Multilingual mathematical e-document processing...Multilingual mathematical e-document processing Azzeddine LAZREK University Cadi Ayyad, Faculty of Sciences Department of Computer

Multilingual mathematical e-document processing

Azzeddine LAZREK

University Cadi Ayyad, Faculty of SciencesDepartment of Computer Science

Marrakech - Morocco

[email protected]://www.ucam.ac.ma/fssm/rydarab

Outline

1 Arabic writingFeatures

2 Arabic mathematical expressionsMathematical languagePracticesArabic mathematical notationInternationalization & Localization

3 Arabic mathematical document compositionProblemsNormalizationMathematical fontSymbols encodingTypesetting system

4 Arabic mathematical expressions on the webMathML I18n

5 Summary

OutlineArabic writing

Arabic mathematical expressionsArabic mathematical document compositionArabic mathematical expressions on the web

Summary

Features

Arabic alphabet

the direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs

Azzeddine LAZREK 3/25 Multilingual mathematical e-document processing



Summary

Features

Arabic alphabetthe direction of writing spreads out from right to left

input order rendering orderthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs




Summary

Features

Arabic alphabetthe direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initial

the cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs




Summary

Features

Arabic alphabetthe direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins characters

Arabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs




Summary

Features

Arabic alphabetthe direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desired

some letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs




Summary

Features

Arabic alphabetthe direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dots

some letters differ only by some parts of glyphs




Summary

Features

Arabic alphabetthe direction of writing spreads out from right to leftthe shape of a letter depends on its position in the word4 forms: isolated final median initialthe cursivity of the writing joins charactersArabic letters represent only consonants or long vowels.Optional diacritical marks for short vowels can be used toannotate text or spell it out in full when desiredsome letters differ only by the presence, the number and theposition of dotssome letters differ only by some parts of glyphs




Summary

Features

the punctuation marks present particularities of orientation andglyph

the letters can be superposed through ligatures as charactersthe letters can be stretched in a curvilinear way through thekashida, which is a curved elongation of charactersome letters and words can also be superposed as noncharactersseveral calligraphic styles can be in use.Shapes of letters, ligatures, calligraphic rules, . . . varyaccording to these styles




Summary

Features

the punctuation marks present particularities of orientation andglyphthe letters can be superposed through ligatures as characters

the letters can be stretched in a curvilinear way through thekashida, which is a curved elongation of charactersome letters and words can also be superposed as noncharactersseveral calligraphic styles can be in use.Shapes of letters, ligatures, calligraphic rules, . . . varyaccording to these styles




Summary

Features

the punctuation marks present particularities of orientation andglyphthe letters can be superposed through ligatures as charactersthe letters can be stretched in a curvilinear way through thekashida, which is a curved elongation of character

some letters and words can also be superposed as noncharactersseveral calligraphic styles can be in use.Shapes of letters, ligatures, calligraphic rules, . . . varyaccording to these styles




Summary

Features

the punctuation marks present particularities of orientation andglyphthe letters can be superposed through ligatures as charactersthe letters can be stretched in a curvilinear way through thekashida, which is a curved elongation of charactersome letters and words can also be superposed as noncharacters

several calligraphic styles can be in use.Shapes of letters, ligatures, calligraphic rules, . . . varyaccording to these styles




Summary

Features

the punctuation marks present particularities of orientation andglyphthe letters can be superposed through ligatures as charactersthe letters can be stretched in a curvilinear way through thekashida, which is a curved elongation of charactersome letters and words can also be superposed as noncharactersseveral calligraphic styles can be in use.Shapes of letters, ligatures, calligraphic rules, . . . varyaccording to these styles




Summary

Mathematical languagePracticesArabic mathematical notationInternationalization & Localization

Most electronic science, technical, engineering and medicaldocuments contain mathematical expressions.Since the renaissance, the mathematical language knew a deep andconstant evolution inside the western natural languages wheremathematical knowledge was produced. Typesetting improvementsfollowed, always in the same languages.That was not the same for the Arabic language. Throughout thisperiod where mathematical development was going with lingualevolution, Arabic mathematical language kept out of themathematical turning out. Countries who have developedmathematics got a mathematical language rooted in their naturallanguage. Arabic mathematical language stood as it was centuriesago until that modern mathematics came. Then, mathematics wasto be taught in foreign languages.Later, in some countries, the teaching of mathematics has beenpartially or totally arabizised.




Summary


There are many mathematical notations according to the regions:? Latin mathematical presentation as in English or French:

Symbols are then imported from one of these Europeanlanguages writing, according to the dominant culturalinfluence. Symbolic writing is then running in the oppositedirection of the natural language (text and expression areintermixed bidirectionally).

