2019/04/30 by Jamshidvand, Sedighe, Ghalandarzadeh, Shaban, Amiraslani, Amirhossein +1
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1904.13169
In this paper, we present methods for solving a system of linear equations, AX=b , over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with fewer equations and variables. We then use the pseudo-inverse of the system matrix to solve the system if solutions exist. Moreover, we propose a new version of Cramer's rule to determine the maximal solution of the system. Maple procedures for computing the pseudo-inverse are included as well.