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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.
 

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.
132
1. INTRODUCTION
For a system of first-order linear differential equa-
tions
(1)
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
equations
(2)

  

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Mathematics; Computer Technologies and Information Sciences