Superscriptsmathplayer

IntroductiontoUsingMathMLPresentedby:RobertMinerDirectorofNewProductDevelopmentBobMathewsDirectorofTrainingWhatwe'llcoverPartI–UnderstandingMathMLOverviewofMathMLPresentationandcontentmarkupMathMLelementsBuildingaMathMLexpressionandinsertingintoHTMLandXMLpages.
Whatwe'llcoverPartI–UnderstandingMathMLPartII–MagicIncantationsDOCTYPEs&MIMEtypesNamespacesObjectTagsandProcessingInstructionsUniversalMathMLStylesheetWhatwe'llcoverPartI–UnderstandingMathMLPartII–MagicIncantationsPartIII–ToolsDesignScienceWebEQDesignScienceMathTypewithMathPagetechnologyTeX4htAmayaNowontoPartI–UnderstandingMathMLOverviewofMathMLTheMathematicalMarkupLanguage(MathML)wasfirstpublishedasarecommendationinApril1998.
Fromthe"MathActivityStatement"oftheW3CMathWorkingGroup:"DesignedasanXMLapplication,MathMLprovidestwosetsoftags,oneforthevisualpresentationofmathematicsandtheotherassociatedwiththemeaningbehindequations.
"TheMathematicalMarkupLanguage(MathML)wasfirstpublishedasarecommendationinApril1998.
Fromthe"MathActivityStatement"oftheW3CMathWorkingGroup:"DesignedasanXMLapplication,MathMLprovidestwosetsoftags,oneforthevisualpresentationofmathematicsandtheotherassociatedwiththemeaningbehindequations.
"OverviewofMathMLOverviewofMathMLTheMathematicalMarkupLanguage(MathML)wasfirstpublishedasarecommendationinApril1998.
Fromthe"MathActivityStatement"oftheW3CMathWorkingGroup:"…twosetsoftags…""MathMLisnotdesignedforpeopletoenterbyhandbutspecializedtoolsprovidethemeansfortypinginandeditingmathematicalexpressions.
"TheMathematicalMarkupLanguage(MathML)wasfirstpublishedasarecommendationinApril1998.
Fromthe"MathActivityStatement"oftheW3CMathWorkingGroup:"…twosetsoftags…""MathMLisnotdesignedforpeopletoenterbyhandbutspecializedtoolsprovidethemeansfortypinginandeditingmathematicalexpressions.
"OverviewofMathMLAttributesgenerallyspecifyadditionaloptionalinformationabouttheelement.
Eachattributehasanameandavalue.
Forexample,themfracelementhasanattributecalledlinethickness.
Mostelementsrepresenttemplatesorpatternsforlayingoutsubexpressions.
Forexample,thereisanmfracelementforfractions,andanmsqrtelementforsquareroots.
AnatomyofaMathMLexpressionAbout30MathMLpresentationelementswhichacceptabout50attributesUsingpresentationmarkup,it'spossibletopreciselycontrolhowanexpressionwilllookwhendisplayed.
About120contentelements,acceptingaboutadozenattributes.
Contentmarkupfacilitatesapplicationsotherthandisplay,likecomputeralgebraandspeechsynthesis.
Mostcontentelementsrepresenteitheroperatorsormathematicaldatatypes.
Forexample,thereisadivide/elementfordivision,andanemptysetelementtodenotetheemptyset.
TwotypesofelementsMostpresentationelementshavestartandendtags,similartothewaysomeHTMLhasstartandendtags.
…Theseelementscanhaveotherdatain-betweenthestartandendtags,suchastext,extendedcharacters,orotherelements.
TwotypesofelementsMostpresentationelementshavestartandendtags,similartothewaysomeHTMLhasstartandendtags.
…TheothertypeofMathMLelementisanemptyelementoftheformTheseelementshavejustonetag.
Thereareonly4emptypresentationelements,butover100emptycontentelements,usedinprefixnotation.
TwotypesofelementsMostpresentationelementshavestartandendtags,similartothewaysomeHTMLhasstartandendtags.
