ABSTRACT
In this chapter we introduce integral recurrence equations and their system atic régularisation. We will base the definition of integral recurrence on the notion of integral index mapping, as an index mapping in Zn which is not required to define an affine transformation. The syntactic form of an integral index mapping is an integer combination of a finite set of directions of the lattice space, in which the coefficients are functions from Zn to Z. With this form we will be able to establish an explicit relation between the index mapping and a finite set of vectors of the space, which can be exploited for régularisation purposes. Based on this syntactic form we will show that affine data dependencies are particular types of integral data dependencies.
