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- Invitation to nonlinear algebra by Mateusz Michałek and Bernd Sturmfels
- Bull. Amer. Math. Soc. 61 (2024), 187-198
- Additional book information: Graduate Studies in Mathematics, no. 211, American Mathematical Society, Providence, RI, no. 211, 2021, xiii+226 pp., ISBN 978-1-4704-5367-1
References
- Grigoriy Blekherman, Pablo A. Parrilo, and Rekha R. Thomas (eds.), Semidefinite optimization and convex algebraic geometry, MOS-SIAM Series on Optimization, vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society, Philadelphia, PA, 2013. MR 3075433
- Grigoriy Blekherman, Gregory G. Smith, and Mauricio Velasco, Sums of squares and varieties of minimal degree, J. Amer. Math. Soc. 29 (2016), no. 3, 893–913. MR 3486176, DOI 10.1090/jams/847
- Paul Breiding, Türkü Özlüm Çelik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, and Oğuzhan Yürük, Nonlinear algebra and applications, Numer. Algebra Control Optim. 13 (2023), no. 1, 81–116. MR 4520402, DOI 10.3934/naco.2021045
- P. Comon, Tensors: a brief introduction, IEEE Sig. Proc. Magazine,31 (2014), no. 3, 44–53.
- David A. Cox, Applications of polynomial systems, CBMS Regional Conference Series in Mathematics, vol. 134, American Mathematical Society, Providence, RI, [2020] ©2020. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck and Jessica Sidman. MR 4284895
- David A. Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms, 4th ed., Undergraduate Texts in Mathematics, Springer, Cham, 2015. An introduction to computational algebraic geometry and commutative algebra. MR 3330490, DOI 10.1007/978-3-319-16721-3
- David A. Cox, John Little, and Donal O’Shea, Using algebraic geometry, 2nd ed., Graduate Texts in Mathematics, vol. 185, Springer, New York, 2005. MR 2122859
- V. Dolotin and A. Morozov, Introduction to non-linear algebra, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. MR 2361550, DOI 10.1142/6508
- Shmuel Friedland and Giorgio Ottaviani, The number of singular vector tuples and uniqueness of best rank-one approximation of tensors, Found. Comput. Math. 14 (2014), no. 6, 1209–1242. MR 3273677, DOI 10.1007/s10208-014-9194-z
- I. M. Gel′fand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1264417, DOI 10.1007/978-0-8176-4771-1
- D. Grayson and M. Stillman, Macaulay 2, a software system for research in algebraic geometry www.math.uiuc.edu/Macaulay2/.
- June Huh, Tropical geometry of matroids, Current developments in mathematics 2016, Int. Press, Somerville, MA, 2018, pp. 1–46. MR 3837872
- J. M. Landsberg, Tensors: geometry and applications, Graduate Studies in Mathematics, vol. 128, American Mathematical Society, Providence, RI, 2012. MR 2865915, DOI 10.1090/gsm/128
- Diane Maclagan and Bernd Sturmfels, Introduction to tropical geometry, Graduate Studies in Mathematics, vol. 161, American Mathematical Society, Providence, RI, 2015. MR 3287221, DOI 10.1090/gsm/161
- Stefan Müller, Elisenda Feliu, Georg Regensburger, Carsten Conradi, Anne Shiu, and Alicia Dickenstein, Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry, Found. Comput. Math. 16 (2016), no. 1, 69–97. MR 3451424, DOI 10.1007/s10208-014-9239-3
- Program of the SIAM Conference on Applied Algebraic Geometry (AG23) https://meetings.siam.org/program.cfm?CONFCODE=AG23.
- OSCAR Computer Algebra System https://www.oscar-system.org/.
- Liqun Qi and Ziyan Luo, Tensor analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017. Spectral theory and special tensors. MR 3660696, DOI 10.1137/1.9781611974751.ch1
- Bernd Sturmfels, Algorithms in invariant theory, Texts and Monographs in Symbolic Computation, Springer-Verlag, Vienna, 1993. MR 1255980, DOI 10.1007/978-3-7091-4368-1
- Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949, DOI 10.1090/ulect/008
- Bernd Sturmfels, Solving systems of polynomial equations, CBMS Regional Conference Series in Mathematics, vol. 97, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2002. MR 1925796, DOI 10.1090/cbms/097
- Bernd Sturmfels, Tensors and their eigenvectors, Notices Amer. Math. Soc. 63 (2016), no. 6, 604–606. MR 3495220, DOI 10.1090/noti1389
Reviewer information
- Reviewer: Alicia Dickenstein
- Affiliation: Universidad de Buenos Aires, and IMAS (UBA-CONICET), Buenos Aires, Argentina
- Email: alidick@dm.uba.ar
- Reviewer: Giorgio Ottaviani
- Affiliation: University of Florence, Italy
- Email: giorgio.ottavianiunifi.it
Additional Information
- Journal: Bull. Amer. Math. Soc. 61 (2024), 187-198
- DOI: https://doi.org/10.1090/bull/1814
- Published electronically: October 6, 2023
- Review Copyright: © Copyright 2023 American Mathematical Society