数式を省略して表示する方法の提案と検討 (数学ソフトウェアと教育 : 数学ソフトウェアの効果的利用に関する研究)
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1 (Hirokazu Murao) Graduate School of Information Science, University of ElectroCommunications (Yuji Kondoh) Department of Information Engineering, Kagawa National College of Technology ( ) (Noriko Hyodo) AlphaOmega Inc. ( ) (Tomokatsu Saito) AlphaOmega Inc. 1 iphone$/ipad$ ( $=$ ) ( ), J.Han(NYU Courant Institute) Perceptive Pixel ( ) 2 (Computer Algebra System. CAS) ( ) / ( ) Google Maps?
2 233 : : [11] 2 2 interaction( $=$ ) W (mathbox ) mathbox mathbox ( ) ltering TeXmacs : MathML[9] (OpenMath[5] ) XHTML (extensible HTML) ( ) XML MathML SVG XML XHTML modularization [10] CAS CAS GoogleMaps MathML XML
3 234 $\searrow$ $\searrow$ MKM, Calculemus, CICM, Math UI, OMW(OpenMath ) I.Stoyanova.H.Davenport OpenMath [7] M.Kohlhase $J$ C.Lange [3] Jacobs University, Bremen JOBAD [1] (active ) 2 ( ) ( ) composite HTML XML XHTML XML MathML active active mathbox
4 235 ma thbox mathbox ( ) mathbox mathbox filtering mathbox 3 CAS $I4Tffi$ 2 : ( ), ( ), ( ). :1 ( / ) ( $=$ ). MathML
5 MathML(3.0) Presentation Markup Content Markup WEB MathML [8] XML MathML 2 OpenMath presentation markup, content markup MathML 3.0 [9] 3 4 Presentation markup ( ) ( ) 2 (displaystyle scriptlevel. ) content markup markup Content markup semantics ( ) (content dictionary) OpenMath Markup 1 MathML 3.0 (bound $\Sigma_{i}$ var.: ) $i$ Content markup (rendering) XSLT( ) [4,6,2] MathML [9] 3 4 presentation markup $$ token :mi( ), mn( ), mo( ), mtext, mspace, ms( ) $$ general :mrow( ), mfrac, msqrt, mroot, mstyle( ), merror, mpadded, mphantom, mfenced, menclose $$ :msub, msup, msubsup, munder, mover, munderover, mmultiscripts $$ :mtable, mlabeledtr, mtr, mtd, maligngroup malignmark elementary math ffl: mstack, mlongdiv, msgroup, msrow, mscarrries, mscarry, msline maction content markup 1
6 237 $$ ci, cn, csymbol, cs, apply, bind, bvar, share, semantics annotation annotationxml, cerror, cbytes $$ / : ( : ) MathML presentation content 2 markup markup MathML markup MathML TR(Technical Report) 5 MathML2 Combining $\lrcorner$ Presentation and Content Markup present content markup 3.0 $Mixing$ Markup Languages for Mathematical $\lrcorner$ Expressions MathML (semantics annotation) MathML markup markup (OpenMath ) MathML presentation markup content markup markup semantics mixed markup, parallel markup annotation ( anno at $t$ $i$ on$>...$ $</$ annotat $i$on ) $>$ annotationxml ( amotat onxml /annotat onxml ), $i$ $>\ldots$ $i$ $>$ semantics ( emantics $s$ $>...$ $</s$ emant cs ) semantics $i$ $>$ presentation content (annotation) MathML annotation (key) (value) annotation/annotationxml semantics semantics MathML [9, \S 5.1] $F$ annotation/annotationxml semantics annotation Content Dictionary symbol annotation/annotationxml cd name symbol attribution semanticattribution role annotation ( ) mathmlkeys CD alternaterepresentation contentequiv
7 238 alternaterepresentation encoding annotation (MathML presentation, OpenMath, T (, Maple ) presentation&content markup [9, \S 5.3]: content presentation (1) token ci cn (2) $<$ $>$ $<$ $>$ csymbol (3) semantics 3 presentation content content wellformed presentation Parallel Markup [9, \S 5.4] markup semantics encoding annotationxml id xref semantics 4 mathbox! ( etc) ( ) $arrow$ ( ) ( 5 ) $arrow$ $$
8 239 ( ) mathbox 4.1 /symbol : / / / $...$ : : / / (... ) ( $n$ ) : /10 ( ) / 10 : / (10 ) / $($ $+\alpha)$ ( ) $+$ ( ) ( (?)) ( or ). : : : / : / : / :
9 $\star$ $\star$ (1)CAS (2) MathML MathML $(+$ $\alpha)$ (3) JavaScript MathML ( ) 3 rendering MathML presentation markup JOBAD ( ) Ajax content CAS : ( 2,3 ) (content ) presentation (content ) presentation content JSON ( $=$ ) content MathML content presentation $XSL/XSLT$ [9, A] XML RelaxNG Schema (DTD XML Schema ), CAS, : JOBAD(JavaScript API for OMDocbased Active Documents) [1] WEB mashup XHTML MathML UI 3 JavaScript module notation definition JOMDoc library content markup ( ) CAS MathML se mact on $>$ (actiontype $i$ lection ) $<$maction $>$
10 $\star$ 241 parallel markup: content presentation xref 6 iphone$/ipad$ composite (CAS, interaction active $)$ MathML XML (RelaxNG, XSL$/XSLT$, Ajax, DOM JavaScript) MathML presentation/content markup semantic annotation active JOBAD XSL$/XSLT$, RelaxNG Schema, DOM JavaScript ( / ) [1] J. Giceva, C. Lange, and F. Rabe. Integrating web services into active mathematical documents. In Intelligent Computer Mathematics: Calculemus $2009/MKM$ 2009, No in LNAI, pp , [2] The $W3C$ Math Working Group. Xslt stylesheets for mathml on the web. http: $// org$/math/$ XSL/.
11 242 [3] M. Kohlhase, C. Lange, and R. Rabe. Presenting mathematical content with flexible elisions. In OpenMath Workshop 2007, [4] E. Pietriga. Mathml content2presentation transformation (mathmlc2p). http: $//www$. lri. fr$/\sim pietriga/mathmlc2p/mathmlc2p$. html. [5] The OpenMath Society. The OpenMath standard. http: $//www$. openmath. $org/$ standard/. [6] The OpenMath Society. $xsl4mathml$ xsl stylesheets for MathML. http: //code. google. $com/p/xsl4mathml/$. [7] I. Stoyanova and J.H. Davenport. Towards intelligent summarising and browsing of mathematical expressions. In Mathematical UserInterfaces Workshop 2010, http: $//www$. act ivemath. org/workshops/mathui/10/. [8] $W3C$. Math home. http: $// [9] $W3C$. Mathematical markup language. http: $// org$/tr/mathml3/$. [10] $W3C$. Xhtml modularization. http: $// $ion/$. [11] 2 DEIM2010 C74, http: $//dbevent$. jpn. org/deim2010/proceedings/f $iles/c74$. pdf.
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