? Arabic mathematical presentation: Specific symbols are usedand the writing follows the direction of the natural languagehandwriting which is from right to left. Arabic presentationuses symbols coming from the Arabic alphabet. Other symbolscan be vertically reflected Latin symbols. The so-called Arabicor Arabic-Indic digits represent numbers.




Summary


? Latin mathematical presentation as in English or French:Symbols are then imported from one of these Europeanlanguages writing, according to the dominant culturalinfluence. Symbolic writing is then running in the oppositedirection of the natural language (text and expression areintermixed bidirectionally).





Summary


? Latin mathematical presentation as in English or French:Symbols are then imported from one of these Europeanlanguages writing, according to the dominant culturalinfluence. Symbolic writing is then running in the oppositedirection of the natural language (text and expression areintermixed bidirectionally).





Summary


Many difficulties in the learning of mathematics are due to theinefficiency of the code of communication, the writing:

Bi-directionality of writing: in handwriting, whenever a linebegins with an Arabic sentence followed by a Latinmathematical expression, it is necessary to know the length ofthis expression a-priori. Otherwise, the symbolic formulationwriting will overpass the sentence or at contrary it will standfar from.Reading symbols: if the pronunciation of a foreign abbreviationis done in conformity with the foreign language, then thecorresponding Arabic word will never be in use. If theabbreviation is done in Arabic, then there won’t be anyrelationship between what is written and what is said.Origins of symbols: the relationship between symbol’s shape andsymbolized concept’s name vanishes completely when the western symbolis used into the Arabic writing. Cohabitation of two punctuation systemswith identical functions.Azzeddine LAZREK 7/25 Multilingual mathematical e-document processing



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Summary






Summary


expressions spread from right to left

alphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbolsthere are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dots

or as i and ı

the alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbolsthere are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text one

instead ofno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbolsthere are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbols

for ∠abcseveral styles are used to extend the amount of symbolsthere are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbols

there are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbolsthere are two numeral systems

and 0123456789Arabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


expressions spread from right to leftalphabetic symbols used are with or without dotsthe alphabetic order uses in mathematics differs from text oneno cursivity is applied between adjacent alphabetic symbolsseveral styles are used to extend the amount of symbolsthere are two numeral systemsArabic abbreviations in use are composed through connectedletters with cursivity but without diacritic signs; with orwithout dots




Summary


superscript and subscript are on the left

for b2 b2

some symbols are mirroredsome literal symbols are usedthere are two punctuation systems

These differences are an additional source of difficulties formathematical documents composition tools in Arabic.Moreover, the use of a mathematical symbol can be localized.There can exist different local options to denote symbols. Both theprevious symbols and can denote the operator sum.




Summary


superscript and subscript are on the leftsome symbols are mirrored

with static symbol

with variable-sized symbolsome literal symbols are usedthere are two punctuation systems





Summary


superscript and subscript are on the leftsome symbols are mirroredsome literal symbols are used

with a curvilinear Kashida

instead of the linear onethere are two punctuation systems





Summary


superscript and subscript are on the leftsome symbols are mirroredsome literal symbols are usedthere are two punctuation systems

and 3, 14





Summary


superscript and subscript are on the leftsome symbols are mirroredsome literal symbols are usedthere are two punctuation systems

These differences are an additional source of difficulties formathematical documents composition tools in Arabic.Moreover, the use of a mathematical symbol can be localized.There can exist different local options to denote symbols. Both the

previous symbols and can denote the operator sum.




Summary


In a multilingual environment, allowing mathematical objects in Arabic to:Pedagogical goals

be composed in a perfect precision with high qualitybe adapted according to the areabe moderated according to the schooling levelbe personalized to handicapsbe translated between notationsbe computed and interacting for learning

Technical goals

separate content from several presentationsoffer several formats allowing exchange between softwarebe published on the webbe platform independent




Summary




Technical goals





Summary




Technical goals


Intend to encode mathematical expressions human legible and hand writablewith preserving all information.




Summary

ProblemsNormalizationMathematical fontSymbols encodingTypesetting system

Image based method

Quality: poor typographical qualitySize: big size files for storing or downloading

Reuse: mathematical expressions can’t be reeditedStructuring: mathematical information is not available for

searching, indexing, . . .Portability: mathematical expressions can’t be processed by a

computer algebra system nor a translation system

NeedsNormalizationMathematical fontSymbols encodingTypesetting system




Summary


Image based method

Quality: poor typographical qualitySize: big size files for storing or downloading

Reuse: mathematical expressions can’t be reeditedStructuring: mathematical information is not available for

searching, indexing, . . .Portability: mathematical expressions can’t be processed by a

computer algebra system nor a translation system

NeedsNormalizationMathematical fontSymbols encodingTypesetting system




Summary


Sources of the standards:handbooksconventions such as the Amman’s conventionstandards of the AMS and the ISOpractices of TEX and MathML




Summary


Creating a mathematical font is a complex artistic and technical task

RamzArabDesign and development of the OpenType font RamzArab thattries to meet, as far as possible, the requirements of:Homogeneity: designing symbols with the same feather for

homogeneous shapes, sizes, boldness, . . .Completeness: regrouping most of the usual specific Arabic

symbols in useOriginality: observing the most of practical calligraphic rules

.




