A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the independence of equations in three variables
Tekijät: Harju T, Nowotka D
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2003
Lehti:: Theoretical Computer Science
Tietokannassa oleva lehden nimi: THEORETICAL COMPUTER SCIENCE
Lehden akronyymi: THEOR COMPUT SCI
Vuosikerta: 307
Numero: 1
Aloitussivu: 139
Lopetussivu: 172
Sivujen määrä: 34
ISSN: 0304-3975
DOI: https://doi.org/10.1016/S0304-3975(03)00098-7
Tiivistelmä
We prove that an independent system of equations in three variables with a nonperiodic solution and at least two equations consists of balanced equations only. For that, we show that the intersection of two different entire systems contains only balanced equations, where an entire system is the set of all equations solved by a given morphism. Furthermore, we establish that two equations which have a common nonperiodic solution have the same set of periodic solutions or are not independent. (C) 2003 Elsevier B.V. All rights reserved.
We prove that an independent system of equations in three variables with a nonperiodic solution and at least two equations consists of balanced equations only. For that, we show that the intersection of two different entire systems contains only balanced equations, where an entire system is the set of all equations solved by a given morphism. Furthermore, we establish that two equations which have a common nonperiodic solution have the same set of periodic solutions or are not independent. (C) 2003 Elsevier B.V. All rights reserved.
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