1、BSI Standards Publication BS ISO/IEC 40314:2016 Information technology Mathematical Markup Language (MathML) Version 3.0 2nd EditionBS ISO/IEC 40314:2016 BRITISH STANDARD National foreword This British Standard is the UK implementation of ISO/IEC 40314:2016. The UK participation in its preparation w
2、as entrusted to Technical Committee ICT/-/1, Information systems co-ordination. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its co
3、rrect application. The British Standards Institution 2016. Published by BSI Standards Limited 2016 ISBN 978 0 580 87547 2 ICS 35.240.30 Compliance with a British Standard cannot confer immunity from legal obligations. This British Standard was published under the authority of the Standards Policy an
4、d Strategy Committee on 31 March 2016. Amendments/corrigenda issued since publication Date Text affected BS ISO/IEC 40314:2016 Information technology Mathematical Markup Language (MathML) Version 3.0 2nd Edition Technologies de linformation Langage de marquage mathmatique (MathML) Version 3.0 2e dit
5、ion INTERNATIONAL STANDARD ISO/IEC 40314 Reference number ISO/IEC 40314:2016(E) First edition 2016-0 3-01 ISO/IEC 2016 BS ISO/IEC 40314:2016 Information technology Mathematical Markup Language (MathML) Version 3.0 2nd Edition Technologies de linformation Langage de marquage mathmatique (MathML) Vers
6、ion 3.0 2e dition INTERNATIONAL STANDARD ISO/IEC 40314 Reference number ISO/IEC 40314:2016(E) First edition 2016-0 3-01 ISO/IEC 2016 BS ISO/IEC 40314:2016ii ISO/IEC 2016 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO/IEC 2016, Published in Switzerland ll rig hts r eser ed. nless otherwise spec
7、iied, no part o this publi cation ma y be r epr oduced or utilied otherwise in an y orm or b y an y means, electr onic or mechanical, including phot ocop ying, or posting on the int ernet or an intr anet , without prior writt en permission. P ermission can be r euest ed r om either at the addr ess b
8、elo w or s member bod y in the country o the requester. cop yrig ht oice Ch. de Blandonnet 8 CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 cop yrig htiso.or g www.iso.org ISO/IEC 40314:2016(E) BS ISO/IEC 40314:2016 FOREWORD ISO (the I nternation al O rgani z
9、atio n fo r Standardization) a nd I EC (the I nter nation al E lec trotechnical Co m m issio n ) fo r m t h e s p ec i a l i z ed s ystem for worldwide s tandardi zation. N ational bo dies that are mem b ers of I SO o r IEC participate in t he d evelop ment o f Int e rna t ion a l S t a nda rds t hr
10、ou gh t echnic a l committ ees e stablished by the resp ective o r g an ization to d eal w it h p ar ti c ular f iel ds of t echnica l acti v i ty . ISO and IEC te ch ni cal c o m mi tte e s co llabo r ate in f i eld s of m utual interest. Other internati onal organiz a tio n s, g overn m ental and
11、no ngovern mental, in l ia iso n w ith IS O and IE C , al s o take p art in the w ork. In the field of i nformatio n technolo g y, I SO a nd IEC ha ve e st a b l i shed a j oin t technical committee, ISO /IEC J TC 1. The pr ocedu r es used to d evelop this document a nd those i nt ended f or it s f
