Schost, Éric; St-Pierre, Catherine \(p\)-adic algorithm for bivariate Gröbner bases. (English) Zbl 07760797 Dickenstein, Alicia (ed.) et al., Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24–27, 2023. New York, NY: Association for Computing Machinery (ACM). 508-516 (2023). MSC: 68W30 PDF BibTeX XML Cite \textit{É. Schost} and \textit{C. St-Pierre}, in: Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24--27, 2023. New York, NY: Association for Computing Machinery (ACM). 508--516 (2023; Zbl 07760797) Full Text: DOI
Elliott, Jesse; Giesbrecht, Mark; Schost, Éric Bit complexity for computing one point in each connected component of a smooth real algebraic set. (English) Zbl 07621046 J. Symb. Comput. 116, 72-97 (2023). MSC: 14Qxx 68Wxx 14Pxx PDF BibTeX XML Cite \textit{J. Elliott} et al., J. Symb. Comput. 116, 72--97 (2023; Zbl 07621046) Full Text: DOI arXiv
Le, Huu Phuoc; Safey El Din, Mohab Solving parametric systems of polynomial equations over the reals through Hermite matrices. (English) Zbl 1487.14130 J. Symb. Comput. 112, 25-61 (2022). Reviewer: Beatriz Pascual Escudero (Madrid) MSC: 14Q30 13P99 12Dxx 14P10 PDF BibTeX XML Cite \textit{H. P. Le} and \textit{M. Safey El Din}, J. Symb. Comput. 112, 25--61 (2022; Zbl 1487.14130) Full Text: DOI arXiv
Dahan, Xavier Lexicographic Gröbner bases of bivariate polynomials modulo a univariate one. (English) Zbl 07457757 J. Symb. Comput. 110, 24-65 (2022). MSC: 68Wxx 13Pxx 12Yxx PDF BibTeX XML Cite \textit{X. Dahan}, J. Symb. Comput. 110, 24--65 (2022; Zbl 07457757) Full Text: DOI arXiv
Emiris, Ioannis Z.; Mantzaflaris, Angelos; Tsigaridas, Elias P. Multilinear polynomial systems: root isolation and bit complexity. (English) Zbl 1475.13051 J. Symb. Comput. 105, 145-164 (2021). MSC: 13P15 68W30 PDF BibTeX XML Cite \textit{I. Z. Emiris} et al., J. Symb. Comput. 105, 145--164 (2021; Zbl 1475.13051) Full Text: DOI Link
Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan Solving determinantal systems using homotopy techniques. (English) Zbl 1461.13034 J. Symb. Comput. 104, 754-804 (2021). Reviewer: Amir Hashemi (Isfahan) MSC: 13P15 65H20 PDF BibTeX XML Cite \textit{J. D. Hauenstein} et al., J. Symb. Comput. 104, 754--804 (2021; Zbl 1461.13034) Full Text: DOI arXiv
Szutkoski, Jonas; van Hoeij, Mark The complexity of computing all subfields of an algebraic number field. (English) Zbl 1419.11143 J. Symb. Comput. 93, 161-182 (2019). MSC: 11Y40 11Y16 68W30 PDF BibTeX XML Cite \textit{J. Szutkoski} and \textit{M. van Hoeij}, J. Symb. Comput. 93, 161--182 (2019; Zbl 1419.11143) Full Text: DOI arXiv
Amzallag, Eli; Sun, Mengxiao; Pogudin, Gleb; Vo, Thieu N. Complexity of triangular representations of algebraic sets. (English) Zbl 1408.14193 J. Algebra 523, 342-364 (2019). Reviewer: Amir Hashemi (Isfahan) MSC: 14Q20 68W30 PDF BibTeX XML Cite \textit{E. Amzallag} et al., J. Algebra 523, 342--364 (2019; Zbl 1408.14193) Full Text: DOI arXiv
Noro, Masayuki; Yokoyama, Kazuhiro Usage of modular techniques for efficient computation of ideal operations. (English) Zbl 1402.13026 Math. Comput. Sci. 12, No. 1, 1-32 (2018). Reviewer: Amir Hashemi (Isfahan) MSC: 13P10 PDF BibTeX XML Cite \textit{M. Noro} and \textit{K. Yokoyama}, Math. Comput. Sci. 12, No. 1, 1--32 (2018; Zbl 1402.13026) Full Text: DOI
Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). (English) Zbl 1415.65121 J. Symb. Comput. 84, 147-171 (2018). MSC: 65H99 12D10 PDF BibTeX XML Cite \textit{T. Ayyildiz Akoglu} et al., J. Symb. Comput. 84, 147--171 (2018; Zbl 1415.65121) 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 PDF BibTeX XML Cite \textit{D. Henrion} et al., SIAM J. Optim. 26, No. 4, 2512--2539 (2016; Zbl 1356.90102) Full Text: DOI arXiv
Mehrabi, Esmaeil; Schost, Éric A softly optimal Monte Carlo algorithm for solving bivariate polynomial systems over the integers. (English) Zbl 1352.68299 J. Complexity 34, 78-128 (2016). MSC: 68W30 11K45 PDF BibTeX XML Cite \textit{E. Mehrabi} and \textit{É. Schost}, J. Complexity 34, 78--128 (2016; Zbl 1352.68299) Full Text: DOI
