An extension allows part of an algebraic expression to be defined only in a subdomain of the left hand side's domain of definition. To be meaningful, there should be a mathematical way of extending functions from the smaller domain to the larger domain. These extensions operators are usually not unique: one could imagine for example to extend by continuity, or to extend by zero, etc.

An extension is requested by passing part of the right hand side in an algebraic expression as first argument function extend, and by passing the left hand side as a second argument. The second argument is necessary for technical reasons, even though it looks redundant.