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Prangle-D-Dissertati.. - Department of Computer Science

1. eene 46 6 2 2 Formalising a Phrase book etes 46 6 3 IHE FUTURE OPENMATH aia iet oa od 47 6 4 SUMMARY tr re e mat er ai en n e ot ree 47 BIBLIOGRAPNY u nement einen tiennent de 48 USER DOCUMENTATION erit nein sinn nein reae poke reet t 50 RAW RESULTS OUTPUT nn 54 CODE snm ee ettet Deve lira 59 11 An OpenMath based Unit Converter List of Figures FIGURE 1 OPENMATH ARCHITECTURE cccececaceusecaueusueaueusueaueusueaueuseuaueusaeaveusevaveusanas 5 FIGURE 2 EVOLUTIONARY DESIGN MODEL cccececeusecuueusucuuausueauausueauauseeauauseuavaunenas 22 FIGURE 3 MAIN SYSTEM STRUCTURE ococoncncononcncnnononcnnnnrncnanarnnnanarnananarnananarnananarnasa 30 FIGURE 4 MAIN SYSTEM GUI c ccceceseuseceseueeecvaueueauaususauaususeuaueueauauseuauauseeaveusanas 33 FIGURE 5 GUI TO DISPLAYING THE RESULT ccccceccceueeceuausueuvaususauaususauausueaueuseuavausenas 34 FIGURE 6 ADDING A CONTENT DICTIONARY cscececeueeccveusucuueususauauseeaueusueaueuseuaueunanas 35 FIGURE 2 TEST 1 RESULTS eio ae tae mcer en eer v c n e eee ea c a a a e c 55 FIGURES TEST 3 RESULTS en urn se dme en er a eva od nr de va o a roa e e n et 55 FIGURE 9 TEST 4 RESULTS ccccccccececausuccueususuuaueusaueusueauausueeuausueauausueaueuseeaueusanas 56 FIGURE 10 TEST 5 RESULTS ccccccececcceeceseueuecuaususauausueauaususaueuteuauauseuauauseuaueunanas 56 FIGURE 11 TEST 6 RESULTS sans ara eigen 56 FIGURE 12
2. Signed II An OpenMath based Unit Converter Abstract The OpenMath framework provides the protocol for interactive mathematics on the Internet this is done through the use of Content Dictionaries that store the semantic meaning of mathematical symbols This facilitates the transformation between the OpenMath representation and their corresponding internal representation within the application and as a result should increase the robustness of mathematical software This dissertation attempts to demonstrate the suitable of OpenMath as a basis for specialised applications In the marketplace there are a number of standard mathematical unit converters however I would like to analyse the efficiency of OpenMath as a platform for a mathematical unit converter OpenMath as a language is still very early in its development cycle and is yet to be utilised by the mathematical community By demonstrating OpenMath as a suitable foundation for a unit converter I hope to create an extensible unit converter and increase the use of OpenMath in future projects III An OpenMath based Unit Converter Contents esp gd gue c emo deheheRernes insg soeadnceadedesdsecdebests I LIST OF FIGURES eene een ei dee teet nn ne iS a aas seei aieeao II LIST OF TABLES sic ccccscictssteccesssecstsscceacsccescceysessnesdeccvaceeuesoasceceesesbonsssesdecseccocasssenssersecceseessessdecsuosanse IV ACKNOWLEDGEMENTS scscscsssscsssssssssssccssssssssce
3. 59 An OpenMath based Unit Converter Pressure ocd lt CD gt lt CDName gt pressure lt CDName gt lt CDStatus gt experimental lt CDStatus gt lt CDDate gt 2007 04 11 lt CDDate gt lt CDVersion gt 1 lt CDVersion gt lt CD lt CDName gt arith1 lt CDName gt lt CDName gt relationl lt CDName gt lt CDUses gt lt Description gt This CD defines symbols to represent pressure measurements lt Description gt lt CDDefinition gt lt Name gt pascal lt Name gt lt Description gt This symbol represents the measure of one Newton per square metre This is the standard SI measure for pressure lt Description gt lt CMP gt 1 pascal 1 newton per sqr metre lt CMP gt lt FMP gt lt OMOBJ gt lt OMA gt OMS name eq cd relationl gt lt OMA gt OMS name times cd arith1 gt lt oMI gt 1 lt OMI gt OMS name pascal cd pressure gt lt OMA gt lt OMA gt OMS name times cd arith1 gt lt oMI gt 1 lt OMI gt OMS name newton per sqr metre cd pressure gt lt OMA gt lt OMA gt lt OMOBJ gt lt FMP gt lt CDDefinition gt lt CDDefinition gt lt Name gt pound per sqr metre lt Name gt lt Description gt This symbol represents the measure of one Pound per square metre This is the standard SI measure for pressure lt Description gt lt CMP gt 1 pound per sqr metre 4 4483 pascal lt CMP gt lt FMP g
4. 6 1 If a file you are attempting to add is not a content dictionary return the appropriate error 18 An OpenMath based Unit Converter 10 11 6 2 If two selected units are not a compatible conversion error handle accordingly 6 3 If any of the required details are not entered before the convert button is pressed return an error Finalise the Process 7 1 When a conversion is carried out the result should be clearly displayed for the user and the system should be ready to carry out another conversion Time to start up 8 1 When the system is turned in it should take no longer than 15 seconds till it is fully operational and all the functionality that it provides is available to the user Time to execute user commands 9 1 When the user instructs the system to perform an operation the system should begin that operation immediately The operation should have provided the user with the desired result within 2 seconds of the user executing the command Reliability 10 1 When the user instructs the system to perform an operation the system should begin that operation immediately The operation should have provided the user with the desired result within 2 seconds of the user executing the command Robustness 11 1 The system should be able to run for long periods of time without failing and causing the user disruption 11 2 The system should recover from failure in under 15 seconds In the event that the system
