Examples

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## Examples

To motivate the discussion, here are some examples of how variable substitution can produce renderings that are easier to understand.

[equation1615]

would be spoken as

i = integral with respect to x from 0 to infinity of f dx,
where f is [tex2html_wrap5790]
This technique is particularly useful when presenting very complex equations. Variable substitution transforms eq:faa-de-bruno to:

[equation1622]

which can now be rendered as:

Enneth derivative with respect to x of w equals
Summation over 0 less than or equal to j less than or equal to n
Summation over lower constraint 1 of
jayth derivative of u with respect to x times the fraction
numerator 1 over denominator 1. where lower constraint 1 is [tex2html_wrap5792],
numerator 1 is [tex2html_wrap5794],
denominator 1 is [tex2html_wrap5796].
It takes [tex2html_wrap5798] seconds to speak eq:faa-de-bruno, making it difficult to perceive the top-level structure from listening to a straight rendering of the expression. Using style variable substitution, the top-level expression is rendered in [tex2html_wrap5800] seconds, and it takes a further [tex2html_wrap5802] seconds to render the substitutions. Thus, though the total time taken to speak the entire expression is more, the listener can understand the top-level structure in about a third of the time it would take to listen to the entire expression.

Variable substitution should be used sparingly, since renderings using this style take a longer time to convey entire expressions, in this example, [tex2html_wrap5804] seconds against [tex2html_wrap5806] seconds-AsTeR uses variable substitution only if an expression is sufficiently complex.

TV Raman
Thu Mar 9 20:10:41 EST 1995