(Bath)

"Functions" such as square root and logarithm are not actually well-defined on the complex plane, being capable of taking on multiple values. The table-maker, or the software library writer, is forced to introduce branch cuts, and sacrifice continuity for uniqueness. Unfortunately, we also sacrifice many identities on the road to uniqueness. Which, where and how do we find out (algorithmically) will be treated in this talk. In particular, why do some remain valid (such as √ 1-x² =√ 1-x √ 1+x ), but others do not (such as √ x²-1 =√ x-1 √ x+1 )?Far-134

Department of Computer Science