5. double dblBase double Integer parseInt srcBase double norm normalise srcVal dblBase invOp 27 An OpenMath based Unit Converter The difference comes when the source unit operator is then passed into the invertOp method this is a straightforward method that returns the opposite of the operator you passed into it public static String invertOp String operator if operator equals times return divide if operator equals divide return times if operator equals add return minus if operator equals minus return add return unknown Finally the amount to convert source unit value and inverted operator are passed into the normalise function public static double normalise double srcVal double baseVal String operator if operator equals divide return srcVal baseVal return 0 This function will apply the inverted operator on the amount you wish to convert and the source unit value By doing this it means that no matter what the source unit value may be it has been catered for leaving a simple method to finish the conversion process Example If I wanted to convert 10 feet into metres The content dictionary defines the conversion as 1 times foot equals 0 3048 times metre but equally it could be defined as 2 times foot equals 0 6096 The normalise function will do e 10 1 10 which will then be times by 0 3048 in the final method e 10 2 5 which will then be time
6. ccscscsssssscsscscscsssssscsscsccessasscsseecacssssescescacacessacscsscecacessares 21 4 1 DESIGN amp IMPLEMENTATION PROCESS in 22 4 2 CREATING AN OPENMATH CONTENT DICTIONARY us 22 An OpenMath based Unit Converter 4 2 1 Anatomy of a Content Dictionary 23 4 3 WHE SIMPLE CASE unicas dle dos 25 4 3 1 Reading in a Content Dictionary 25 4 3 2 Extracting a list of relevant Conversions 26 4 3 3 Searching the List of Nodes s 26 4 3 4 Extract the Deals ie s de Gare E ido ti 27 4 3 5 Carry out the Conversion iii 29 4 4 HIGHILEVEL DESIGN terrm ene e EROR ele ie e ERGO OR 29 4 4 1 Carrying out longer transformations 3l 442 Developing a CU a ce bm st e eade 33 443 Adding Multiple Dictionaries tette 35 444 Reading Searching multiple dictionaries 37 TESTING amp RESULTS ire Rete te aH Ree ne none in teen nn intenses nee 38 Sl OTESTAPLANS n eee EGET Re o UP o ER M ete n 39 5 2 TESTING FUNCTIONAL REQUIREMENTS sen 39 5 3 TESTING NON FUNCTIONAL REQUIREMENTS sise 41 5 3 1 Usability Study im cg tte da Eee SL ABI bene 41 5 3 2 Usability Study RESUIES ui 42 5 3 3 T SUNG SUPUTIGIV is ete SS 42 CONCLUSIONS CAR en AO RT 44 6 1 PROJECT CRITIQUE cists es none ihren 45 6 2 THE FUTURE THE UNIT CONVERTER ener nnne 46 6 2 1 Writing Content Dictionaries
7. Element srcOma Element XPath selectSingleNode el OMA OMS name srcUnit Element dstOma Element XPath selectSingleNode el OMA OMS name dstUnit 4 3 4 Extract the Details Now the required elements have been established I need to extract all of the information about the destination unit so the conversion can be carried out It is simple a case of applying XPaths to the element dstOma extracting the conversion operator as an attribute and the conversion value as an element which then needs to be cast from a String to a Double String dstOp Attribute XPath selectSingleNode dstOma OMS name getValue String dstBase Element XPath selectSingleNode dstOma OMI getValue trim dblBase double Integer parseInt dstBase InvertOp Previously I stated that the content dictionary defined the conversion between feet and metres as 1 times foot equals 0 3048 times metre This posses a problem because there is no guarantee that it will always be 1 times the source unit To solve this problem I had to gather the source unit information in the same manner as with the destination unit details as you can see the same XPaths as before are used to extract the source operator as an attribute and the source unit value as an element String invOp invertOp Attribute XPath selectSingleNode srcOma OMS name getValue String srcBase Element XPath selectSingleNode srcOma OMI getValue trim
8. lt OMA gt lt OMOBJ gt lt FMP gt lt CDDefinition gt As I have previously stated one of the main advantages of XML is that it is designed to be both human and machine readable although a great deal of the content dictionary is simple to understand for completeness I will run through want each section The previous example shows how to derive metres from feet It states that 1 times foot equals 0 3048 times metre most content dictionaries definitions follow the same format lt CDDefinition gt Element This defines the starting point at which a definition will come together for a conversion 23 An OpenMath based Unit Converter lt Name gt Element This simply defines the name given to the conversion that is about to be formalised lt Description gt Element This is a standard written description of what conversion is about to be defined lt CMP gt Element The CMP stands for the Commented Mathematical Properties This is another written description of the conversion but in a more formalized manner lt FMP gt Element The FMP stands for the Formal Mathematical Properties This is where the formalized mathematical definition of an element is included in the dictionary lt OMOBJ gt Element The OMOBJ element defines an OpenMath Object Formally an OpenMath object is a labelled tree whose leaves are the basic OpenMath objects integers IEEE double precision floats unicode strings byte array
