Preprints, work in progress

1. On the complexity of the truncated moment problem
   D. Henrion, S. Naldi and M. Safey El Din
   — In preparation, 2022
   
   
2. Certifying moment semidefinite representations of convex semialgebraic sets
   D. Henrion and S. Naldi
   — In preparation, 2022
   
   
3. Gröbner bases, syzygies and polynomial matrix multiplication
   S. Naldi and V. Neiger
   — In preparation, 2022
   
   

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

1. 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
   
   
2. 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
   
   
3. Spectrahedral representations of plane hyperbolic curves
   M. Kummer, S. Naldi and D. Plaumann
   — Pac. J. Math. 303(1):243--263 (2019)
   
   
4. 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)
   
   
5. 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
   
   
6. Symbolic computation in hyperbolic programming
   S. Naldi and D. Plaumann
   — J. Algebra Appl. 17:10 (2018) (included in the Proceedings of MEGA 2017)
   
   
7. 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)
   
   
8. Exact algorithms for linear matrix inequalities
   D. Henrion, S. Naldi and M. Safey El Din
   — SIAM J. Optimiz. 26(4):2512--2539 (2016)
   
   
9. 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
   
   
10. Real root finding for determinants of linear matrices
    D. Henrion, S. Naldi and M. Safey El Din
    — J. Symb. Comput. 74:205--238 (2016)
    
    
11. 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
    
    
12. 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. Patient identification and tumor identification management: quality program in a cancer multicentric clinical data warehouse (with K. Pallier, O. Prot, F. Silva, T. Denis, O. Giry, S. Leobon, E. Deluche, N. Tubiana-Mathieu) — Subm. to Cancer Informatics, 2022
3. The CHSH inequality for a single qutrit (with D. J. B. Anoman and F. Arnault) — Poster at QCRYPT 2019 (August 2019, Montreal, Canada)
4. Exact algorithms for determinantal varieties and semidefinite programming — PhD thesis, INSA Université de Toulouse, September 2015 — tel-01212502