The uniform representation of mathematical objects by truncated power series . ∗

structure). Now it will be shown how the enrichment of the definition of algebraic structures is possible, thus giving rise to abstract structures in which computing methods become available components. In fact as far as method abstraction is concerned, the inheritance allows us to use the code provided for a higher structure in all its subdomains, without any redefinition, as (Limongelli et al., 1990) and (Limongelli & Temperini, 1992) show. The approach to numeric computation through truncated p-adic arithmetic (Hensel, 1908) has been widely analyzed (Gregory & Krishnamurthy, 1984; Colagrossi et al., 1994). As a matter of fact, the truncated p-adic representation can be viewed as the truncation of the p-adic series representing the rational number. The degree r, chosen for the approximation, depends on the characteristics of the problem. The same approach can be used to treat problems in abstract structures. In particular it is possible to exploit the uniformity between the truncated p-adic expansion of a rational number (Hensel code) and the p-adic polynomial expansion by power series. The theory and construction of Hensel Code for arithmetic of a rational function over a finite field is analogous to the truncated p-adic arithmetic. So a rational polynomial function can be represented in the form of Hensel code like the Example 3.1 shows. Example 3.1 Given the univariate polynomial P (x) = x + 3x − 2x + 1