# 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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