Groebner Basis for Polynomials with Parametric Exponents

For some classes of singularities there exist defining equations with parametric coefficients and exponents. We can treat these defining equation with parametric exponents as sequences and calculate their Grobner bases. Grobner bases are useful for clarifying the structure of the parameters of the defining equation, which will enable us to discover some interesting properties about them. The purpose of this paper is to illustrate the power of this approach by using examples of its usefulness in analyzing some phenomena.