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- Sergei A. Abramov, Denis E. Khmelnov
- Programming and Computer Software
- 2012

An algorithm for finding a universal denominator of rational solutions of a system of linear difference equations with polynomial coefficients is proposed. The equations may have arbitrary orders.

- Sergei A. Abramov, A. Gheffar, Denis E. Khmelnov
- Programming and Computer Software
- 2011

Complexities of some well-known algorithms for finding rational solutions of linear difference equations with polynomial coefficients are studied.

Search for Liouvillian solutions of linear recurrence equations in the MAPLE computer algebra system

- Denis E. Khmelnov
- Programming and Computer Software
- 2008

The paper considers implementation of the Singer-Hendriks algorithm in the MAPLE computer algebra system. The algorithm finds Liouvillian solutions of linear recurrence equations with coefficients inâ€¦ (More)

We consider linear homogeneous difference equations with rational-function coefficients. The search for solutions in the form of the minterlacing (1 â‰¤ m â‰¤ ord L, where L is a given operator) ofâ€¦ (More)

- Sergei A. Abramov, Anna A. Ryabenko, Denis E. Khmelnov
- Programming and Computer Software
- 2016

Construction of Laurent, regular, and formal (exponentialâ€“logarithmic) solutions of full-rank linear ordinary differential systems is discussed. The systems may have an arbitrary order, and theirâ€¦ (More)

- Sergei A. Abramov, Anna A. Ryabenko, Denis E. Khmelnov
- Programming and Computer Software
- 2018

Systems of linear q-difference equations with polynomial coefficients are considered. Equations in the system may have arbitrary orders. For such systems, algorithms for searching polynomial,â€¦ (More)

- Sergei A. Abramov, Moulay A. Barkatou, Denis E. Khmelnov
- J. Symb. Comput.
- 2015

- Anna A. Ryabenko, Denis E. Khmelnov
- Programming and Computer Software
- 2010

In the paper, an implementation in the computer algebra system Maple of an approach to summation based on hypergeometric pattern matching is considered. In spite of a number of existing modernâ€¦ (More)

- Sergei A. Abramov, Denis E. Khmelnov
- Programming and Computer Software
- 2014

The following problem is considered: given a system of linear ordinary differential equations of arbitrary order with power series coefficients, to recognize whether it has regular solutions at pointâ€¦ (More)