Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p ,κ, on a given finite field F(p k ), and conversely. There exists an interpretation Ф₁ of the variety V(L p ,κ) generated by L p ,κ into the variety V(F(p k )) generated by F(p k ) and an interpretation Ф₂ of V(F(p k )) into V(L p ,κ) such that Ф₂Ф₁(B) = B for every B ϵ V(L p ,κ) and Ф₁₂ (R) = R for every R ϵ V(F(p k )). In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple.