In algebraic geometry, a regular function on an open subset 
of an algebraic variety is a function that can
be expressed locally as a quotient 
of polynomials, with 
nonzero on the neighborhood in question.
More generally, regular functions on a scheme are the
sections of its structure sheaf.
In older complex-analysis terminology, a function is termed regular iff it is analytic and single-valued
throughout a region 
.