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice Separating linear forms and rational univariate representations of bivariate systems. (English) Zbl 1328.13041 J. Symb. Comput. 68, Part 1, 84-119 (2015). MSC: 13P15 68W30 PDF BibTeX XML Cite \textit{Y. Bouzidi} et al., J. Symb. Comput. 68, Part 1, 84--119 (2015; Zbl 1328.13041) Full Text: DOI
Orange, Sébastien; Renault, Guénaël; Yokoyama, Kazuhiro Efficient arithmetic in successive algebraic extension fields using symmetries. (English) Zbl 1300.12006 Math. Comput. Sci. 6, No. 3, 217-233 (2012). Reviewer: Vilmar Trevisan (Porto Alegre) MSC: 12F10 12Y05 68W30 PDF BibTeX XML Cite \textit{S. Orange} et al., Math. Comput. Sci. 6, No. 3, 217--233 (2012; Zbl 1300.12006) Full Text: DOI
van Hoeij, Mark; Pal, Vivek Isomorphisms of algebraic number fields. (English. French summary) Zbl 1282.11142 J. Théor. Nombres Bordx. 24, No. 2, 293-305 (2012). Reviewer: Andreas Stein (Oldenburg) MSC: 11R04 11Y40 PDF BibTeX XML Cite \textit{M. van Hoeij} and \textit{V. Pal}, J. Théor. Nombres Bordx. 24, No. 2, 293--305 (2012; Zbl 1282.11142) Full Text: DOI arXiv
Gaudry, Pierrick; Schost, Éric Genus 2 point counting over prime fields. (English) Zbl 1267.11127 J. Symb. Comput. 47, No. 4, 368-400 (2012). MSC: 11Y16 11G20 11T71 14G50 94A60 PDF BibTeX XML Cite \textit{P. Gaudry} and \textit{É. Schost}, J. Symb. Comput. 47, No. 4, 368--400 (2012; Zbl 1267.11127) Full Text: DOI
Dahan, Xavier; Kadri, Abdulilah; Schost, Éric Bit-size estimates for triangular sets in positive dimension. (English) Zbl 1246.13039 J. Complexity 28, No. 1, 109-135 (2012). Reviewer: Vasilis Dimitriou (Chania) MSC: 13P10 65H10 PDF BibTeX XML Cite \textit{X. Dahan} et al., J. Complexity 28, No. 1, 109--135 (2012; Zbl 1246.13039) Full Text: DOI arXiv
Ayad, A. Complexity of solving parametric polynomial systems. (English) Zbl 1334.12013 J. Math. Sci., New York 179, No. 6, 635-661 (2011) and Zap. Nauchn. Semin. POMI 381, 5-52 (2011). MSC: 12Y05 68W30 13P15 PDF BibTeX XML Cite \textit{A. Ayad}, J. Math. Sci., New York 179, No. 6, 635--661 (2011; Zbl 1334.12013) Full Text: DOI Link
Ayad, Ali On computing absolutely irreducible components of algebraic varieties with parameters. (English) Zbl 1198.13025 Computing 89, No. 1-2, 45-68 (2010). Reviewer: Juan Gerardo Alcazar (Alcala da Henares) MSC: 13P10 68W30 12D05 PDF BibTeX XML Cite \textit{A. Ayad}, Computing 89, No. 1--2, 45--68 (2010; Zbl 1198.13025) Full Text: DOI
Kaltofen, Erich Exact certification in global polynomial optimization via rationalizing sums-of-squares. (English) Zbl 1191.13001 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 219-227 (2009). MSC: 13-02 13P99 12Y05 68W30 65F30 14P99 90C22 PDF BibTeX XML Cite \textit{E. Kaltofen}, in: Approximate commutative algebra. Berlin: Springer. 219--227 (2009; Zbl 1191.13001) Full Text: DOI
Gao, Xiao-Shan; Luo, Yong; Yuan, Chunming A characteristic set method for ordinary difference polynomial systems. (English) Zbl 1164.39008 J. Symb. Comput. 44, No. 3, 242-260 (2009). Reviewer: Jurang Yan (Taiyuan) MSC: 39A12 65Y10 PDF BibTeX XML Cite \textit{X.-S. Gao} et al., J. Symb. Comput. 44, No. 3, 242--260 (2009; Zbl 1164.39008) Full Text: DOI
Dahan, Xavier; Jin, Xin; Moreno Maza, Marc; Schost, Éric Change of order for regular chains in positive dimension. (English) Zbl 1131.14065 Theor. Comput. Sci. 392, No. 1-3, 37-65 (2008). MSC: 14Q99 13P99 68W30 PDF BibTeX XML Cite \textit{X. Dahan} et al., Theor. Comput. Sci. 392, No. 1--3, 37--65 (2008; Zbl 1131.14065) Full Text: DOI
Moreno Maza, Marc; Reid, Greg; Scott, Robin; Wu, Wenyuan On approximate triangular decompositions in dimension zero. (English) Zbl 1146.68484 J. Symb. Comput. 42, No. 7, 693-716 (2007). MSC: 68W30 13P05 PDF BibTeX XML Cite \textit{M. Moreno Maza} et al., J. Symb. Comput. 42, No. 7, 693--716 (2007; Zbl 1146.68484) Full Text: DOI