9. not crash and was still operational 5 3 Testing Non Functional Requirements The non functional requirements specify those requirements that cannot be precisely measured by success or failure they are subjective For this reason testing in real world environments and user feedback often plays a key part in the validation of non functional requirements 5 3 1 Usability Study There are a number of different ways to carry out a usability study I decided to carry out some short exercises with a sample of possible users Ten people were given the user guide and asked to play with the system for five to ten minutes To ensure the users tested all aspects of the system they were given a small list of tasks they were asked to complete add at least one content dictionary carry out at least one successful conversion and try to break the system They were then asked to give it a mark out of ten for e How simple and easy to use the front end is e How useable they felt the system is Although the design and completeness of the user interface was always secondary in importance to the process of converting units using OpenMath the results of the usability study were still important because even the most advanced unit converter is pointless without a means to interact efficiently with it 41 An OpenMath based Unit Converter 5 3 2 Usability Study Results After all ten users had tested my system the results came out as follow Table 1
10. source unit and destination unit all need to be considered The system will have to search through the content dictionaries to match the source and destination units with a valid definition and use that information to carry out the conversion 3 1 4 Searching Content Dictionaries When a conversion is carried out by the user the system will need to search through the bank of content dictionaries to ensure firstly the conversion is possible and secondly how the conversion will be carried out This will need to work for a number of content dictionaries and shouldn t be constrained by the layout or design of any particular dictionary It may well be the case that for some conversions there is not a direct mapping from the source unit to the destination unit In this case is will be necessary for the system to search through multiple content dictionaries to create a chain of conversions in order to find a route from the source to the destination unit 3 1 5 Adding New Libraries Having reviewed a number of unit converters on the Internet it was quite apparent that they all had limitations when it came to the number of units it is possible to convert between When carrying out the literature review quite a few advantages of OpenMath were highlighted the central reason for using OpenMath as a foundation for a specific application is that it is extensible It is essential that the system be able to add new content dictionaries the content dictionaries
11. JPanel new FlowLayout Dave fc new Dave new File this Box box Box createVerticalBox box add Box createRigidArea new Dimension 0 10 box add fc pane add box setSize 500 370 setLocation 400 200 setContentPane pane public void launchFrame setVisible true private class Dave extends JFileChooser FileChoose chooser public Dave File f FileChoose chooser super f this chooser chooser public void approveSelection I the selected file is a directory open it if getSelectedFile isDirectory setCurrentDirectory getSelectedFile else Otherwise check to make sure the last 4 digits are ocd if so add the CD to the system String filename getSelectedFile toString int filenameLength filename length if filenameLength lt 4 filename substring filenameLength 4 filenameLength equalsIgnoreCase ocd 62 An OpenMath based Unit Converter If the last 4 digits are not ocd display an error message JOoptionPane showMessageDialog null Error Please add a valid Content Dictionary else Unit Converter addcd getSelectedFile chooser dispose public void cancelSelection chooser dispose 63 An OpenMath based Unit Converter Unit_Converter java import java util import java net import java io import
