APPLICATIONS OF ALGORITHMS IN PURE MATHEMATICS
Keywords:
MATHEMATICSAbstract
The main interest of algorithms in algebraic number theory is that they provide number theorists with a means of satisfying their professional curiosity. The praise of numerical experimentation in number theoretic research is as widely sung as purely numerological investigations are indulged in, and for both activities good algorithms are indispensable. Algebraic number theory has in recent times been applied to the solution of algorithmic problems that, in their formulations, do not refer to algebraic number theory at all. so a description of algorithm along with its applications is necessary.
References
G. Greaves, Sieves in Number Theory. Results in Mathematics and Related Areas (3), 43. SAvigad, Jeremy (2006). Methodology and metaphysics in the development of Dedekind's theory of ideals". In: The Architecture of Modern Mathematics. Ed. by Jose Ferreiros and Jeremy Gray. Oxford University Press, pp. 159{186 (cit. on pp. 8, 30).
pringer-Verlag, Berlin, 2001.
Gabor Ivanyos, Marek Karpinski, Lajos Ronyai, and Nitin Saxena. Trading GRH for algebra: algorithms for factoring polynomials and related structures. CoRR, abs/0811.3165, 2008. 30
H.Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin, 1993. MR 94i:11105