12、u r t he r m ai nt e n anc e ar e de scri b e d in t he IS O / I EC Di r ec t i ves , P ar t 1. In p a rti cu la r t he different a pproval criter ia needed fo r the different types of d oc ument shoul d b e noted. T his document was drafted in a ccordance with the editorial rul e s of the ISO /I EC
13、 Directives, Part 2 (see www.iso.org/directives). Atte nti o n i s d r awn to t h e po s s i bi li ty t h at s o me o f th e e l e me nts of t h i s d oc u men t m a y b e t h e s u bj ec t of p atent rights. ISO and IEC shall not be he ld r e sponsible f or identifying a ny or all such patent right
14、s. Detail s of a ny pat ent rights identified during the d eve l o p m e nt of t he d oc um e nt w il l b e in t h e Introduction and/or on t he ISO lis t of patent declarations rec eived (see ww w.is o.org/patents ). Any tr ade na me used in t his document is i nformation given for th e c o n ve ni
15、ence of u s ers a nd does not constitu t e an endorsement. For an e xpl a nati on on t he meanin g of I SO s peci fic terms an d expr essions related to c o nf o rm ity assessment, as well as informati on about ISO s adherence to the W TO p ri nciples in the T echnical Barriers to Trade (TBT), see t
16、he following URL: Foreword Supplementary information. ISO/IEC 40314 was prepared by W3C and was adopted, under the PAS procedure, by Joint Technical Committee ISO/IEC JTC 1, Information technology, in parallel with its approval by national bodies of ISO and IEC. ISO/IEC 40314:201 6(E) ISO/IEC 2016 A
17、ll rights reserved i i BS ISO/IEC 40314:2016ii ISO/IEC 2016 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO/IEC 2016, Published in Switzerland ll rig hts r eser ed. nless otherwise speciied, no part o this publi cation ma y be r epr oduced or utilied otherwise in an y orm or b y an y means, ele
18、ctr onic or mechanical, including phot ocop ying, or posting on the int ernet or an intr anet , without prior writt en permission. P ermission can be r euest ed r om either at the addr ess belo w or s member bod y in the country o the requester. cop yrig ht oice Ch. de Blandonnet 8 CP 401 CH-1214 Ve
19、rnier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 cop yrig htiso.or g www.iso.org ISO/IEC 40314:2016(E) BS ISO/IEC 40314:2016 FOREWORD ISO (the I nternation al O rgani z atio n fo r Standardization) a nd I EC (the I nter nation al E lec trotechnical C o m m issio n ) fo r m t h e
20、 s p ec i a l i z ed s ystem for worldwide s tandardi zation. N ational bo dies that are mem b ers of I SO o r IEC participate in t he d evelop ment o f Int e rna t ion a l S t a nda rds t hrou gh t echnic a l committ ees e stablished by the resp ective o r g an ization to d eal w it h p ar ti c ula
21、r f iel ds of t echnica l acti v i ty . ISO and IEC te ch ni cal c o m mi tte e s co llabo r ate in f i eld s of m utual interest. Other internati onal organiz a tio n s, g overn m ental and no ngovern mental, in l ia iso n w ith IS O and IE C , al s o take p art in the w ork. In the field of i nfor
22、matio n technolo g y, I SO a nd IEC ha ve e st a b l i shed a j oin t technical committee, ISO /IEC J TC 1. The pr ocedu r es used to d evelop this document a nd those i nt ended f or it s f u r t he r m ai nt e n anc e ar e de scri b e d in t he IS O / I E C Di r ec t i ves , P ar t 1. In p a rti c