…TheothertypeofMathMLelementisanemptyelementoftheformElementscanalsoacceptattributes.
Ifanelementhasbothstart&endtags,theattributeimmediatelyprecedesthe>inthestarttag.
TwotypesofelementsMostpresentationelementshavestartandendtags,similartothewaysomeHTMLhasstartandendtags.
…TheothertypeofMathMLelementisanemptyelementoftheformElementscanalsoacceptattributes.
Inemptyelements,attributesimmediatelyprecedethe/>.
Examplesofattributes……Insertsa12-ptspace.
For12pixels,use"12px".
Basicpresentationelements–identifier,suchasavariable,functionname,constant,etc.
example:xrendering:xexample:sinrendering:sinBasicpresentationelements–identifier,suchasavariable,functionname,constant,etc.
–operator,suchasasummation,fence(parentheses,brace,etc.
),accent,etc.
example:(rendering:(example:∑rendering:SThisisanexampleofanentityreference.
Entityreferencesarejustkeywordsinaspecialformat,whichrepresentextendedcharacters.
Otherexamplesareα(lower-caseGreekalpha),and∞(infinity).
Basicpresentationelements–identifier,suchasavariable,functionname,constant,etc.
–operator,suchasasummation,fence(parentheses,brace,etc.
),accent,etc.
–numberCanyouidentifythisexpressionx–(3+y)x–(3+y)TokenelementsMostMathMLelements,likethemfracelementmentionedearlier,expecttoonlyfindotherMathMLelementsintheircontent……butsomepresentationelements–,,and,forexample–aredifferent.
Theyareexamplesoftokenelements.
Tokenelementsaretheonlyelementswhichdirectlycontaincharacterdata.
ScriptsSuperscriptsandsubscriptsareubiquitousinmathematicalnotation,andalthoughyouwon'tbedoingmuchMathMLwritingmanually,ithelpstofamiliarizeyourselfwiththeschemata.
MathMLcontainssevenpresentationelementsfordifferentkindsofscripts,butwe'lltakealookatthemostcommon.
Scripts–sub&superThesearethefirstelementswe'veseenindetailthatnormallyhavemorethanoneargument.
Subscript:basescriptSuperscript:basescriptUsage:x1x1x2x2x1x122Whycan'twecodeitthisway:x1IncludingMathMLinyourpageWeneedsomewaytoidentifythemathmarkuptoourbrowser,plug-in,orapplet.
MathMLmarkupisinsertedbetweenandtagstodistinguishMathMLfromothermarkup.
Althoughmosttagswilldifferfrompresentationmarkuptocontentmarkup,thetagiscommontoboth.
CodingsimpleexpressionsAswestatedatthebeginning,itisnotourgoalinthistutorialtomakeyouproficientatwritingMathML.
You'lllikelyuseasoftwareproducttoproducetheMathMLmarkupratherthanwriteityourself.
OurgoalistofamiliarizeyouenoughwiththeMathMLsyntaxandconstructionthatyoucanreadandunderstandablockofcode,andcanperhapsmakechangestoitbyhand.
CodingsimpleexpressionsAswestatedatthebeginning,itisnotourgoalinthistutorialtomakeyouproficientatwritingMathML.
Thatbeingthecase,youknowenoughMathMLnowtotryyourhandatcodingacoupleofsimpleexpressions…Example1–trycodingthis…Don'tforgettobeginwiththestarttagandendwiththeendtagDon'tforgettobeginwiththestarttagandendwiththeendtagExample1–trycodingthis…b2–4b2–4⁢a⁢cExample1ab2–4acor…b2–4⁢a⁢cThisentitydoesn'tappearinprint,butherewehaveaddedittofacilitatevoicesynthesisandheuristicevaluationbycomputeralgebrasystems.
Horizontalrowofexpressionsalignedonthebaseline.
Wrappinganmrowaroundanelementorelementsisalwayspermissible,andoftennecessaryinordertogrouptermstogether,forexample,foruseinascript,etc.
