| Abstrakt: |
The research on cardinality of polynomials was started by Mohd Atan [1] when he considered a set, V (f;pα) = {umod pα : f(u) ≅ 0mod pα}, where α > 0 and f = (f1,f2,...,fn). The term f(u) ≅ 0mod pα means that we are considering all congruence equations of modulo pα 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;pα). 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;pα) = card V(f;pα). The notation N(f;pα) 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;pα) ≤mp½ordpD, where D ≠ 0, α > ord pD 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. [ABSTRACT FROM AUTHOR] |