12. McLaughlin B 2001 Java amp XML 2 Edition United States O Reilly 8 Associates Inc 48 An OpenMath based Unit Converter e Neimeyer P Knudsen J 2005 Learning Java 3 Edition United States O Reilly Media Inc e OpenMath Consortium 1999 The OpenMath Project Final Report Available at http www openmath org projects esprit final index html e Piroumian V 1999 Java GUI Development United States Sams Publishing e Seppala M 1995 Report of OpenMath Activities Editing and Computing Available at http www openmath org projects EditingAndComputingReport pdf e Sommerville I 2001 Software Engineering 6 Edition United States Addison Wesley e Stiller E LeBlanc C 2002 Project Based Software Engineering United States Addison Wesley e Van Der Vlist E 2002 XML Schema United States O Reilly amp Associates Inc e Walsh N 1998 A Technical Introduction to XML Available at http www xml com e W3C 2005 Document Object Model DOM Available at http www w3 org DOM e Yu Terrance 1998 Poly Math Available at http pdg cecm sfu ca openmath0 5 lib phrasebook html 49 An OpenMath based Unit Converter Appendix A User Documentation 50 An OpenMath based Unit Converter 51 An OpenMath based Unit Converter 52 An OpenMath based Unit Converter 53 An OpenMath based Unit Converter Appendix B Raw results output 54 An OpenMath based Unit Converter Figure 7 Test 1 R
13. Search CD for the new units available add them to the GUI 35 An OpenMath based Unit Converter The add new library button also has an ActionListener when this button is pressed a new instance of the class FileChoose launches This opens a new JPanel that contains a JFileChooser a JFileChooser provides a simple mechanism for the user to choose a file ES Look In 3 vo FE ms 1 File Name Files of Type AI Files x Open Cancel The file chooser works in the standard manner the user can search through the directories and when they have found the required content dictionary can use the Open button to load it into the system When the Open button is pressed the approveSelection method is called Once the file chooser has verified that the file selected is not a directory it will then check the length of the filename and last 4 digits This is a verification process that checks to ensure the file selected is a content dictionary the last 4 digits of a content dictionary should always be ocd A check for ocd at the end of the file means if the user has selected the wrong type of file the system can return and error and the user can try again See the code over page 36 An OpenMath based Unit Converter int filenameLength filename length if filenameLength lt 4 filename substring filenameLength 4 filenameLength equalsIgnoreCase ocd JOptionPane showMes
14. TEST 7 RESULTS ei ne dida 57 FIGURE 13 TEST 8 RESULTS d is fo ed o da 57 FIGURE 14 TEST 9 RESULTS cccccccecescueuccueususaueusueauausueauaususaueutecauausueauauseuaueusanas 57 FIGURE 15 TEST 10 RESULTS ccccccccsseccscuseccvaueueauausueauaususauaueaeaueusueaueusevaveusanas 58 111 An OpenMath based Unit Converter List of Tables TABLE 1 USABILITY STUDY RESULTS iv An OpenMath based Unit Converter Acknowledgements I would like to thank Professor Davenport and the rest of the computer science department both staff and students for all of their help and guidance I would also like to say thank you to my family and friends their relentless support really pulled me through Thank You An OpenMath based Unit Converter Introduction An OpenMath based Unit Converter The Internet is growing rapidly and as a result is bringing around some exciting opportunities in the computing community People are able to communicate at a much faster rate and as the Internet becomes an ever increasing part of our everyday lives access to particular fields of interest is greatly improved OpenMath is one of those fields as a language it is relatively young development was started just 13 years ago Due to the relatively minute amount of research made into OpenMaths it is highly under utilised research to date has mainly been focusing on the improvement of the language and as a result the development of OpenMath is yet to manifes
15. Using the front end add a number of different content dictionaries from the OpenMath website Expected Result The content dictionaries should be added to the system and all of the expected units are made available for conversions Successful No Some of the content dictionaries where not compatible with the system as a result the units were added but the conversions are not available Test 3 4 8 5 Requirements 2 amp 7 Carry out conversions using just one content dictionary achieving a 99 success rate Test Carried Out Using 1 as the conversion amount converted between Pascal and Newton s per square Metre Pascal and Pound s per square Metre Pascal and Pound s per square Foot Expected Result The answer should return for each conversion respectively Successful Yes see Figures 5 2 5 3 5 4 in Appendix B 39 An OpenMath based Unit Converter Test 6 Requirement 3 Carry out conversions using multiple units achieving a 99 success rate Test Carried Out Using 1 as the conversion amount converted between Miles and Metres Expected Result Although this conversion isn t formally defined it should use feet as an intermediate step the answer should return for the conversion Successful Yes see Figure 5 5 in Appendix B Test 7 Requirements 4 amp 8 Provide a simple front end that collates all of the functionality of the system Test Carried Out Run the System Expected Result The front end should appear within 2 seconds