23、u la r t he different a pproval criter ia needed fo r the different types of d oc ument shoul d b e noted. T his document was drafted in a ccordance with the editorial rul e s of the ISO /I EC Directives, Part 2 (see www.iso.org/directives). A tte nti o n i s d r awn to t h e po s s i bi li ty t h a
24、t s o me o f th e e l e me nts of t h i s d oc u men t m a y b e t h e s u bj ec t of p atent rights. ISO and IEC shall not be he ld r e sponsible f or identifying a ny or all such patent rights. Detail s of a ny pat ent rights identified during the d eve l o p m e nt of t he d oc um e nt w il l b e
25、 in t h e Introduction and/or on t he ISO lis t of patent declarations rec eived (see ww w.is o.org/patents ). Any tr ade na me used in t his document is i nformati on given for th e c o n ve nience of u s ers a nd does not constitu t e an endorsement. For an e xpl a nati on on t he meanin g of I SO
26、 s peci fic terms an d expr essions related to c o nf o rm ity assessment, as well as information about ISO s adherence to the W TO p ri nciples in the T echnical Barriers to Trade (TBT), see the following URL: Foreword Supplementary information. ISO/IEC 40314 was prepared by W3C and was adopted, un
27、der the PAS procedure, by Joint Technical Committee ISO/IEC JTC 1, Information technology , in parallel with its approval by national bodies of ISO and IEC. ISO/IEC 40314:201 6(E) ISO/IEC 2016 All rights reserved i i BS ISO/IEC 40314:2016BS ISO/IEC 40314:2016 Contents 1 Introduction 9 1.1 Mathematic
28、sanditsNotation . 9 1.2 OriginsandGoals . 1 0 1.2.1 DesignGoalsofMathML 1 0 1.3 Overview . 1 1 1.4 AFirstExample 1 1 2 MathMLFundamentals 14 2.1 MathMLSyntaxandGrammar 1 4 2.1.1 GeneralConsiderations 1 4 2.1.2 MathMLandNamespaces 1 4 2.1.3 ChildrenversusArguments 1 5 2.1.4 MathMLandRendering . 1 5 2
29、.1.5 MathMLAttributeValues 1 5 2.1.6 AttributesSharedbyallMathMLElements . 2 0 2.1.7 CollapsingWhitespaceinInput . 2 1 2.2 TheTop-LevelElement . 2 2 2.2.1 Attributes . 2 2 2.2.2 DeprecatedAttributes 2 4 2.3 Conformance . 2 4 2.3.1 MathMLConformance 2 4 2.3.2 HandlingofErrors 2 7 2.3.3 Attributesforu
30、nspecieddata 2 7 3 PresentationMarkup 28 3.1 Introduction 2 8 3.1.1 WhatPresentationElementsRepresent . 2 8 3.1.2 TerminologyUsedInThisChapter 2 9 3.1.3 RequiredArguments . 3 0 3.1.4 ElementswithSpecialBehaviors . 3 1 3.1.5 Directionality . 3 2 3.1.6 DisplaystyleandScriptlevel . 3 3 3.1.7 Linebreaki
31、ngofExpressions . 3 4 3.1.8 Warningaboutne-tuningofpresentation 3 5 3.1.9 SummaryofPresentationElements . 3 7 3.1.10 Mathematicsstyleattributescommontopresentationelements . 3 8 3.2 TokenElements 3 8 3.2.1 TokenElementContentCharacters, . 3 9 3.2.2 Mathematicsstyleattributescommontotokenelements 4 1
32、 3.2.3 Identier 4 5 4 ISO/IEC 40314:2016(E) ISO/IEC 2016 All rights reserved BS ISO/IEC 40314:2016 CONTENTS 5 3.2.4 Number . 4 6 3.2.5 Operator,Fence,SeparatororAccent . 4 7 3.2.6 Text . 6 0 3.2.7 Space 6 2 3.2.8 StringLiteral 6 4 3.3 GeneralLayoutSchemata . 6 4 3.3.1 HorizontallyGroupSub-Expression
33、s 6 4 3.3.2 Fractions 6 7 3.3.3 Radicals, . 6 9 3.3.4 StyleChange . 6 9 3.3.5 ErrorMessage 7 2 3.3.6 AdjustSpaceAroundContent 7 3 3.3.7 MakingSub-ExpressionsInvisible 7 8 3.3.8 ExpressionInsidePairofFences 8 0 3.3.9 EncloseExpressionInsideNotation 8 3 3.4 ScriptandLimitSchemata 8 5 3.4.1 Subscript .
