Procedures to search for Laurent and regular solutions of linear ordinary differential equations with truncated power series coefficients
We previously published algorithms for searching the so-called Laurent and regular solutions of linear ordinary differential equations with infinite formal power series in the role of coefficients. The question of infinite series representation is very important for computer algebra. In those algorithms the series are given in truncated form, which means that we do not have complete information about the equation under consideration. Based on this incomplete information, algorithms give the maximum possible number of terms of the series included in the solutions. We are interested in the information about these solutions that is invariant to possible prolongations of those truncated series that represent the coefficients of the equation. The mentioned publications reported preliminary (trial) versions for procedures, which implement these algorithms, as well as experiments with them. To date, the procedures have been improved, the interface and data presentation are designed for them in a uniform manner. The advanced procedures are discussed in the current paper. The various examples are presented which illustrates the use of the procedures, including their optional parameters. These procedures are available from the web page http://www.ccas.ru/ca/TruncatedSeries.