A lot of information is conveyed by the relative location of symbols in a formula. Operations such as exponentiation and implicit multiplication use the relative positions of symbols to indicate the operation intended. This is in contrast to operations that use an explicit symbol to indicate the operation, such as addition where a ``+'' will always appear between its operands.
Integration uses a symbol to indicate the operation, but uses the relative positioning of symbols to indicate the parameters for the integration. The limits appear near the top and bottom of the integral symbol, and the integrand between the symbol and the differential.
(a) 
(b) 
(c) |
Because so much information is conveyed by the relative positions of symbols it is important, when interpreting a formula, to correctly identify the intended relative positioning between symbols. In many cases there is a grey area between alternatives. Figure 2.3 illustrates this. In the context of a mathematical formula, it is reasonably ``obvious'' that Figure 2.3(a) is ``a times x'' and that Figure 2.3(c) is ``a to the power of x'', but what about Figure 2.3(b)?
This is primarily a problem for the processing of handwritten formulae, as there must be a degree of leniency in the allowable positions that a user can write symbols, but it does also apply to the processing of typeset formulae.
Geometric relationships between symbols, or groups of symbols, can be determined by using:
Template based equation editors, where the user selects a template for the operator they want and then fills in the boxes in the template, avoid this problem of having to determine the correct geometric relationship between symbols. By having the user select operators from menus and then fill in the appropriately positioned boxes for the operator's arguments, the user is explicitly specifying the structure of the formula, even to the extent of what the arguments for each operator are.