I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 1, PAGES 3-21
On singular points of solutions of linear differential systems with
S. A. Abramov
D. E. Khmelnov
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We consider systems of linear ordinary differential equations
containing unknown functions of
a single variable .
The coefficients of the systems are polynomials over
a field of
Each of the systems consists of equations
independent over .
The equations are of arbitrary orders.
We propose a computer algebra algorithm that, given
a system of this form, constructs
a polynomial such that if
a solution in for some and
a component of this solution has a nonzero polar part, then
In the case where and
analytic solution having a singularity of an arbitrary type (not
necessarily a pole) at , the equality
is also satisfied.
Last modified: January 31, 2012