ИСТИНА

We consider linear differential-algebraic systems for which some components of vector of unknowns are selected. We present the algorithm ExtrAB which for a full rank linear differential system S of the form A1y'+A_0y=0 (where A1, A0 are matrices above a differential field K of characteristic 0) produces, first, a normal differential system Sd (i.e. a system of the form ỹ′=Aỹ), whose unknowns are a part of the selected unknowns of the original system and some of their derivatives, and, second, an algebraic system Sa, by means of witch other selected unknowns can be linearly expressed only via the selected unknowns from Sd. Suppose that we are interested in solutions whose selected components belong to some differential extension of K. Then the projection of the space of such solutions of the original system onto the selected unknowns coincides with the similar projection of the space of such solutions of Sd and Sa. Furthermore if the system Sd has a solution, whose selected components belong to some differential extension of K then all other components of this solution also belong to the same extension. The sizes of the systems Sd and Sa obtained by ExtrAB are as minimal as possible. The algorithm is implemented in Maple.