16. given a project of this type DOM is definitely a more suitable choice 2 2 2 DOM The Document Object Model DOM is a tree structure based parsing API and part of W3C recommendation SAX provides access to data during the parsing process whereas DOM has the facility to provide access to the data both during and after the parsing process 2 2 3 JDOM JDOM is a Java based Document Object Model for XML that integrates with DOM and SAX and uses parsers to build the document Similarly to DOM JDOM provides the tree structure representation of XML documents JDOM has been developed specifically for Java and is often more convenient as it requires less coding in purely Java applications as my project will focus on Java 1 have decided to use JDOM 11 An OpenMath based Unit Converter 2 3 Existing Projects OpenMath is still in its early stages of development and as a result there are very few projects utilising it 2 3 1 OpenMath Browser This project attempted to demonstrate the possibility of constructing an automatic query system which can benefit both human readers and Phrasebooks or other OpenMath aware applications that need to access content dictionaries remotely The implemented system was developed as a Java XML Web Application and comprised of two parts e One part of the system was based on SOAP and handled queries from applications e The second part was based on Cocoon XSP and handled queries from human readers The two part
17. manipulate the content dictionaries to draw on a result for a conversion requested by the user The main strength of OpenMath is that applications can be used which can handle every Content Dictionary or a changeable number of Content Dictionaries perhaps after being sent Content Dictionaries in some way Buswell at al 2004 This is the main reason OpenMath was decided upon as a foundation There are a number of unit converters written in many different languages that are readily available on the Internet by not using OpenMath the converters have limitations Current converts in the marketplace can only carry out conversions that have been written into the system OpenMath is extensible by basing a converter on OpenMath it means any number of content dictionaries can be added to the program at any time these new Dictionaries can then be used to carry out more conversions An OpenMath based Unit Converter 2 Literature Survey An OpenMath based Unit Converter 2 1 An Introduction to OpenMath OpenMath as a language was formalized in The OpenMath Standard Caprotti et al 2004 2 1 1 OpenMath The Background OpenMath is a standard for representing mathematical data in as unambiguous a way as possible it can be used to exchange mathematical objects between computer programs stored in databases or published on the worldwide web Caprotti 2004 It is tightly focused on representing semantic information and is not intended to be
18. operator equals divide 64 An OpenMath based Unit Converter return srcVal baseVal return 0 Carry out the final operation public static double apply double argl double arg2 String operator if operator equals times return argl arg2 return 0 Find the value within the Element whether thats the source or destination Element public static double getValue Element oma Search the OMA for the element value this method makes it independent of whether it s a float or integer try Element ele String value Integer le Element XPath selectSingleNode oma OMI if ele null Trim the content dictionary value value ele getValue trim return double Integer parselnt value Float le Element XPath selectSingleNode oma OMF if ele null value ele getValue trim return double Double parseDouble value catch Exception e return 0 0 Do the maths public static double convert Element el String sourceUnit String destinationUnit double value double result 0 0 try Search the list to find the section that focuses on the srcUnit amp dstUnit Match the Source and Destination values 65 An OpenMath based Unit Converter Element srcOma Element XPath selectSingleNode el OMA OMS fname sourceUnit Element
19. org jdom import org jdom xpath import org jdom output XMLOutputter import org jdom input SAXBuilder import java awt import java awt event import javax swing import javax swing border public class Unit Converter extends JFrame implements ActionListener Initialise global variables public static JFrame frame new JFrame public static JPanel screen new JPanel new FlowLayout public static JTextField convertAmount new JTextField 1 public static JComboBox convertFrom new JComboBox public static JComboBox convertTo new JComboBox public static JButton processButton new JButton Add public static JButton convertButton new JButton Convert po static JFileChooser addNewLibrary new JFileChooser new File public static java util List files new LinkedList Add the new Content Dictionary to the current list public static void addcd File f files add f toString readCD f toString Invert the operator applied to the srcUnit public static String invertOp String operator if operator equals times return divide if operator equals divide return times if operator equals add return minus if operator equals minus return add return unknown Carry out the operator applied to the srcUnit public static double normalise double srcVal double baseVal String operator if