Example2–onemore…x2+y2=r2OtherpresentationelementsPresentationelementsaregrouped:TokenElementsidentifiernumberoperator,fence,orseparatortextOtherpresentationelementsPresentationelementsaregrouped:TokenElementsGeneralLayouttogroupsubexpressionsformfractionfrom2subexpressionsradicalwithaspecifiedindexsurroundcontentwithapairoffencesOtherpresentationelementsPresentationelementsaregrouped:TokenElementsGeneralLayoutScriptsandLimits,,attachascriptunderabaseattachascriptoverabaseattachascriptbothunderandoverabaseOtherpresentationelementsPresentationelementsaregrouped:TokenElementsGeneralLayoutScriptsandLimitsTablestableormatrixrowinatableormatrixoneentryinatableormatrixOtherpresentationelementsPresentationelementsaregrouped:TokenElementsGeneralLayoutScriptsandLimitsTablesActionsbindsactionstoasubexpressionContentelementsMostfundamentaltocontentmarkupistheelement,whichenablestheexplicitapplicationofafunctiontoitsargument.
Contentelementsapplicationofafunctiontoargument.
TokenElementscontentnumbercontentidentifierContentelementsapplicationofafunctiontoargument.
TokenElementsBasicContentElementsgenericinversecompose2ormorefunctionspiecewisedefinedfunctionContentelementsapplicationofafunctiontoargument.
TokenElementsBasicContentElementsArithmetic,Algebra,andLogicdivisiontothepowerofnthrootcomplexconjugateContentelementsapplicationofafunctiontoargument.
TokenElementsBasicContentElementsArithmetic,Algebra,andLogicRelationsequalgreaterthanorequalthe"divides"operatorContentelementsapplicationofafunctiontoargument.
TokenElementsBasicContentElementsArithmetic,Algebra,andLogicRelationsCalculusandSetTheorypartialderivativelowerlimit(ofintegral,etc.
)unionormeetContentelementsapplicationofafunctiontoargument.
TokenElementsBasicContentElementsArithmetic,Algebra,andLogicRelationsCalculusandSetTheoryFurtherelementgroupsincludesequences&series,elementaryclassicalfunctions,statistics,linearalgebra,semanticmappingelements,andconstants.
Example3–contentmarkupWewanttocodethisexpressionincontentmarkup:Weknowweneedtosurroundthecodewiththe…element……butwehaven'tseenyethowtocombinecontentelementstocreateanentireexpression,soheregoes…Example3–contentmarkupπ1Example3–contentmarkupπ1Example3–contentmarkupπ1Example3–contentmarkupπ1totheleftofthe=totherightofthe=Example3–contentmarkupπ1Example3–compareπ1cosπ=–1SummaryPresentationmarkupisfordescribingmathnotation,andcontentmarkupisfordescribingmathematicalobjectsandfunctions.
Inpresentationmarkup,expressionsarebuilt-upusinglayoutschemata,whichtellhowtoarrangetheirsubexpressions(i.
e.
,mfracormsup).
SummaryPresentationmarkup…&contentmarkupMathMLelementseitherhavestartandendtagstoenclosetheircontent,oruseasingleemptytag.
SummaryPresentationmarkup…&contentmarkupMathMLelements…Attributesmaybespecifiedinastartoremptytag.
Attributevaluesmustbeenclosedinquotes.
SummaryPresentationmarkup…&contentmarkupMathMLelements…Attributes…inastartoremptytag.
Allcharacterdatamustbeenclosedintokenelements.
SummaryPresentationmarkup…&contentmarkupMathMLelements…Attributes…inastartoremptytag.
Allcharacterdata…tokenelements.
Extendedcharactersareencodedasentityreferences.
SummaryPresentationmarkup…&contentmarkupMathMLelements…Attributes…inastartoremptytag.
Allcharacterdata…tokenelements.
Extendedcharactersas…entityreferences.
Wediscussedotherlayoutschemata–math,mfrac,mrow,etc.
ThenextsessionofthetutorialwilldealwithdisplayingMathMLinbrowsers.
PartII–MagicIncantationsDOCTYPEs&MIMEtypesNamespacesObjectTagsandProcessingInstructionsUniversalMathMLStylesheetTriggeringMathMLrenderinginbrowsersrequiresspecialdeclarationsinthepage.
