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\centerline{\bf Factorization of Linear Differential Operators}

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\centerline{Mark van Hoeij}
\centerline{Catholic University}
\centerline{Department of Mathematics}
\centerline{NL - 6525 Nijmegen, The Netherlands}
\centerline{Email: hoeij@sci.kun.nl}

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Summary: Factoring differential operators is reducing differential
equations to other differential equations of lower order. There exists
a method for computing such factorizations that is more than 100 years
old. However, there are a number of disadvantages to this method that
make it unsuitable for ``complicated'' differential operators.

In the talk I will describe a new method. First I will introduce
a number of properties of local (i.e., over the power series)
differential operators, such as the generalized exponents. These
properties will be used to show how local factorizations can be
used to compute global (i.e., over the rational functions) factorizations.

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