20. store all of the conversion details and by being able to add further content dictionaries to the system it will provide more possible conversions In theory as OpenMath grows as a language more content dictionaries will be produced hence increasing the conversions available in the converter Secondly when the content dictionaries are added to the system it is essential that the new units are made available to the user This is a similar process to when a conversion is carried out but rather than extracting the conversion details the unit details will need to be gathered and added to the interface 3 1 6 User Interface It should be noted that at this point the design and completeness of the user interface is secondary in importance to the process of converting units using OpenMath As I am using OpenMath as the foundation of the unit converter the 16 An OpenMath based Unit Converter back end is going to be very different to that of the unit converters currently available hence there was very little merit behind me carrying out a thorough review of existing products However even the most advanced unit converter is pointless without the means to interact efficiently with it A graphical interface will be design and implemented but some attention to styling will be sacrificed in order to allow additional effort to be placed upon the primary focus of the project 17 An OpenMath based Unit Converter 3 2 Requirements Specification
21. systems cutting and pasting for use in different contexts testing to see if mathematically sound increasing document interaction 2 1 2 1 The Architecture Within OpenMath there are three layers of representation of a mathematical object The first is the internal representation used by an application the private layer The second is an abstract layer this is the representation as an OpenMath object these two layers may in some cases be the same The third is a communication layer that translates the OpenMath object representation into a stream of bytes An application dependent program manipulates the mathematical objects using its internal representation it can convert them to OpenMath objects and communicate them by using the byte stream representation of OpenMath objects shown below Figure 1 OpenMath Architecture Program A Program B A Specific B Specific Representation Representation Phrasebook A Phrasebook B CDs CDs A Specific A Specific Representation Possible Object Representation Shortcut OpenMath Encoding OpenMath Encoding A Specific A Specific Representation General Transport Representation Layer XML or Binary 5 An OpenMath based Unit Converter 2 1 2 2 Content Dictionaries Content Dictionaries CDs are central to the OpenMath philosophy of transmitting mathematical information they actually hold the meanings of the objects being transmitted For
22. the core conversion details a phrase book could then be used to produce the content dictionary on their behalf 6 2 2 Formalising a Phrase book Suppose you have two applications communicating by sending OpenMath objects to each other a client program and a computational server It is very unlikely that the applications internal data structure will be OpenMath hence translations between the internal representation and OpenMath are going to have to take place The piece of software that does this is usually called the phrase book 46 An OpenMath based Unit Converter It is possible to write a phrase book which can handle any piece of OpenMath in practice this means you can write an OpenMath phrase book that will handle a fixed set of content dictionaries and symbols What handle means will vary from case to case in my system it attempts to evaluate the input and return a result or an error At present my system is interpreting content dictionaries using a standard XPath location This enables access to a number of different units and conversions but only those of the same format If I were to continue developing this project the main area worth developing is to write a formal phrase book Within the phrase book I would be able to define a number of ways of interpreting the content dictionaries and in doing so I would be able to access a great deal more conversions increasing the extensibility of the converter 6 3 The Future OpenM
23. the requirements validation will ensure that the requirements specification satisfies the original problem and that all requirements are complete consistent verifiable and realistic 3 1 Requirements elicitation and analysis 3 1 1 Methodology The requirements elicitation will focus on a few primary sources of requirements Firstly a number of requirements can be drawn from the core goals identified in the Literature Survey Furthermore the literature survey has enabled me to review previous OpenMath projects and existing unit converters in the marketplace by examining the flaws within these systems 1 will be able to draw upon further requirements and constraints for my system 3 1 2 Hardware and Software Considerations Most unit converters have been made available on the Internet this is because they do not require a great deal of processing power and the Internet acts as a gateway to the largest concentration of users It is important to note a few things firstly for the converter to compete in the existing marketplace it should be easily transferable to become an Internet application and it should run on most standard PC s The system is going to be written in XML and Java on a 4 year old laptop running a Pentium 4 processor so no obvious issues should arise with respect to these requirements 15 An OpenMath based Unit Converter 3 1 3 Carrying out Conversions When a user attempts to carry out a conversion the amount to convert