WhichBrowsersInternetExplorer(requiresadd-onsoftware)Themainchoicesare:MathPlayer(IE5.
5orhigherunderWindows)Techexplorer(IE5orhigher,manyplatforms)JavaScript/CSS(IE6Windows,otherssoon)Netscape(add-onsrequiredbeforeNS7PR1)Somethingstonote:MathMLdoesn'tyetworkontheMacThedecisiontoincludeMathMLisn'tfinalDOCTYPEsandMIMEtypesTherearetwowaysbrowsersdeterminewhatkindofdataneedstobedisplayed.
Localfilesindicatetheirtypewithafilenameextension(Windows,Unix)orextradataincludedinthefile(Mac).
Datacomingoveranhttpconnectiondoesn'thaveafilename.
Thus,webserversincludeextradataaboutwhatkindoffileisbeingsent.
ThisextradataiscalledaMIMEtype.
DOCTYPEsandMIMEtypesWebserversgenerallyusefileextensionstopicktheMIMEtype.
Thisdoesn'talwayswork…Netscape7isfanaticalaboutusingonlytheMIMEtypetodeterminehowtodisplayadocument.
InternetExplorerisextremelycavalierinusingtheMIMEtype,preferringtosniffinsidethedocumenttoguessitstype.
MIMEtypesWeareconcernedwiththreekindsoffiles:XMLfiles.
ThisincludesXHTMLfiles.
Netscape7willonlyrenderMathMLinthiskindoffile.
HTMLfiles.
InternetExplorerwillonlyrenderMathMLinHTMLfiles.
XSLfiles.
ThesearealsoXMLfiles,buttheyusuallyend.
xslinsteadof.
xml,whichscrewsupmany/mostwebservers.
XHTMLvsHTMLStartandendtagsmustalwaysmatch.
Thingssuchasmustbeemptytags.
AllattributesmusthavequotesaroundthemYourcodeactuallyhastobecorrect!
XHTMLandHTMLarenearlythesame.
ThemaindifferenceisthatXHTMLispickywhileHTMLislax.
Themostimportantthingsare:MIMEtypesTheupshotis:ToworkinNetscape,youneedanXMLdocument.
ToworkinInternetExploreryouneedanHTMLdocument.
So,inpracticeyoucreateanXHTMLdocument,andfiddlewiththeMIMEtypeOntheserverusingscripts,etc.
OntheclientusingXSLstylesheets.
DOCTYPEsADOCTYPEisaspecialdeclarationatthebeginningofanHTMLorXMLdocumentthatdefineswhatkindofmarkupisinthedocument.
DOCTYPEsarereallyforvalidation,notidentification.
DOCTYPEspointtoaDTD,whichdefinesthesyntaxofthemarkupinthedocument.
DOCTYPEs]>TypicalDOCTYPEdeclarationslooklikethis:DOCTYPEsNetscape7requiresaDOCTYPE,butdoesn'tactuallylookattheDTDtowhichitpoints.
InsteadtheDTDmustmatchoneofafewpredefinedvalues.
InternetExplorerdoesn'trequireaDOCTYPE,butitdoesdownloadtheDTDanduseitifthereisone.
DOCTYPEsTheupshotis:InyourXHTMLdocument,youputaDOCTYPE,andTheW3CMathWGpullsitshairouttryingtomakeaDTDavailablethatisbothcorrectandworksaroundthebugsintheIEparser.
NamespacesXMLlanguagesareidentifiedbyaURI.
MathMLishttp://www.
w3.
org/1998/Math/MathMLXHTMLishttp://www.
w3.
org/1999/xhtmlTheycanbeindicatedintwoways.
ByusinganxmlnsattributeonanelementByaddingaprefixtoelementnamesComplexitiesarisewhentwoXMLdialectsmustmix.
ThecaseofinterestisXHTML+MathML.
Thesolutionistousenamepaces.
Namespaces…x+2…Usethexmlnsattributeontheoutermostelementoftheembeddedmarkup.
