On the independence of equations in three variables



: Harju T, Nowotka D

Publisher: ELSEVIER SCIENCE BV

: 2003

Theoretical Computer Science

THEORETICAL COMPUTER SCIENCE

: THEOR COMPUT SCI

: 307

: 1

: 139

: 172

: 34

: 0304-3975

DOI: https://doi.org/10.1016/S0304-3975(03)00098-7


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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