in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

A polynomial invariant under the action of a finite group can be rewritten using generators of the invariant ring. We investigate the complexity aspects of this rewriting process; we show that evaluation techniques enable one to reach a polynomial cost.