Multivariate Difference–Differential Dimension Polynomials

  • Alexander LevinEmail author


We present a method of characteristic sets with respect to several term orderings that allows one to prove the existence and determine invariants of multivariate difference–differential dimension polynomials associated with arbitrary partitions of the sets of basic derivations and translations. Our results essentially extend existing results on difference–differential dimension polynomials; we also determine invariants of such polynomials and show how these invariants can be applied to the equivalence problem for systems of algebraic partial difference–differential equations.


Difference–differential polynomial Autoreduced set Characteristic set Dimension polynomial 

Mathematics Subject Classification

Primary 12H05 Secondary 12H10 



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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsThe Catholic University of AmericaWashingtonUSA

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