Regular systems of linear functional equations and applications

ABSTRACT

The algorithmic classification of singularities of linear differential systems via the computation of Moser- and super-irreducible forms as introduced in [21] and [16] respectively has been widely studied in Computer Algebra ([8, 12, 22, 6, 10]). Algorithms have subsequently been given for other forms of systems such as linear difference systems [4, 3] and the perturbed algebraic eigenvalue problem [18]. In this paper, we extend these concepts to the general class of systems of linear functional equations. We derive a definition of regularity for these type of equations, and an algorithm for recognizing regular systems. When specialised to q-difference systems, our results lead to new algorithms for computing polynomial solutions and regular formal solutions.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms

General Terms:
Algorithms

Keywords:
computer algebra, moser-reduction, singularities, super-reduction, systems of linear functional equations