Satellite Unknowns in Irreducible Differential Systems
In this paper, the concept of satellite unknowns in differential systems with selected unknowns is considered in the context of irreducible systems. It is proved that any unselected unknown in an irreducible differential system is linearly satellite for any nonempty set of selected unknowns. An algo...
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| Vydané v: | Programming and computer software Ročník 44; číslo 2; s. 105 - 111 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Moscow
Pleiades Publishing
01.03.2018
Springer Nature B.V |
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| ISSN: | 0361-7688, 1608-3261 |
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| Abstract | In this paper, the concept of satellite unknowns in differential systems with selected unknowns is considered in the context of irreducible systems. It is proved that any unselected unknown in an irreducible differential system is linearly satellite for any nonempty set of selected unknowns. An algorithm for factorization of differential systems is proposed that is not always applicable but executable in polynomial time. Cases where the algorithm cannot be applied are also recognized in polynomial time. |
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| AbstractList | In this paper, the concept of satellite unknowns in differential systems with selected unknowns is considered in the context of irreducible systems. It is proved that any unselected unknown in an irreducible differential system is linearly satellite for any nonempty set of selected unknowns. An algorithm for factorization of differential systems is proposed that is not always applicable but executable in polynomial time. Cases where the algorithm cannot be applied are also recognized in polynomial time. |
| Author | Panferov, A. A. |
| Author_xml | – sequence: 1 givenname: A. A. surname: Panferov fullname: Panferov, A. A. email: ast.a_s@mail.ru organization: Faculty of Computational Mathematics and Cybernetics, Moscow State University, Dorodnicyn Computing Centre, Federal Research Center Computer Science and Control, Russian Academy of Sciences |
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| References | Panferov (CR2) 2017; 85 Minchenko, Ovchinnikov, Singer (CR5) 2015; 215 Beke (CR15) 1894; 45 Schwarz (CR16) 1989 Tsarev (CR20) 1996 Hrushovski (CR6) 2002; 58 Compoint, Singer (CR12) 1999; 28 van Hoeij (CR21) 1997; 24 Grigoriev (CR22) 1990 Abramov, Bronshtein (CR8) 2006; 46 Panferov (CR1) 2016 Panferov (CR10) 2015; 41 Singer (CR19) 1996; 7 Bolibrukh (CR14) 2009 Panferov (CR7) 2017 van der Put, Singer (CR4) 2003 Feng (CR9) 2015; 65 Grigoriev (CR18) 1990; 10 Bronstein (CR17) 1992; 13 Panferov (CR11) 2016; 42 Panferov (CR3) 2017; 43 Cluzeau (CR13) 2003 E. Compoint (6378_CR12) 1999; 28 M. Bronstein (6378_CR17) 1992; 13 A.A. Panferov (6378_CR10) 2015; 41 A.A. Panferov (6378_CR7) 2017 E. Beke (6378_CR15) 1894; 45 M. Hoeij van (6378_CR21) 1997; 24 A.A. Panferov (6378_CR11) 2016; 42 R. Feng (6378_CR9) 2015; 65 S.P. Tsarev (6378_CR20) 1996 E. Hrushovski (6378_CR6) 2002; 58 M.F. Singer (6378_CR19) 1996; 7 F. Schwarz (6378_CR16) 1989 A.A. Panferov (6378_CR3) 2017; 43 A.A. Bolibrukh (6378_CR14) 2009 S.A. Abramov (6378_CR8) 2006; 46 D.Yu. Grigoriev (6378_CR22) 1990 A.A. Panferov (6378_CR2) 2017; 85 D.Yu. Grigoriev (6378_CR18) 1990; 10 T. Cluzeau (6378_CR13) 2003 M. Put van der (6378_CR4) 2003 A. Minchenko (6378_CR5) 2015; 215 A.A. Panferov (6378_CR1) 2016 |
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| Title | Satellite Unknowns in Irreducible Differential Systems |
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