# Algorithms of SageMath designed to construct optimal sets of subalgebras of Lie algebra of symmetries for 3D plasticity equations with Huber - von Mises criterion

## Description

For Lie algebra of point symmetries g, admitted by the system of differential equations for a quasi-static state of a perfectly rigid-plastic solid with Huber – von Mises yield criterion, we classify subalgebras up to dimension three. The group of inner automorphisms Int(g), generated by the adjoint algebra ad(g), is the principal tool to divide all subalgebras of g into classes of equivalence. Sometimes external discrete automorphisms of g are used to reduce the number of such classes and finally to form a set of representatives of each class. Such set is called the optimal system of subalgebras. To realize the classification, a set of algorithms was designed and implemented in CAS SageMath. Although the classification process was not completely automated, its semi-automatic application was what allowed the result to be obtained. The algorithms and the files that are the result of the classification can be viewed in corresponding folders: Algorithms and Results. Files: CompiladoAlgoritmos_2022, AnalisisSubalgebras, AutomorfismoRotacion, Automorfismos, AutomorfismosAE, CambioVariableNuevo, CondicionSubalgebra, ContenenciaSubalgebras, ImprimirTexto, ReduccionGaussiana, varios with extension .ipynb are the modules that store the algorithms, which are executed from the SageMath notebook CompiledAlgorithms_2022.ipynb. File tables_subalgebras_2D.pdf contains the classification results for two-dimensional subalgebras. File tables_subalgebras_3D.pdf includes all non-similar classes of three-dimensional subalgebras.