CISE-CCF-AF-Algebra: SGER: Computational Methods for Systems of Difference Equations

Alexey I.Ovchinnikov建议开发有效的算法，使用微分、差分和计算机代数的方法来确定差分方程解的微分、差分和代数结构。这位研究人员对计算微分理想理论和线性微分方程组的伽罗瓦理论的发展做出了成功的贡献。他将应用这些结果和方法来给出有效的算法来计算差分方程组的性质。这些性质反映在方程的特征集和伽罗瓦群中。特别是，研究人员将开发算法，将非线性差分方程组简化为更简单的系统。这些算法测试输入系统的一致性，并从系统方程中消除变量。他还将给出一个带差分参数的线性差分方程组的伽罗瓦理论，以研究差分方程解之间的差分几何依赖性。

Alexey I. Ovchinnikov proposes to develop efficient algorithms thatdetermine the differential, difference, and algebraic structure ofsolutions of difference equations using methods of differential,difference, and computer algebra. The investigator has successfullycontributed to the development of computational differential ideal theory and the Galois theory of linear differential equations. He willapply these results and methods to give efficient algorithms that computeproperties of systems of difference equations. These properties arereflected in characteristic sets and Galois groups of the equations. In particular, the investigator will develop algorithms to reduce systemsof non-linear difference equations to simpler systems. These algorithmstest consistency of the input system and eliminate variables from theequations of the system. He will also give a Galois theory of lineardifference equations with difference parameters to study differencealgebraic dependences among solutions of difference equations.