Giménez, Nardo; Matera, Guillermo; Pérez, Mariana; Privitelli, Melina On the computation of rational solutions of underdetermined systems over a finite field. (English) Zbl 07655185 J. Complexity 75, Article ID 101712, 31 p. (2023). MSC: 68W40 11Y16 11G25 14G05 14G15 PDFBibTeX XMLCite \textit{N. Giménez} et al., J. Complexity 75, Article ID 101712, 31 p. (2023; Zbl 07655185) Full Text: DOI arXiv
Faugère, Jean-Charles; Labahn, George; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan Computing critical points for invariant algebraic systems. (English) Zbl 1499.14096 J. Symb. Comput. 116, 365-399 (2023). MSC: 14Q15 13A50 PDFBibTeX XMLCite \textit{J.-C. Faugère} et al., J. Symb. Comput. 116, 365--399 (2023; Zbl 1499.14096) Full Text: DOI arXiv
Henrion, Didier; Naldi, Simone; Safey El Din, Mohab Exact algorithms for semidefinite programs with degenerate feasible set. (English) Zbl 1460.90128 J. Symb. Comput. 104, 942-959 (2021). MSC: 90C22 68W30 90C51 90C05 90C60 13P15 14P10 PDFBibTeX XMLCite \textit{D. Henrion} et al., J. Symb. Comput. 104, 942--959 (2021; Zbl 1460.90128) Full Text: DOI arXiv
Henrion, Didier; Naldi, Simone; Safey El Din, Mohab Real root finding for low rank linear matrices. (English) Zbl 1445.13026 Appl. Algebra Eng. Commun. Comput. 31, No. 2, 101-133 (2020). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 13P15 14Q20 14Q30 68W30 PDFBibTeX XMLCite \textit{D. Henrion} et al., Appl. Algebra Eng. Commun. Comput. 31, No. 2, 101--133 (2020; Zbl 1445.13026) Full Text: DOI arXiv
Henrion, Didier; Naldi, Simone; El Din, Mohab Safey Exact algorithms for linear matrix inequalities. (English) Zbl 1356.90102 SIAM J. Optim. 26, No. 4, 2512-2539 (2016). MSC: 90C22 68W30 14Q20 PDFBibTeX XMLCite \textit{D. Henrion} et al., SIAM J. Optim. 26, No. 4, 2512--2539 (2016; Zbl 1356.90102) Full Text: DOI arXiv
Henrion, Didier; Naldi, Simone; Safey El Din, Mohab Real root finding for determinants of linear matrices. (English) Zbl 1329.65090 J. Symb. Comput. 74, 205-238 (2016). MSC: 65F40 65H04 14Q15 PDFBibTeX XMLCite \textit{D. Henrion} et al., J. Symb. Comput. 74, 205--238 (2016; Zbl 1329.65090) Full Text: DOI arXiv
Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno On the complexity of the \(F_5\) Gröbner basis algorithm. (English) Zbl 1328.68319 J. Symb. Comput. 70, 49-70 (2015). MSC: 68W30 13P10 PDFBibTeX XMLCite \textit{M. Bardet} et al., J. Symb. Comput. 70, 49--70 (2015; Zbl 1328.68319) Full Text: DOI arXiv
Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo Degeneracy loci and polynomial equation solving. (English) Zbl 1341.14022 Found. Comput. Math. 15, No. 1, 159-184 (2015). Reviewer: Noémie Combe (Marseille) MSC: 14M10 14M12 14Q20 14P05 68W30 PDFBibTeX XMLCite \textit{B. Bank} et al., Found. Comput. Math. 15, No. 1, 159--184 (2015; Zbl 1341.14022) Full Text: DOI arXiv
Storjohann, Arne; Yang, Shiyun Linear independence oracles and applications to rectangular and low rank linear systems. (English) Zbl 1325.68300 Nabeshima, Katsusuke (ed.), Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23–25, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2501-1). 381-388 (2014). MSC: 68W30 15A06 68Q25 68W20 PDFBibTeX XMLCite \textit{A. Storjohann} and \textit{S. Yang}, in: Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23--25, 2014. New York, NY: Association for Computing Machinery (ACM). 381--388 (2014; Zbl 1325.68300) Full Text: DOI
Greuet, Aurélien; El Din, Mohab Safey Probabilistic algorithm for polynomial optimization over a real algebraic set. (English) Zbl 1327.90232 SIAM J. Optim. 24, No. 3, 1313-1343 (2014). Reviewer: Stephan Dempe (Freiberg) MSC: 90C26 13P25 14Q20 68W30 PDFBibTeX XMLCite \textit{A. Greuet} and \textit{M. S. El Din}, SIAM J. Optim. 24, No. 3, 1313--1343 (2014; Zbl 1327.90232) Full Text: DOI arXiv
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic Solving polynomial systems over finite fields: improved analysis of the hybrid approach. (English) Zbl 1323.68583 van der Hoeven, Joris (ed.) et al., Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22–25, 2012. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-1269-1). 67-74 (2012). MSC: 68W30 11T06 11Y16 PDFBibTeX XMLCite \textit{L. Bettale} et al., in: Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22--25, 2012. New York, NY: Association for Computing Machinery (ACM). 67--74 (2012; Zbl 1323.68583) Full Text: DOI
