We define standardized constructions of finite fields, and generators (multiplicative) cyclic subgroups in these fields. The motivation is to provide a substitute for Conway polynomials which can be used by various software packages collections mathematical data involve

We develop the notational system developed by Conway and Sloane for working with quadratic forms over the 2-adic integers, and prove its validity. Their system is far better for actual calculations than earlier methods, and has been used for many years, but it seems that no proof has been published before now. Throughout, an integer means an element of the ring Z2 of 2-adic integers, and we wri...

After defining reduced minimum braid word and criteria for a braid family representative , different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established .