calculatorsmathplayer

Text-basedinputformatsformathematicalformulasPeterJipsenChapmanUniversityDecember8,2006PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20061/22TheproblemHowtomakecomputersdisplayandunderstande.
g.
:sin1logee=π2Mathematicalnotationusescomplex2DpositioningTheinformationhastobeenteredinsomeformConvertedtoaninternalrepresentationDisplayed/printed/spoken/archived/searched/.
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PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20062/22CreatingmathematicalcontentTraditionaldocument:HandwrittenAdvantagesversatilesimplefastDisadvantageshardtodigitizehardtoparsecan'teditorcopy/pasteeasilysemanticsPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20063/22CreatingmathematicalcontentTraditionaldocument:usingpointandclickformulaeditorAdvantageseasytousewysiwygcapturesstructureDisadvantagesslownonstandarddiculttoaddtoexistingtoolsdisplayqualityPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20064/22CreatingmathematicalcontentTraditionaldocument:usingatypesettingsystemAdvantageshighqualityoutputimport/exportfeaturesforlargersystemsexpectedbypublishersDisadvantagescrypticcommandstedioustextediting/proofreading"nonstandard"PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20065/22DisplayingmathematicalcontentMathonwebpagesscanhandwrittenpagespostdigitalphotoofawhiteboarduseatabletPC,postinputaspicturepostavideoofapresentationuseaconvertertochangeeachformulatogiforpng(e.
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LaTeX2HTML,Wikipedia,.
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)useHTML/ASCIIapproximations(handedit,TtH,TeX2HTML,.
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)positionfontswithCSS(jsMath,.
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)MathMLPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20066/22TextbasedinputKeyboardsarethemostwidelyusedformofcharacter-basedinputLikelytoremaintrueforatleastanotherdecadeWanttocommunicatemathcontenteasilyChat,read,editemailrepliesinanon-proprietarywayAlinearcharacter-basedformattswellManydierentmathinputsyntaxeshavebeendevelopedforprogramminglanguages:Fortran,APL,Lisp,C,Pascal,Java,.
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scriptinglanguages:JS,Perl,PHP,Python,.
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calculators:TI-83,TI-89,CasioFX,HP,.
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computeralgebrasystems:Macsyma,Reduce,Mathematica,Maple,ScienticNotebook,SAGE,.
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typesettingsystems:tro,TeX/LaTeX,DocBook,.
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PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20067/22CommonfeaturesofmostlinearmathnotationPrexfunctionnotationwithinxoperationsSomeprecedenceofoperationsisusedParenthesisareusedforgrouping,overrideprecedenceVariablenamesmayconsistofseveralcharactersIncorrectsyntaxraiseserrorsTherstthreearestandardinhandwrittenformulasTheothertwoarelessusualinmathematicsPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20068/22ManydierencesofvariousinputformatsForexample:sin1logee=π2ArcSin[Sqrt[Log[E]]]==Pi/2MathematicaMath.
asin(Math.
sqrt(Math.
log(Math.
E)))==Math.
Pi/2JavaScript\sin^{-1}\sqrt{\log_ee}=\frac{\pi}{2}jsMathorLaTeXsin-1logee=π2PresentationMathMLsin^-1sqrt(log_ee)=pi/2ASCIIMathPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,20069/22WhyuseformulasformathematicsFormulasareusedtopreciselyspecifyconceptsinacompactandstandardwayconvenientformanualmanipulation(replacingequalsbyequals)a"canonicalform"acrossdiverseareasofmathacommonlanguagewithmnemonicrecognitionvalueaninformalstandardformathnotation;quiteinternationalTypedmathnotationdeservesasimilarinformalstandardLaTeXisadefactostandardforresearchpublicationsButnotwidelyusedinschoolorundergraduatemathNotcompactoreasytoreadortype(fornon-technicalusers)PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200610/22AimsofaconvenientlinearmathnotationClosetostandardmathematicsMotto:ifitlookslikemath,itshouldworkEasytoreadEasytotypeFormulasshouldbeshortNoobscuresyntaxerrorsSyntaxeasytodeneandrememberMostlylanguageindependentSimpletoextendormodify(localization)PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200611/22ASCIIMathAlinearmathnotationwith8syntaxrules;designedin2004Basedonwell-knownASCIImathconventions+someLaTeXc::=[A-Za-z]|greekchr|numbers|.
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constantsymbolsu::=sqrt|text|bb|.