Li, Xin; Moreno Maza, Marc; Rasheed, Raqeeb; Schost, Éric The modpn library: bringing fast polynomial arithmetic into Maple. (English) Zbl 1217.65092 J. Symb. Comput. 46, No. 7, 841-858 (2011). MSC: 65H10 65H04 68W30 12Y05 65Y15 65Y20 PDFBibTeX XMLCite \textit{X. Li} et al., J. Symb. Comput. 46, No. 7, 841--858 (2011; Zbl 1217.65092) Full Text: DOI
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. (English) Zbl 1321.68529 Watt, Stephen M. (ed.), Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25–28, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0150-3). 257-264 (2010). MSC: 68W30 15A18 68Q25 94A60 PDFBibTeX XMLCite \textit{J.-C. Faugère} et al., in: Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25--28, 2010. New York, NY: Association for Computing Machinery (ACM). 257--264 (2010; Zbl 1321.68529) Full Text: DOI
El Din, Mohab Safey Testing sign conditions on a multivariate polynomial and applications. (English) Zbl 1126.14068 Math. Comput. Sci. 1, No. 1, 177-207 (2007). MSC: 14Q20 14P10 PDFBibTeX XMLCite \textit{M. S. El Din}, Math. Comput. Sci. 1, No. 1, 177--207 (2007; Zbl 1126.14068) Full Text: DOI Link
Bauer, Aurélie; Joux, Antoine Toward a rigorous variation of Coppersmith’s algorithm on three variables. (English) Zbl 1141.94341 Naor, Moni (ed.), Advances in cryptology – EUROCRYPT 2007. 26th annual international conference on the theory and applications of cryptographic techniques, Barcelona, Spain, May 20–24, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72539-8/pbk). Lecture Notes in Computer Science 4515, 361-378 (2007). MSC: 94A60 11Y16 68W30 PDFBibTeX XMLCite \textit{A. Bauer} and \textit{A. Joux}, Lect. Notes Comput. Sci. 4515, 361--378 (2007; Zbl 1141.94341) Full Text: DOI
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise Algorithms in real algebraic geometry. 2nd ed. (English) Zbl 1102.14041 Algorithms and Computation in Mathematics 10. Berlin: Springer (ISBN 3-540-33098-4/hbk). x, 662 p. (2006). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14P10 14-02 14Q99 68W30 13P10 PDFBibTeX XMLCite \textit{S. Basu} et al., Algorithms in real algebraic geometry. 2nd ed. Berlin: Springer (2006; Zbl 1102.14041) Full Text: DOI Backlinks: MO MO
Yang, Bo-Yin; Chen, Jiun-Ming; Courtois, Nicolas T. On asymptotic security estimates in XL and Gröbner bases-related algebraic cryptanalysis. (English) Zbl 1109.94353 Lopez, Javier (ed.) et al., Information and communications security. 6th international conference, ICICS 2004, Malaga, Spain, October 27–29, 2004. Proceedings. Berlin: Springer (ISBN 3-540-23563-9/pbk). Lecture Notes in Computer Science 3269, 401-413 (2004). MSC: 94A60 68Q25 68W30 PDFBibTeX XMLCite \textit{B.-Y. Yang} et al., Lect. Notes Comput. Sci. 3269, 401--413 (2004; Zbl 1109.94353) Full Text: DOI
Basiri, Abdolali; Faugère, Jean-Charles Changing the ordering of Gröbner bases with LLL: case of two variables. (English) Zbl 1072.68645 Sendra, J. Rafael (ed.), ISSAC 2003. Proceedings of the 2003 international symposium on symbolic and algebraic computation, Philadelphia, PA, USA, August 3–6, 2003. New York, NY: ACM Press (ISBN 1-58113-641-2/pbk). 23-29 (2003). MSC: 68W30 68W40 13P10 PDFBibTeX XMLCite \textit{A. Basiri} and \textit{J.-C. Faugère}, in: Proceedings of the 2003 international symposium on symbolic and algebraic computation, ISSAC 2003, Philadelphia, PA, USA, August 3--6, 2003. New York, NY: ACM Press. 23--29 (2003; Zbl 1072.68645)
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise Algorithms in real algebraic geometry. (English) Zbl 1031.14028 Algorithms and Computation in Mathematics. 10. Berlin: Springer. viii, 602 p. (2003). Reviewer: Eugenii I.Shustin (Tel Aviv) MSC: 14P10 14-02 14Q99 68W30 13P10 PDFBibTeX XMLCite \textit{S. Basu} et al., Algorithms in real algebraic geometry. Berlin: Springer (2003; Zbl 1031.14028)
Rouillier, F.; Roy, M.-F.; Safey El Din, M. Finding at least one point in each connected component of a real algebraic set defined by a single equation. (English) Zbl 1009.14010 J. Complexity 16, No. 4, 716-750 (2000). Reviewer: Joos Heintz (Buenos Aires) MSC: 14Q10 65H10 14P05 PDFBibTeX XMLCite \textit{F. Rouillier} et al., J. Complexity 16, No. 4, 716--750 (2000; Zbl 1009.14010) Full Text: DOI Link