M = generalizedSplines(E,I)
This method returns the module of generalized splines on a graph with edgeset E on v vertices, whose edges are labelled by ideals of some ring R. By definition this is the submodule of $R^v$ consisting of tuples of polynomials such that the difference of polynomials corresponding to adjacent vertices are congruent module the ideal labelling the edge between them.




If edge labels are integers, generalizedSplines is computed as a ZZ module by default.



The above splines may also be computed over ZZ modulo some integer.



Arbitrary ideals may also be entered as edge labels.




This method can be used to compute splines over nonlinear partitions. The example below can be found in Exercise 13 of Section 8.3 in the book Using Algebraic Geometry by Cox,Little, and O'Shea.




The object generalizedSplines is a method function with options.