ISO_IEC_40314_2016.pdf

Information technology Mathematical Markup Language(MathML)Version 3.0 2nd EditionTechnologies de linformation Langage de marquage mathmatique(MathML)Version 3.0 2e ditionINTERNATIONAL STANDARDISO/IEC40314Reference numberISO/IEC 40314:2016(E)First edition2016-03-01 ISO/IEC 2016 ii ISO/IEC 2016 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO/IEC 2016,Published in SwitzerlandAllrightsreserved.Unlessotherwisespeci?ied,nopartofthispublicationmaybereproducedorutilizedotherwiseinanyformorbyanymeans,electronicormechanical,includingphotocopying,orpostingontheinternetoranintranet,withoutpriorwrittenpermission.Permissioncanbere?uestedfromeitherISOattheaddressbeloworISO?smemberbodyinthecountryofthe requester.ISOcopyrightof?iceCh.de Blandonnet 8 CP 401CH-1214 Vernier,Geneva,SwitzerlandTel.+41 22 749 01 11Fax+41 22 749 09 47copyright?iso.orgwww.iso.orgISO/IEC 40314:2016(E)FOREWORDISO(theInternationalOrganizationforStandardization)andIEC(theInternationalElectrotechnicalCommission)formthespecializedsystemforworldwidestandardization.NationalbodiesthataremembersofISOorIECparticipateinthedevelopmentofInternationalStandardsthroughtechnicalcommitteesestablishedbytherespectiveorganizationtodealwithparticularfieldsoftechnicalactivity.ISO and IEC technical committees collaborate in fields of mutual interest.Otherinternationalorganizations,governmentalandnongovernmental,inliaisonwithISOandIEC,alsotakepartinthework.Inthefieldofinformationtechnology,ISOandIEChaveestablishedajointtechnicalcommittee,ISO/IECJTC1.TheproceduresusedtodevelopthisdocumentandthoseintendedforitsfurthermaintenancearedescribedintheISO/IECDirectives,Part1.Inparticularthedifferentapprovalcriterianeededforthedifferenttypesofdocumentshouldbenoted.ThisdocumentwasdraftedinaccordancewiththeeditorialrulesoftheISO/IECDirectives,Part2(seewww.iso.org/directives).Attentionisdrawntothepossibilitythatsomeoftheelementsofthisdocumentmaybethesubjectofpatentrights.ISOandIECshallnotbeheldresponsibleforidentifyinganyorallsuchpatentrights.DetailsofanypatentrightsidentifiedduringthedevelopmentofthedocumentwillbeintheIntroductionand/orontheISOlistofpatentdeclarationsreceived(seewww.iso.org/patents).Anytradenameusedinthisdocumentisinformationgivenfortheconvenienceofusersanddoesnotconstituteanendorsement.ForanexplanationonthemeaningofISOspecifictermsandexpressionsrelatedtoconformityassessment,aswellasinformationaboutISOsadherencetotheWTOprinciplesintheTechnicalBarrierstoTrade(TBT),seethefollowingURL:ForewordSupplementaryinformation.ISO/IEC 40314 was prepared by W3C and was adopted,under the PAS procedure,by JointTechnical Committee ISO/IEC JTC 1,Information technology,in parallel with its approval bynationalbodiesofISOandIEC.ISO/IEC 40314:2016(E)ISO/IEC 2016 All rights reservedi?i Contents1Introduction91.1Mathematics and its Notation.91.2Origins and Goals.101.2.1Design Goals of MathML.101.3Overview.111.4A First Example.112MathML Fundamentals142.1MathML Syntax and Grammar.142.1.1General Considerations.142.1.2MathML and Namespaces.142.1.3Children versus Arguments.152.1.4MathML and Rendering.152.1.5MathML Attribute Values.152.1.6Attributes Shared by all MathML Elements.202.1.7Collapsing Whitespace in Input.212.2The Top-Level Element.222.2.1Attributes.222.2.2Deprecated Attributes.242.3Conformance.242.3.1MathML Conformance.242.3.2Handling of Errors.272.3.3Attributes for unspecified data.273Presentation Markup283.1Introduction.283.1.1What Presentation Elements Represent.283.1.2Terminology Used In This Chapter.293.1.3Required Arguments.303.1.4Elements with Special Behaviors.313.1.5Directionality.323.1.6Displaystyle and Scriptlevel.333.1.7Linebreaking of Expressions.343.1.8Warning about fine-tuning of presentation.353.1.9Summary of Presentation Elements.373.1.10 Mathematics style attributes common to presentation elements.383.2Token Elements.383.2.1Token Element Content Characters,.393.2.2Mathematics style attributes common to token elements.413.2.3Identifier .454ISO/IEC 40314:2016(E)ISO/IEC 2016 All rights reservedCONTENTS53.2.4Number .463.2.5Operator,Fence,Separator or Accent .473.2.6Text .603.2.7Space.623.2.8String Literal .643.3General Layout Schemata.643.3.1Horizontally Group Sub-Expressions .643.3.2Fractions .673.3.3Radicals,.693.3.4Style Change .693.3.5Error Message.723.3.6Adjust Space Around Content .733.3.7Making Sub-Expressions Invisible.783.3.8Expression Inside Pair of Fences .803.3.9Enclose Expression Inside Notation .833.4Script and Limit Schemata.853.4.1Subscript .863.4.2Superscript .873.4.3Subscript-superscript Pair .873.4.4Underscript .883.4.5Overscript.893.4.6Underscript-overscript Pair .913.4.7Prescripts and Tensor Indices,933.5Tabular Math.953.5.1Table or Matrix .953.5.2Row in Table or Matrix .993.5.3Labeled Row in Table or Matrix.993.5.4Entry in Table or Matrix.1013.5.5Alignment Markers,.1013.6Elementary Math.1103.6.1Stacks of Characters.1113.6.2Long Division .1133.6.3Group Rows with Similiar Positions.1143.6.4Rows in Elementary Math .1153.6.5Carries,Borrows,and Crossou