34、 8 6 3.4.2 Superscript 8 7 3.4.3 Subscript-superscriptPair 8 7 3.4.4 Underscript 8 8 3.4.5 Overscript . 8 9 3.4.6 Underscript-overscriptPair . 9 1 3.4.7 PrescriptsandTensorIndices, 93 3.5 TabularMath . 9 5 3.5.1 TableorMatrix 9 5 3.5.2 RowinTableorMatrix 9 9 3.5.3 LabeledRowinTableorMatrix 9 9 3.5.4
35、 EntryinTableorMatrix .1 0 1 3.5.5 AlignmentMarkers, 1 0 1 3.6 ElementaryMath .1 1 0 3.6.1 StacksofCharacters .1 1 1 3.6.2 LongDivision .1 1 3 3.6.3 GroupRowswithSimiliarPositions 1 1 4 3.6.4 RowsinElementaryMath .115 3.6.5 Carries,Borrows,andCrossouts .1 1 5 3.6.6 ASingleCarry .1 1 6 3.6.7 Horizont
36、alLine .1 1 7 3.6.8 ElementaryMathExamples .1 1 8 3.7 EnliveningExpressions 1 2 4 3.7.1 BindActiontoSub-Expression .1 2 4 3.8 SemanticsandPresentation 1 2 6 4 ContentMarkup 127 4.1 Introduction 1 2 7 4.1.1 TheIntentofContentMarkup 1 2 7 4.1.2 TheStructureandScopeofContentMathMLExpressions .1 2 8 4.1
37、.3 StrictContentMathML 1 2 8 4.1.4 ContentDictionaries .1 2 9 4.1.5 ContentMathMLConcepts .1 3 0 4.2 ContentMathMLElementsEncodingExpressionStructure .1 3 1 ISO/IEC 40314:2016(E) ISO/IEC 2016 All rights reserved BS ISO/IEC 40314:2016BS ISO/IEC 40314:2016 Contents 1 Introduction 9 1.1 Mathematicsandi
38、tsNotation . 9 1.2 OriginsandGoals . 1 0 1.2.1 DesignGoalsofMathML 1 0 1.3 Overview . 1 1 1.4 AFirstExample 1 1 2 MathMLFundamentals 14 2.1 MathMLSyntaxandGrammar 1 4 2.1.1 GeneralConsiderations 1 4 2.1.2 MathMLandNamespaces 1 4 2.1.3 ChildrenversusArguments 1 5 2.1.4 MathMLandRendering . 1 5 2.1.5
39、MathMLAttributeValues 1 5 2.1.6 AttributesSharedbyallMathMLElements . 2 0 2.1.7 CollapsingWhitespaceinInput . 2 1 2.2 TheTop-LevelElement . 2 2 2.2.1 Attributes . 2 2 2.2.2 DeprecatedAttributes 2 4 2.3 Conformance . 2 4 2.3.1 MathMLConformance 2 4 2.3.2 HandlingofErrors 2 7 2.3.3 Attributesforunspec
40、ieddata 2 7 3 PresentationMarkup 28 3.1 Introduction 2 8 3.1.1 WhatPresentationElementsRepresent . 2 8 3.1.2 TerminologyUsedInThisChapter 2 9 3.1.3 RequiredArguments . 3 0 3.1.4 ElementswithSpecialBehaviors . 3 1 3.1.5 Directionality . 3 2 3.1.6 DisplaystyleandScriptlevel . 3 3 3.1.7 LinebreakingofE
41、xpressions . 3 4 3.1.8 Warningaboutne-tuningofpresentation 3 5 3.1.9 SummaryofPresentationElements . 3 7 3.1.10 Mathematicsstyleattributescommontopresentationelements . 3 8 3.2 TokenElements 3 8 3.2.1 TokenElementContentCharacters, . 3 9 3.2.2 Mathematicsstyleattributescommontotokenelements 4 1 3.2.
