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x </blockquote>as opposed to <blockquote> log of x to the base a </blockquote><OL><LI><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><!WA123><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec8-ex1.au"> audio </A><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><!WA124><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx34.tex"> LaTeX </A><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><!WA125><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx34.ps"> Postscript </A><LI><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><!WA126><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec8-ex2.au"> audio </A><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><!WA127><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx35.tex"> LaTeX </A><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><!WA128><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx35.ps"> Postscript </A><LI><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><!WA129><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec8-ex3.au"> audio </A><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><!WA130><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx36.tex"> LaTeX </A><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><!WA131><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx36.ps"> Postscript </A><LI><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><!WA132><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec8-ex4.au"> audio </A><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><!WA133><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx37.tex"> LaTeX </A><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><!WA134><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx37.ps"> Postscript </A></OL><h2><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><!WA135><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 asexponents.  Such interpretation is not hard-wired into the renderings; it isfully customizable by the user.<OL><LI><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><!WA136><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-ex1.au"> audio </A><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><!WA137><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx38.tex"> LaTeX </A><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><!WA138><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx38.ps"> Postscript </A><LI><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><!WA139><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-ex2.au"> audio </A><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><!WA140><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx39.tex"> LaTeX </A><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><!WA141><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx39.ps"> Postscript </A><LI><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><!WA142><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-ex3.au"> audio </A><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><!WA143><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx40.tex"> LaTeX </A><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><!WA144><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx40.ps"> Postscript </A><LI><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><!WA145><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-ex4.au"> audio </A><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><!WA146><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx41.tex"> LaTeX </A><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><!WA147><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx41.ps"> Postscript </A><LI><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><!WA148><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec9-ex5.au"> audio </A><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><!WA149><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx42.tex"> LaTeX </A><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><!WA150><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx42.ps"> Postscript </A></OL><h2><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><!WA151><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-title.au">Section 10 </A> Integrals.</h2>The first of these examples, probably the most innocuous, is also the mostdifficult to recognize; it is impossible to determine the variable ofintegration.<p>Notice that AsTeR interprets triple integrals as the nested application of theintegral operator.A user can browse the triple integral and listen to its sub-pieces.<p>The integrals  shown in examples 3 and 4 can trick the most experienced ofhuman readers into an error. <OL><LI><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><!WA152><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex1.au"> audio </A><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><!WA153><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx43.tex"> LaTeX </A><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><!WA154><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx43.ps"> Postscript </A><LI><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><!WA155><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex2.au"> audio </A><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><!WA156><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx44.tex"> LaTeX </A><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><!WA157><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx44.ps"> Postscript </A><LI><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><!WA158><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex3.au"> audio </A><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><!WA159><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx45.tex"> LaTeX </A><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><!WA160><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx45.ps"> Postscript </A><LI><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><!WA161><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex4.au"> audio </A><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><!WA162><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx46.tex"> LaTeX </A><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><!WA163><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx46.ps"> Postscript </A><LI><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><!WA164><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex5.au"> audio </A><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><!WA165><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx47.tex"> LaTeX </A><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><!WA166><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx47.ps"> Postscript </A><LI><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><!WA167><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec10-ex6.au"> audio </A><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><!WA168><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx48.tex"> LaTeX </A><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><!WA169><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx48.ps"> Postscript </A></OL><h2><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><!WA170><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec11-title.au">Section 11 </A> Summations.</h2>Notice that the same expression can be written in more than one way. <OL><LI><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><!WA171><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec11-ex1.au"> audio </A><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><!WA172><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx49.tex"> LaTeX </A><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><!WA173><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx49.ps"> Postscript </A><LI><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><!WA174><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec11-ex2.au"> audio </A><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><!WA175><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx50.tex"> LaTeX </A><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><!WA176><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx50.ps"> Postscript </A><LI><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><!WA177><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec11-ex3.au"> audio </A><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><!WA178><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx51.tex"> LaTeX </A><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><!WA179><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx51.ps"> Postscript </A></OL><h2><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><!WA180><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec12-title.au">Section 12 </A> Limits.</h2><OL><LI><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><!WA181><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec12-ex1.au"> audio </A><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><!WA182><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx52.tex"> LaTeX </A><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><!WA183><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx52.ps"> Postscript </A><LI><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><!WA184><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/math-examples/sec12-ex2.au"> audio </A><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><!WA185><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx53.tex"> LaTeX </A><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><!WA186><A HREF = "http://www.cs.cornell.edu/Info/People/raman/aster/latex/xx53.ps"> Postscript </A></OL><h2><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><!WA187><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 section is meant to illustrate AsTeR's rendering ofcross-references, and is most effective when AsTeR is used interactively.<p>AsTeR enables the listener to give meaningful names to cross-referenceable

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