http:^^www.cs.cornell.edu^info^people^raman^aster^aster-toplevel.html

This data set contains WWW-pages collected from computer science departments of various universities

The first of these
<!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-10.html">
6 integrals</a>, probably the most innocuous, is also the most
difficult to recognize; it is impossible to determine the variable of
integration.


<h2>
<!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec11-title.au">
Section 11 </A> Summations.
</h2>
Here are
<!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-11.html">
3 summations.</a>
Notice that the same expression can be written in more than one way. 

<h2>
<!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec12-title.au">
Section 12 </A> Limits.
</h2>
Here are <!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-12.html">
2 limits</a>

<h2> <!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec13-title.au"> Section 13 </A> Cross
referenced equations.  </h2> The following <!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-13.html">
example</a> is meant to illustrate AsTeR's rendering of cross-references, and
is most effective when AsTeR is used interactively.  <p>

AsTeR enables the listener to give meaningful names to cross-referenceable
objects, and uses these names when referring to such objects in later
cross-references.



<h2>
<!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec14-title.au">
Section 14 </A> Distance formula.
</h2>

Notice that AsTeR produces good intonational structure when speaking text that
is intermixed with mathematics. 
<!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec14-ex1.au">
<!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx57.gif" alt="Math">
Audio </A>
<!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx57.tex"> LaTeX </A>
<!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx57.ps"> Postscript </A>

<h2>
<!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec15-title.au">
Section 15 </A> Quantified expression.
</h2>
The quantifiers present an interesting challenge to AsTeR's recognizer.

<!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec15-ex1.au">
<!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx58.gif" alt="Math">
Audio </A>
<!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx58.tex"> LaTeX </A>
<!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx58.ps"> Postscript </A>


<h2>
<!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><!WA48><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec16-title.au">
Section 16 </A> Exponentiation.
</h2>
Once again, perceptible monotonicity allows AsTeR to convey the following
<!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><!WA49><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-16.html">
3 examples</a>
deeply nested expressions succinctly.
<p>
These examples were produced with the Emacs Calculator, a full-fledged
symbolic algebra system.
AsTeR  interfaces directly with this calculator, and renders the output just
as well as  any document. 


<h2>
<!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><!WA50><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec17-title.au">
Section 17 </A> A generic matrix.
</h2>
AsTeR uses stereo effects to convey the two-dimensional structure of the
matrix.  Rendering commences on the left, and moves progressively right as
each element of any row is spoken.
<p>

<!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><!WA51><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec17-ex1.au">
<!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><!WA52><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx61.gif" alt="Math">
Audio </A>
<!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><!WA53><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx61.tex"> LaTeX </A>
<!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><!WA54><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx61.ps"> Postscript </A>

<h2>
<!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><!WA55><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-title.au">
Section 18 </A> Faa de Bruno's formula.
</h2>
This section presents Faa De Bruno's formula, taken from Knuth's Art Of
Computer Programming, Vol. 1.
I first heard it spoken by a RFB reader on a talking book; it took 120 seconds
to speak.
<p>

Since the renderings produced by AsTeR utilize features of the audio space not
available to a human reader (I still have not met a reader who can change the
size and shape of her head as she talks:-) the rendering takes under 80
seconds.

<p>
As you will hear soon, even this is too long; you forget the beginning by the
time you hear the end.
<p>

Later, we present rendering using variable substitution, a powerful technique
for conveying top-level structure of complex expressions.
<p>
<ul> 
<li> Notice the proper intonational structure produced for text intermixed
     with mathematics.  <br>
     <!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><!WA56><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex1.au">
     <!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><!WA57><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx62.gif" alt="Math">
     Audio </A>
     <!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><!WA58><a href="http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx62.tex"> LaTeX</a>
     <!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><!WA59><a href="http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx62.ps">Postscript</a>
<li> <!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><!WA60><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex2.au">
     <!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><!WA61><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx62a.gif" alt="Math">
     Audio </A>
<!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><!WA62><a href="http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx62a.tex"> LaTeX</a>
     <!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><!WA63><a href="http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx62a.ps"> Postscript</a>
<li> Here is Faa De Bruno's formula in all its glory:-<br> 
     <!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><!WA64><a href="http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex3.au">
     <!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><!WA65><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx63.gif" alt="Math">
     Audio (66 seconds)</a>
     <!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><!WA66><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx63.tex"> LaTeX </A>
<!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><!WA67><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx63.ps"> Postscript </A>
</ul> 
AsTeR can process complex expressions like the above, and upon request,
replace complex sub-expressions with meaningful identifiers. Such renderings
convey top-level structure; the listener can then listen to the
sub-expressions separately.  <p>

Since this substitution process is performed by AsTeR, there is no LaTeX or
Postscript equivalent for the audio output in this case.
<UL> 
<li> The top-level formula.
<!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><!WA68><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex4.au"> audio (20 seconds) </A>
<li> Lower constraint 1. 
     <!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><!WA69><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex5.au"> audio (20 seconds) </A>
<li> Numerator. <!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><!WA70><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex6.au"> audio (15 seconds) </A>
<li> Denominator. <!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><!WA71><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec18-ex7.au"> audio (14 seconds) </A>
</ul>


<hr>
<address>T.V. Raman [e-mail] </address>
<!-- hhmts start -->
Last modified: Wed Aug 10 19:56:56 1994
<!-- hhmts end -->
</body> </html>