The main routine computes .  There is a subroutine Lookup which computes a suitable origin for .  There is a subroutine Plan which determines the proper sequence of shift operators and inverse shift operators , , , and which should be applied to to produce .  After the plan is computed, a loop executes the plan by calling subroutines Shift and Unshift.  The Unshift routine calls a routine Contig which computes contiguity relations and also calls Shift. 

For aesthetic reasons (i.e. pretty answers) all the routines work, until the very last moment, in terms of a -module basis .  In fact, in the current implementation, is always (z), is a positive integer, and the answer will be after each step of the main loop where is a coefficient vector.  The basis is generally some vector of expressions involving special functions.  The derivative matrix which has elements in satisfies the equation where .  At the last moment, is replaced by since we are interested in computing instead of .  Often, , but not always.