This is a preview. Log in through your library . Abstract Suppose F is a polynomial and $\sum\nolimits_{h \geqslant 0} {F\left( {{b_h}} \right)} {X^h}$ represents a rational function. If the bh all ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

We construct a family of high order iteration functions for finding polynomial roots of a known multiplicity s. This family is a generalization of a fundamental family of high order algorithms for ...