Summary: ISSN 0361-7688, Programming and Computer Software, 2007, Vol. 33, No. 3, pp. 132138. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © S.A. Abramov, S.P. Polyakov, 2007, published in Programmirovanie, 2007, Vol. 33, No. 3.
For a system of first-order linear differential equa-
where aij, bi, and ci are polynomials over some field K
of zero characteristic, = , i = 1, ..., n, we will
extend the notion of universal denominator [1--3] in
the following way: vector (u1, ..., un) (K[x])n will be
referred to as universal denominator for the left-hand
side of system (1) if any component yi in an arbitrary
vector (y1, ..., yn) (K(x))n that turns the left-hand
sides of the system into polynomials can be represented
in the form , zi K[x].
Similarly, we can define universal denominator for
the left-hand side of a system of first-order difference