On the symbolic manipulation for the cardinality of certain degree polynomials

The research on cardinality of polynomials was started by Mohd Atan [1] when he considered a set, V(f-;p?)={umodp?:f-(u)?0modp?}, where ? > 0 and f-=(f1,f2,?fn). The term f-(u)?0-modp? means that we are considering all congruence equations of modulo p? and we are looking for u that makes the congruence equation equals zero. This is called the zeros of polynomials. The total numbers of such zeros is termed as N(f-;p?). The above p is a prime number and Zp is the ring of p-adic integers, and x-=(x1,x2, ?xn). He later let N(f-;p?)=card V(f-;p?). The notation N(f-;p?) means the number of zeros for that the polynomials f-. For a polynomial f (x) defined over the ring of integers Z, Sandor [2] showed that N(f;p?)? mp12ordpD, where D ? 0, ? > ordpD and D is the discriminant of f. In this paper we will try to introduce the concept of symbolic manipulation to ease the process of transformation from two-variables polynomials to one-variable polynomials. � 2016 Author(s).