A1 Refereed original research article in a scientific journal
On the independence of equations in three variables
Authors: Harju T, Nowotka D
Publisher: ELSEVIER SCIENCE BV
Publication year: 2003
Journal:: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Volume: 307
Issue: 1
First page : 139
Last page: 172
Number of pages: 34
ISSN: 0304-3975
DOI: https://doi.org/10.1016/S0304-3975(03)00098-7
Abstract
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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