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oai:docta.ucm.es:20.500.14352/570742025-09-01T13:42:58Zcom_20.500.14352_14col_20.500.14352_15

An algorithm to describe the solution set of any tropical linear system A x=B x Puente Muñoz, María Jesús De La Lorenzo, Elisa 512 Tropical linear system Algorithm Álgebra 1201 Álgebra An algorithm to give an explicit description of all the solutions to any tropical linear system A x=B x is presented. The given system is converted into a finite (rather small) number p of pairs (S,T) of classical linear systems: a system S of equations and a system T of inequalities. The notion, introduced here, that makes p small, is called compatibility. The particular feature of both S and T is that each item (equation or inequality) is bivariate, i.e., it involves exactly two variables; one variable with coefficient 1 and the other one with -1. S is solved by Gaussian elimination. We explain how to solve T by a method similar to Gaussian elimination. To achieve this, we introduce the notion of sub-special matrix. The procedure applied to T is, therefore, called sub-specialization. La Caixa Universidad Complutense de Madrid Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:48:19Z 2023-06-20T16:48:19Z 2001 journal article https://hdl.handle.net/20.500.14352/57074 0024-3795 10.1016/j.laa.2011.02.014 eng 910444 open access application/pdf Elsevier