This article is cited in 4 scientific papers (total in 4 papers)
On solvability of systems of symbolic polynomial equations
Oleg I. Egorushkin, Irina V. Kolbasina, Konstantin V. Safonov
Institute of Computer Science and Telecommunications, Reshetnev Siberian State Aerospace University, Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660014, Russia
Approaches to solving the systems of non-commutative polynomial equations in the form of formal power series (FPS) based on the relation with the corresponding commutative equations are developed. Every FPS is mapped to its commutative image — power series, which is obtained under the assumption that all symbols of the alphabet denote commutative variables assigned as values in the field of complex numbers. It is proved that if the initial non-commutative system of polynomial equations is consistent, then the system of equations being its commutative image is consistent. The converse is not true in general.
It is shown that in the case of a non-commutative ring the system of equations can have no solution, have a finite number of solutions, as well as having an infinite number of solutions, which is fundamentally different from the case of complex variables.
non-commutative ring, polynomial equations, formal power series, commutative image.
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Received in revised form: 24.01.2016
Oleg I. Egorushkin, Irina V. Kolbasina, Konstantin V. Safonov, “On solvability of systems of symbolic polynomial equations”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 166–172
Citation in format AMSBIB
\by Oleg~I.~Egorushkin, Irina~V.~Kolbasina, Konstantin~V.~Safonov
\paper On solvability of systems of symbolic polynomial equations
\jour J. Sib. Fed. Univ. Math. Phys.
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O. I. Egorushkin, I. V. Kolbasina, K. V. Safonov, “O sovmestnosti sistem simvolnykh polinomialnykh uravnenii i ikh prilozhenii”, PDM. Prilozhenie, 2016, no. 9, 119–121
O. I. Egorushkin, I. V. Kolbasina, K. V. Safonov, “Analog teoremy o neyavnom otobrazhenii dlya formalnykh grammatik”, PDM. Prilozhenie, 2017, no. 10, 149–151
O. I. Egorushkin, I. V. Kolbasina, K. V. Safonov, “O primenenii mnogomernogo kompleksnogo analiza v teorii formalnykh yazykov i grammatik”, PDM, 2017, no. 37, 76–89
K. V. Safonov, O. I. Egorushkin, I. V. Kolbasina, “Sintaksicheskii analiz programm metodom integralnykh predstavlenii”, PDM. Prilozhenie, 2018, no. 11, 128–130
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