Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MO_2024_110_2_a3, author = {A. D. Polyanin and I. K. Shingareva}, title = {Non-classical symmetries and reductions of algebraic equations and systems of equations}, journal = {Matemati\v{c}eskoe obrazovanie}, pages = {22--34}, publisher = {mathdoc}, volume = {110}, number = {2}, year = {2024}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MO_2024_110_2_a3/} }
TY - JOUR AU - A. D. Polyanin AU - I. K. Shingareva TI - Non-classical symmetries and reductions of algebraic equations and systems of equations JO - Matematičeskoe obrazovanie PY - 2024 SP - 22 EP - 34 VL - 110 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MO_2024_110_2_a3/ LA - ru ID - MO_2024_110_2_a3 ER -
A. D. Polyanin; I. K. Shingareva. Non-classical symmetries and reductions of algebraic equations and systems of equations. Matematičeskoe obrazovanie, Tome 110 (2024) no. 2, pp. 22-34. http://geodesic.mathdoc.fr/item/MO_2024_110_2_a3/
[1] H. W. Turnbull, Theory of Equations, Oliver and Boyd, Edinburgh, 1947 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=222'>222</ext-link>
[2] B. L. Van der Waerden, A History of Algebra: From Al-Khwarizmi to Emmy Noether, Springer, Berlin, 1985 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=803326'>803326</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0569.01001'>0569.01001</ext-link>
[3] S. G. Gindikin, Rasskazy o fizikakh i matematikakh, 3-e izd., MTsNMO, M., 2001
[4] I. N. Bronshtein, K. A. Semendyaev, Spravochnik po matematike dlya inzhenerov i uchaschikhsya vtuzov, Nauka, M., 1980
[5] G. Korn, T. Korn, Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1984
[6] A. D. Polyanin, A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton–London, 2007 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=2271585'>2271585</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1267.00006'>1267.00006</ext-link>
[7] M. D. Yacoub, G. A. Fraidenraich, “A solution to the quartic equation”, The Mathematical Gazette, 96:536 (2012), 271–275 <ext-link ext-link-type='doi' href='https://doi.org/10.1017/S002555720000454X'>10.1017/S002555720000454X</ext-link>
[8] F. T. Tehrani, G. Leversha, “A simple approach to solving cubic equations”, The Mathematical Gazette, 100:548 (2016), 225–232 <ext-link ext-link-type='doi' href='https://doi.org/10.1017/mag.2016.58'>10.1017/mag.2016.58</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=3520815'>3520815</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1386.65136'>1386.65136</ext-link>
[9] M. Cháves-Pichardo, M. A. Martínez-Crus, A. Trejo-Martínez, A. B. Vega-Crus, T. Arenas-Resendis, “On the practicality of the analytical solutions for all third- and fourth-degree algebraic equations with real coefficients”, Mathematics, 11:6 (2023), 1447 <ext-link ext-link-type='doi' href='https://doi.org/10.3390/math11061447'>10.3390/math11061447</ext-link>
[10] A. Ya. Belov, “Ob odnom sposobe reshat uravneniya chetvertoi stepeni”, Matematicheskoe obrazovanie, 2023, no. 3 (107), 24–26
[11] B. Sobirov, “Sposob resheniya uravnenii 4-i stepeni s pomoschyu simmetrii”, Matematicheskoe obrazovanie, 2023, no. 3 (107), 35–37
[12] V. M. Siadat, A. Tholen, “Omar Khayyam: Geometric Algebra and Cubic Equations”, Math Horizons, 28:1 (2021), 12–15 <ext-link ext-link-type='doi' href='https://doi.org/10.1080/10724117.2020.1770495'>10.1080/10724117.2020.1770495</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4145462'>4145462</ext-link>
[13] D. J. Struik (ed.), A Source Book in Mathematics: 1200–1800, Princeton University Press, Princeton, 1986 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=858706'>858706</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0657.01001'>0657.01001</ext-link>
[14] R. B. King, Beyond the Quartic Equation, Birkhäuser, Boston, 1996 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1401346'>1401346</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0905.12002'>0905.12002</ext-link>
[15] A. D. Polyanin, Handbook of Exact Solutions to Mathematical Equations, CRC Press, Boca Raton, 2024, 376 pp.
[16] V. G. Boltyanskii, N. Ya. Vilenkin, Simmetriya v algebre, 2-e izd., Nauka, M., 2002