Summary


CurExtConception of CurExt system designing some dynamic symbols.The parentheses and Kashida symbols are representative of thepossible cases of horizontal and vertical curvilinear extensibility.So, that can be easily generalized to other variable-sized symbols.A lengthening of the straight line is not in conformity with theArabic calligraphy rules.




Summary


UnicodeThe Unicode Standard provides a quite complete set of standardmathematical characters. There are a good deal of symbols foundin Arabic mathematical handbooks that are not yet part of theUnicode Standard and can’t be obtained through a simple mirroringnor through a simple implementation process. Some of such specialcharacters, designed in RamzArab, are proposed for inclusion intothe Unicode Standard and now are on discussion.Until their adoption by Unicode, the symbols used in these toolswill be located in the Private Use Area E000-F8FF in the BasicMultilingual Plane.




Summary


RydArabDevelopment of RydArab system as a TEX package. It preserves allthe distinguished qualities:

a full numerical compositiona high typographical qualityoffering several options to adapt it to areas and levelssame commands structure in order to automatize translationgenerating documents in several formats (DVI, PS, PDF)producing documents in format HTML with image basedmathematical expressionstowards transformation from/to OpenMath

⊗MathML




Summary

MathML I18n

Content MathML

Semantically, an Arabic mathe-matical expression has the samefunctionality as its Latin equiv-alent: same content MathMLtree skeleton but with differentcontent for token elements.




Summary

MathML I18n

Presentation MathML

Only rendering aspects needto be taken into account:same presentation MathML treeskeleton with different contentfor token elements is insuffi-cient.




Summary

MathML I18n

MathML extension

After examining all notational conventions, in current use withArabic, the following step is to clarify the specification of MathML,proposing extensions where needed, so that MathML has thebroadest coverage possible proposals:

Direction: the overall mathematical directionality should be determinedby a dir attribute on the outermost math element; which takes one ofthe values ltr or rtl. The text content of each token element should betreated as a separate directional segment and the bidirectional algorithmshould be applied to each independently

Additional Mathvariants: isolated, initial, tailed, looped,stretched and double-struck

Mirroring: codepoints for Arabic mathematical symbols are not availableyet, but appropriately marked for mirroring

Arabic specific notation: additional allowed value madruwb for thenotation attribute menclose of factorial symbol.




Summary

MathML I18n

MathML extension









Summary

MathML I18n

MathML extension









Summary

MathML I18n

MathML extension









Summary

MathML I18n

MathML CtoAPContent MathML is generally language-neutral. In contrary,presentation MathML necessarily targets a specific language andnotational conventions.After carrying out mathematical operations on content code, theusual situation is that the result is rendered.CtoAP is an XSLT stylesheet that converts a Content MathML toArabic Presentation MathML.There may be several notations for one concept in the Arabicmathematical notation to choose:




Summary

MathML I18n

Dadzilla

Dadzilla is a MathML browser for Arabic mathematicalpresentation. It is an adapted version of Mozilla. Already existingMathML elements can be used for both Latin and Arabicmathematical presentations after specifying the environment by thesingle attribute dir="rtl" in <math> element.To correctly display MathML documents in Arabic presentation,some fonts must be installed: Mirrored BaKoMa ComputerModern fonts & Adapted Arabic mathematical symbols fontRamzArab.The mathematical expression editor mathmled is integrated afterits adaptation for Arabic mathematical presentation.In the future version of Dadzilla, some improvements should bemade. In particular, using stretched Arabic alphabetical symbols,offering some localization choices and improving the interface. .




Summary

Conclusion

The ambitious project for the development of communication andpublication tools for Arabic scientific and technical e-documents inmultilingual environment presents many challenges. Our goal wasto identify the difficulties and limitations that can obstruct the useof existing tools for composing mathematics in Arabic presentation.

Arabic mathematical e-documents can be composed, structuredand published on the web using these developed tools. Thus, suchdocuments benefit from all the advantages of using available norms.

We hope that the previous proposals can help in finding suitablerecommendations for multilingual mathematics in appropriatestandards (Unicode, MathML, OpenMath, . . . ).




Summary

/ RamzArabAzzeddine LAZREK 23/25 Multilingual mathematical e-document processing



Summary

/ Dadzilla

.Azzeddine LAZREK 24/25 Multilingual mathematical e-document processing



Summary

/ Dadzilla


Documents

Multilingual mathematical e-document processing...Multilingual mathematical e-document processing Azzeddine LAZREK University Cadi Ayyad, Faculty of Sciences Department of Computer