42、3 Identier 4 5 4 ISO/IEC 40314:2016(E) ISO/IEC 2016 All rights reserved BS ISO/IEC 40314:2016 CONTENTS 5 3.2.4 Number . 4 6 3.2.5 Operator,Fence,SeparatororAccent . 4 7 3.2.6 Text . 6 0 3.2.7 Space 6 2 3.2.8 StringLiteral 6 4 3.3 GeneralLayoutSchemata . 6 4 3.3.1 HorizontallyGroupSub-Expressions 6 4
43、 3.3.2 Fractions 6 7 3.3.3 Radicals, . 6 9 3.3.4 StyleChange . 6 9 3.3.5 ErrorMessage 7 2 3.3.6 AdjustSpaceAroundContent 7 3 3.3.7 MakingSub-ExpressionsInvisible 7 8 3.3.8 ExpressionInsidePairofFences 8 0 3.3.9 EncloseExpressionInsideNotation 8 3 3.4 ScriptandLimitSchemata 8 5 3.4.1 Subscript . 8 6
44、3.4.2 Superscript 8 7 3.4.3 Subscript-superscriptPair 8 7 3.4.4 Underscript 8 8 3.4.5 Overscript . 8 9 3.4.6 Underscript-overscriptPair . 9 1 3.4.7 PrescriptsandTensorIndices, 93 3.5 TabularMath . 9 5 3.5.1 TableorMatrix 9 5 3.5.2 RowinTableorMatrix 9 9 3.5.3 LabeledRowinTableorMatrix 9 9 3.5.4 Entr
45、yinTableorMatrix .1 0 1 3.5.5 AlignmentMarkers, 1 0 1 3.6 ElementaryMath .1 1 0 3.6.1 StacksofCharacters .1 1 1 3.6.2 LongDivision .1 1 3 3.6.3 GroupRowswithSimiliarPositions 1 1 4 3.6.4 RowsinElementaryMath .115 3.6.5 Carries,Borrows,andCrossouts .1 1 5 3.6.6 ASingleCarry .1 1 6 3.6.7 HorizontalLin
46、e .1 1 7 3.6.8 ElementaryMathExamples .1 1 8 3.7 EnliveningExpressions 1 2 4 3.7.1 BindActiontoSub-Expression .1 2 4 3.8 SemanticsandPresentation 1 2 6 4 ContentMarkup 127 4.1 Introduction 1 2 7 4.1.1 TheIntentofContentMarkup 1 2 7 4.1.2 TheStructureandScopeofContentMathMLExpressions .1 2 8 4.1.3 St
47、rictContentMathML 1 2 8 4.1.4 ContentDictionaries .1 2 9 4.1.5 ContentMathMLConcepts .1 3 0 4.2 ContentMathMLElementsEncodingExpressionStructure .1 3 1 ISO/IEC 40314:2016(E) ISO/IEC 2016 All rights reserved BS ISO/IEC 40314:2016BS ISO/IEC 40314:2016 6 CONTENTS 4.2.1 Numbers 1 3 2 4.2.2 ContentIdenti
48、ers .1 3 8 4.2.3 ContentSymbols 1 4 0 4.2.4 StringLiterals .1 4 2 4.2.5 FunctionApplication 1 4 3 4.2.6 BindingsandBoundVariablesand .1 4 6 4.2.7 StructureSharing 1 4 8 4.2.8 Attributionviasemantics 1 5 0 4.2.9 ErrorMarkup .1 5 1 4.2.10 EncodedBytes 1 5 2 4.3 ContentMathMLforSpecicStructures .1 5 2
49、4.3.1 ContainerMarkup 1 5 3 4.3.2 Bindingswith .1 5 4 4.3.3 Qualiers .1 5 6 4.3.4 OperatorClasses .1 6 2 4.3.5 Non-strictAttributes .1 6 9 4.4 ContentMathMLforSpecicOperatorsandConstants .1 7 0 4.4.1 FunctionsandInverses 1 7 0 4.4.2 Arithmetic,AlgebraandLogic 1 8 0 4.4.3 Relations .2 0 0 4.4.4 CalculusandVectorCalculus 2 0 5 4.4.5 TheoryofSets 2 2 4 4.4.6 SequencesandSeries .2 3
