A package to work with linear partial differential operators

The paper describes package LPDO, which is designed for work with linear partial differential operators with symbolic coefficients in the computer algebra system MAPLE. In addition to basic procedures (operator creation, determination, modification, and various simplifications of their coefficients, as well as algebraic operations on them), it implements generating systems of gauge invariants for separate operators and operator pairs, the Laplace transformation method (not related to the integral Laplace method), procedures returning necessary and sufficient conditions for factoring third-order operators in the plane into compositions of operators of one or another form in terms of invariants, and several procedures related to the Darboux transformations.