Division Safe Calculation in Totalised Fields

A 0-totalised field is a field in which division is a total operation with 0(−1)=0. Equational reasoning in such fields is greatly simplified but in deriving a term one still wishes to know whether or not the calculation has invoked 0(−1). If it has not then we call the derivation division safe. We propose three methods of guaranteeing division safe calculations in 0-totalised fields.