Building the Initial Graph

The tuples are used to build a graph encoding their information. A node is created for each symbol in the formula, and the data and type attributes for each node are both initially set to the symbol's identity. These may be changed in the later preprocessing step which will perform an initial categorisation of the symbols and will group basic collections of symbols such as multi-digit numbers, into a single node.

  

Figure 3.6: Preprocessing and parsing of a simple formula.

(a) Initial graph.

(b) Initial graph with arcs built.

(c) After the preprocessing step.

(d) After applying the ``superscript'' rule.

(e) After applying the ``fraction'' rule.

(f) The final graph, after applying the ``integral'' rule.

Figure 3.6(a) shows the initial graph built, prior to the preprocessing and initial building of arcs. The nodes are represented by rectangles. The position and size of each rectangle conveys the position and size information encoded within the node. The top label in each node shows the ``data'' value for the node, what the node actually is, and the lower label is the ``type'' value, which holds the node's lexical class.