi). Discrete Comput. Geom. 51(3):559--568 (2014)

Software

1. SPECTRA — A Maple library for Linear Matrix Inequalities (cf. this paper). The source code of SPECTRA is available here.
2. HYPER — Implementations of algorithms for Hyperbolic Programming (cf. this paper)
3. Maple code — from the paper Real root finding for low rank linear matrices.

Other research works

1. Quantum Random Number Generator based on Violations of the Free CHSH-3 Inequality (with F. Arnault, Don J-B. Anoman) — arXiv pre-print
2. The CHSH inequality for a single qutrit (with D. J. B. Anoman and F. Arnault) — Poster at QCRYPT 2019 (August 2019, Montreal, Canada)
3. Exact algorithms for determinantal varieties and semidefinite programming — PhD thesis, INSA Université de Toulouse, September 2015 — tel-01212502