In polynomial algebra there is a powerful tool for treating system of polynomial equations. It is standard or Groebner Bases. It allows to verify if system is consistent, eliminate variables, reduce overdetermined systems. Algebraically it is a canonical basis for ideal, generated by finite system of polynomials. For differential system Groebner Bases of ideal (generated by finite system) is not always finite, but it is possible to characterize radical by Ritt-Wu method and consequently to have similar tool for differential case. From the point of view of algebra it could be also generalized to system of difference equations (because of similar properties, as it was shown by Cohn). But according to literature this work is still not finished. And I wonder why.

From the point of view of application is this topic interesting or not?


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