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Ta b l e 7 . 1 2 The pointer structure of Fig. 7.21 in XML format
< list >
< element # p 1 >
< content > a </ content >
< pointer 1 > p2 </ pointer >
< pointer 2 > p3 </ pointer >
</ element >
< element # p 2 >
< content > b </ content >
</ element >
<
element # p 3
>
<
content
>
d
</
content
>
>
< pointer 2 > p2 </ pointer >
< pointer 3 > p4 </ pointer >
</ element >
<
pointer
1
>
p5
</
pointer
< element # p 4 >
< content > c </ content >
< pointer 1 > p2 </ pointer >
< pointer 2 > p5 </ pointer >
</ element >
< element # p 5 >
< content > e </ content >
</ element >
< /list >
represented by expressions of parentheses. But if we extend parentheses with tags
possibly including links (or keys), then we can easily represent graphs.
Parentheses were introduced in mathematical notation relatively late (Girard,
17th century). Before them, other methods for aggregating symbols were based on
vincula and dots. Vinculum (used by Viete, the same mathematician who introduced
letters in algebraic manipulations, in 15th century) is a line over/below the symbols
it connects. Table 7.10 expresses the resolution formula of second degree equations
in terms of vincula notations (for root square and fraction).
A dotted notation was systematically used by the Italian mathematician Giuseppe
Peanoinhis Formulario Mathematico (1908), and this notation was also inherited
by Bertrand Russell and Alfred Whitehead in their Principia Mathematica .When
dots are put next to operation symbols, they can denote a priority of their application
(a smaller number of dots means a greater priority). In specific contexts, operation
 
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