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prefixunarysymbolsb::=frac|root|stackrelprefixbinarysymbolslleftbracketsrrightbracketsS::=c|lEr|uS|bSS|"any"SimpleexpressionI::=S_S|S^S|S_S^S|SIntermediateexpressionE::=IE|I/IExpressionPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200612/22TranslationtoMathMLEachterminalsymbolistranslatedtoacorrespondingMathMLnodeConstantsaremostlyconvertedtotheirrespectiveUnicodesymbolslSr→mrowlSr/mrow(bracketsdon'thavetomatch)sqrtS→msqrtS/msqrt"any"→mtextany/mtextfracS1S2→mfracS1S2/mfracrootS1S2→mrootS2S1/mrootstackrelS1S2→moverS2S1/moverS1/S2→mfracS1S2/mfracS1S2→msubS1S2/msubS1∧S2→msupS1S2/msupS1S2∧S3→msubsupS1S2S3/msubsupormunderoverNote:SisthesameasS,exceptthatifShasanouterlevelofbrackets,thenSistheexpressioninsidethesebracketsPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200613/22ExamplesofASCIIMathlimx→∞tan1x=π2lim_(x->oo)tan^-1x=pi/2∞n=11n2=π26sum_(n=1)^oo1/n^2=pi^2/611√1x2dx=π2int_-1^1sqrt(1-x^2)dx=pi/2[0,1)={x∈R:0≤xSomeformulas:'sum_(i=1)^ni=(n(n+1))/2'and$\int_0^{\frac{pi}{2}}\sinx\dx=1$.
PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200616/22ASCIIMathiswidelyusedDownloadedbythousandsofusersaroundtheglobeIntegratedintomanywikis,blogs,coursemanagementsystemsAugmentedwithASCIIsvgandaJSscienticcalculator[J2004]MergedintoWYSIWYGwebeditorsHTMLArea,Xinha[J,Lippman2006]AddedtoTiddlyWiki(client-sidewiki)→ASciencePadASCIIMathserversideinPHP[Chan2004],Perl[Nodine2006]ModiedtoLaTeXMathML.
js[Woodall2006]DemoofASciencePadPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200617/22FutureofASCIIMathMLStandardizelanguageasshorthandforapMathMLsubsetDevelopMathML→ASCIIMath(reverse)translatorExpandlanguagetouseUnicodesymbols,i.
e.
UnicodeMathML.
jsAdapttotheMSWord2007linearformulasyntaxThissyntaxisquitesimilartoASCIIMathDevelopedbyMurraySargentsincethe1970sMSWordiswidelyused,sothiswillbecomeadefactostandardPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200618/22AconvenientstandardfortypingmathUnicodeKeyboardsare"fairly"standardCansitatacomputerinGreeceorJapanandtypeanemailCanhandwriteformulasandcommunicatewithnonenglishspeakersButcan'tjuststartamathprogramandtypemathThisisastandardizationproblemMathematicsisalanguageItneedsastandardkeyboardinputformatLaTeX/Mathematica/Maple/MaximasyntaxisnottheanswerStudentsshouldn'thavetolearntotype\sin\piorSin[Pi]PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200619/22WhythisisurgentFew(school/undergrad)studentsknowhowtotypemathematicsMostmathhomeworkishandwrittenMathtestsareoftenmultiplechoice(presentationnottested)MathematicsseemsoldfashionedtocomputersavvyyouthMathematicseducationisaectednegativelyDiculttohelpstudentsbyemailorchatOnlineinteractivemathcontentislowIronically,it'shardtodomathonacomputer!
PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200620/22ConclusionMathusesformulassincetheyareshortandpreciseTypedlinearmathnotationneedstobestandardizedASCIIMathissystemneutralandfairlylanguageindependentAlsoeasytolearn,useandimplement(ontopofMathML)Translatesintoawell-denedsubsetofPresentationMathMLMatcheswellwithexistingtypedmathnotationsItllsaneedformathematicalcommunicationhttp://asciimathml.
sourceforge.
net/PeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200621/22AcknowledgementsManythankstotheInstituteforMathematicsanditsApplicationsWorldWideWebConsortium(HTML,MathML,SVG)DesignScience(MathPlayer),Adobe(SVGview)Netscape(JavaScript)Mozilla(Firefox)SourceForge.
netandtheopen-sourcecommunityPeterJipsen(ChapmanUniversity)Text-basedmathematicalinputformatsDecember8,200622/22