The order

Basically the algorithm just bisect the box TestDomain until one of the criteria described in 2.3.4.6 is satisfied. The boxes resulting from the bisection process are stored in a list and the boxes in the list are treated sequentially. If we are looking only for one solution of the equation or for the first Nb solutions of a system (see the Stop variable) it is important to store the new boxes in the list in an order which ensure that we will treat first the boxes having the highest probability of containing a solution. Two types of ordering may be used, see section 2.3.1.2, indicated by the flag MAX_FUNCTION_ORDER or MAX_MIDDLE_FUNCTION_ORDER.

Note that if we are looking for all the solutions of the system the order has still an importance: although all the boxes of the list will be treated the order define how close solution intervals will be distinguished (see for example section 2.3.5.2).