The function tpsform(p, var, order) creates a truncated power series (a series data structure) in var.  This truncated series is equal to p up to, but not including, the term containing x^order.

In some cases tpsform can determine when the series is exact and so it drops the  term. Formal power series created using powpoly fall into this category.

The command with(powseries,tpsform) allows the use of the abbreviated form of this command.