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

would be spoken as

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

where f is [tex2html_wrap5790]

which can now be rendered as:

Enneth derivative with respect to x of w equalsIt 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

Summation over 0 less than or equal to j less than or equal to n

Summation overlower constraint 1of

jayth derivative of u with respect to x times the fraction

numerator 1overdenominator 1. wherelower constraint 1is [tex2html_wrap5792],

numerator 1is [tex2html_wrap5794],

denominator 1is [tex2html_wrap5796].

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