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<html> <head><title>Mathematics For Computer Generated Spoken Documents</title><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><!WA0><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/title.au"> Title in audio </A></head><body><h1>ASTER Demonstration</h1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><!WA1><a href="http://www.cs.cornell.edu/Info/People/raman/aster/dedication.au"> <!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><!WA2><img alt="AsTeR" src="http://www.cs.cornell.edu/Info/People/raman/aster/aster.gif"> </a> isdedicated to my Guide-Dog.AsTeR --Audio System For Technical Readings-- is a computing system forrendering technical documents in audio. AsTeR was developed by <!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><!WA3><ahref="http://www.cs.cornell.edu/Info/People/raman/aster/raman.html"><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><!WA4><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/raman.gif" alt="T. V. Raman"></a> for his <!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><!WA5><a href="http://www.cs.cornell.edu/Info/People/raman/aster/aster-thesis.ps"> PhD. (141 pages)</a> <footnote> An audio formatted version of the thesis, (approximately 6 hours) produced by AsTeR, is being made available by <!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><!WA6><a href="http://www.cs.cornell.edu/Info/People/raman/rfb-math-workshop/summary.html">RFB (Recordings For the Blind</a> as the first computer generated talking book. </footnote> Here is the <!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><!WA7><ahref="http://www.cs.cornell.edu/Info/People/raman/aster/abstract.html"> abstract </a> in print, and <!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><a href="http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/abstract.au">here</a> is an audio formatted version. <p>This hypertext document demonstrates the audio renderings generated by AsTeR.Each example is made up of three components:<ol> <li> The original LaTeX input. <li> The audio formatted output produced by AsTeR. The speech is produced by a Dectalk, and has been digitized at 8-bit mulaw<footnote> AsTeR uses stereo to render tables, an effect that is not conveyed by the8-bit mono encoding. </footnote> <li> The visually formatted version produced by LaTeX and DVIPS. </ol><h2><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec1-title.au">Section 1 </A> simple fractions and expressions.</h2>This set of <!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-01.html"> 8 examples </a> demonstrates the use ofvoice inflection and pauses to convey grouping of sub-expressions succinctly.<p>The state of the <em>audio formatter</em>is a point in audio space. Here, audio state was varied along a dimension in audio space before renderingsub-expressions.This is equivalent to parenthesizing in the visual context. <h2><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec2-title.au">Section 2 </A> superscripts and subscripts.</h2>To convey subscripts, superscripts, and other visual attributes, AsTeR variesaudio state along a dimension that is<em> orthogonal to </em> (independent of ) thedimension used to convey sub-expressions. This allows the nesting ofthese mutually independent concepts.The following<!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-02.html">6 examples</a>demonstrate how superscripts and subscripts are rendered unambiguously. <p><h2><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec3-title.au">Section 3 </A> Knuth's examples of fractions and exponents.</h2>These examples are taken verbatim from the TeX Book, by Donald Knuth.They are used in the TeX Book to demonstrate the power of the TeX layoutoperators.Notice that all of these examples comprise of the same 6 symbols, but are verydifferent!AsTeR renders these <!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-03.html"> 7examples </a>as unambiguously as TeX. <h2><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec4-title.au">Section 4 </A> A continued fraction.</h2>Moving along a dimension in audio space defines a perceptibly monotonicchange. This notion of perceptible monotonicity is vital in conveying nesting.<p><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec4-ex1.au"><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><img align="middle" src="http://www.cs.cornell.edu/Info/People/raman/aster/gifs/xx20.gif" alt="Math">Audio </A><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx20.tex"> LaTeX </A><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx20.ps"> Postscript </A><h2><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec5-title.au">Section 5 </A> Simple School algebra.</h2>Here are <!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-05.html">3 examples</a> from school algebra. <h2><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec6-title.au">Section 6 </A> square roots.</h2>Notice the choice of unambiguous renderings for the following<!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-06.html">3 expressions:</a><h2><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec7-title.au">Section 7 </A> Trigonometric identities.</h2>Written mathematical notation can be ambiguous and hard to recognize.Notice the complete absence of parenthesis in some of the examples below.AsTeR uses several heuristics to construct the correct tree structure forthese<!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-07.html">7 expressions. </a><h2><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec8-title.au">Section 8 </A> Logarithms.</h2>Notice the context-specific rendering of these <!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-08.html"> 4expressions</a> when speaking the base of the logarithm. The renderings arechosen to reduce cognitive load; <blockquote>log base a of x </blockquote> asopposed to <blockquote> log of x to the base a </blockquote><h2> <!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-title.au"> Section 9 </A> Series. </h2>Context-specific rendering rules allow AsTeR to interpret the superscripts inthese <!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><a href="http://www.cs.cornell.edu/Info/People/raman/aster/sec-09.html"> 5 examples </a> as exponents. Suchinterpretation is not hard-wired into the renderings; it is fully customizableby the user.<h2><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-title.au">Section 10 </A> Integrals.</h2>⌨️ 快捷键说明
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