Factorization of Differential Operators with Rational Functions Coefficients

This paper gives a new method to factor differential operators with rational functions coefficients. It is based on the following two ingredients:

*) For a "well-chosen" local factor it is possible (given certain bounds on degrees) to construct a corresponding global (i.e. with rational functions coefficients) factor of a differential operator.

*) To choose such "well-chosen" local factor we need to study local differential operators. This is done in jsc1997b .

To compute the bounds on the degrees the concept of "generalized exponents" is introduced, in a way similar to how "exponential parts" were defined in jsc1997b . These generalized exponents are also introduced at the same time in [mega1996].

Note that the method in this paper can also be applied for factorizing bivariate polynomials over an algebraically closed field.

For the implementation see the files DFactor and try_factorization in the diffop package.

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