Thisplacestheelementonwhichtheattributeisset,anditschildrenintheindicatednamespace.
Namespaces…x+2…Touseprefixes,youmustAssociateaprefixandanamespaceusinganxmlns:prefixattributeonacontainingelement.
Usetheprefixtoidentifyelementsthatshouldbeinthenamespace.
Namespaces&DOCTYPEs]>x+2…SincetheURIsfornamespacesarelong,onetricksomepeoplelikeistodeclareanentityreferenceforitintheDOCTYPE:ObjectsandPIsTheelementinstructsIEwhatpieceofsoftwaretoload.
Aprocessinginstruction(orPI)isusedtoassigntheadd-onsoftwaretorendermarkupfromaparticularnamespace.
Twoadditionaldeclarationsarerequiredtotriggeradd-onsoftwareformathrenderinginInternetExplorer:ObjectsandPIsWindowsusesalongstringofdigitsandletterscalledaclassidtouniquelyidentifysoftwarecomponents.
Theobjecttagusesanattributetospecifyaclassid:ObjectsandPIsTherearemanykindsofprocessinginstructions,withdifferentattributes.
For"IEbehaviors"onespecifiesanamespace,andtheIDofanobject:ObjectsandPIsBehaviorsareactuallytriggeredbyanamespaceprefix,andnotthenamespaceitself.
Theupshotis,touseadd-onssuchasMathPlayerorTechexplorer,YoumustincludeanOBJECTandPI.
Youmustusetheprefixmethodfornamespaces.
OnecomplexityarisesfromabuginInternetExplorerbehaviors:PuttingItTogetherWriteXHTMLIncludeaDOCTYPEIncludeanOBJECTandPIIncludeanamespacedeclarationUsenamespaceprefixesontheMathMLAltogetherthen,tocreateadocumentthatworksinbothIEandNetscape,youmust:PuttingItTogetherNetscapewillonlyrenderyourdocumentifitisXML.
InternetExplorerwillonlyrenderitifitisHTML.
ThesolutionXSLstylesheets…Butwait!
Evenifyoudoallthat,thereisstilltheinsurmountableproblemofMIMEtypes:TheMathMLStylesheetYouaddanXSLstylesheettoanXMLdocumentusingaPI.
Thestylesheetsitsontheserverwithyourdocument.
Thestylesheetrunsintheclienttotransformyourdocumentforviewing.
AnXSLstylesheetisasetoftemplatesfortransforminganinputdocumentintoanoutputdocument.
TheMathMLStylesheetDetectwhatbrowseritisrunninginandoutputeitherXMLorHTMLaccordinglyDetectwhatadd-onsareinstalledandoutputthenecessaryObjectandPIdeclarationsConvertcontenttopresentationmarkupXSLispowerful.
TheW3CMathWGhascreatedaUniversalMathMLStylesheetwhichcan:TheMathMLStylesheetTheMathMLstylesheetPIlookslikethis:TheMathMLStylesheetIncludethestylesheetPI.
WriteXHTML.
Don'tuseentityreferences.
Usenumericreferencesinstead.
UsenamespacestoindicatetheMathML.
Don'tuseObjecttagsorbehaviorPIs.
It'snotnecessarytouseaDOCTYPE.
InordertousetheMathMLstylesheet,SummaryThedocumentmustbeXHTML(NS).
ItneedsaDOCTYPE(NS).
TheMathMLmustbeinanamespace(both,)andyouhavetousetheprefixmethod(IE).
YouneedanelementandbehaviorPI(IE).
ServeitasXMLforNS,andHTMLforIE.
GettingMathMLinadocumenttorenderinbothIEandNetscapeisquiteatrick.
Thenecessaryingredientsare:SummaryThedocumentmustbeXHTMLwithoutentitynames.
IncludethestylesheetPI.
TheMathMLmustbeinanamespace(eithermethod).
YoucanomittheDOCTYPE,elementandbehaviorPI.
Asimpler,alternativemethodwhichalsodealswiththeMIMEtypesistousetheUniversalMathStylesheet: