Application of the Homomorphism Theorem for Rings to Linearization of Systems of Partial Differential Equations

We propose an algorithm for linearizing systems of partial differential equations at constant solutions. The algorithm is based on an isomorphism constructed between the ring of linearized functions and the ring of special matrices, which makes it possible to simplify calculations in the process of linearization. The algorithm is illustrated by applying it to the quasigasdynamic system.