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An introduction to pseudo-linear algebra. (English) Zbl 0868.34004
Summary: Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differential and difference equations in closed form.

MSC:
34A30 Linear ordinary differential equations and systems
39-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations
34A05 Explicit solutions, first integrals of ordinary differential equations
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