24. 2 corresponds to 1 2 e Binding Is constructed from an object a sequence of zero or more other variables followed by another object The first object is the Binder Example binding lambda x application plus x 2 corresponds to x x 2 e Attribution Decorates an object with a sequence of one or more pairs made up of an OpenMath symbol the attribute and an associate object the value of the attribute The value of the attribute can be an attribute itself An OpenMath based Unit Converter Example attribution attribution A S A ShAn Sh 1Ah 1r SnAn S equivalent to attribution A S A SpAn Sh 1Ah 1 SnAn e Error Is made up from an OpenMath symbol and a sequence of zero or more OpenMath objects Interesting Note OpenMath objects do not specify any computational behaviour they merely represent mathematical expressions The OpenMath philosophy is to leave an application to decide what it does with an object once it has received it OpenMath is not a query or programming language Because of this OpenMath does not prescribe a way of forcing evaluation or simplification of objects Thus the same object 2 3 could be transformed to 5 by a computer algebra system or displayed as 2 3 by a typesetting tool 2 1 2 6 Symbols A symbol is used to construct an OpenMath object if it is the first child of an OpenMath application binding or error object or an even indexed child of an attribution
25. 3 2 1 Functional requirements The functional requirements are a specification stating what the system will and won t do the system will 1 Be able to add new content dictionaries to the system 1 1 Search and add content dictionary via the front end Simple Case 2 1 Carry out conversions using just one content dictionary achieving a 99 success rate 2 1 1 Search through a content dictionary to find a conversion that matches the given source and destination units 2 1 2 Extract the corresponding conversion amount from the content dictionary 2 1 3 Interpret the conversion and apply it to the figure the user inputted Complex Case 3 1 Carry out conversions using multiple units achieving a 99 success rate 3 1 1 Search through all content dictionaries to find conversions that include the source unit 3 1 2 If a direct conversion is not available carry out an intermediate conversion 3 1 3 Continue the loop taking the intermediate destination unit as your new source unit until the requested destination unit is reached Provide a simple front end that collates all of the functionality of the system Display all available units on the front end 5 1 When the system is initially ran it should search through all existing content dictionaries to add the units to the front end 5 2 When adding new content dictionaries the system must make the new units available as source and destination units on the front end Error Handling
26. An OpenMath based Unit Converter David Prangle Batchelor of Science in Computer Science with Honours The University of Bath May 2007 An OpenMath based Unit Converter This dissertation may be made available for consultation within the University Library and may be photocopied or lent to other libraries for the purposes of consultation Signed An OpenMath based Unit Converter An OpenMath based Unit Converter Submitted by David Prangle COPYRIGHT Attention is drawn to the fact that copyright of this dissertation rests with its author The Intellectual Property Rights of the products produced as part of the project belong to the University of Bath see http www bath ac uk ordinances intelprop This copy of the dissertation has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the dissertation and no information derived from it may be published without the prior written consent of the author Declaration This dissertation is submitted to the University of Bath in accordance with the requirements of the degree of Batchelor of Science in the Department of Computer Science No portion of the work in this dissertation has been submitted in support of an application for any other degree or qualification of this or any other university or institution of learning Except where specifically acknowledged it is the work of the author
27. Successful Yes see Figure 5 6 in Appendix B Tests 8 9 amp 10 Requirement 6 Error Handling Test Carried Out Attempt to carry out a conversion without a conversion amount filled in Expected Result An error should be returned Successful Yes see Figure 5 7 in Appendix B Test Carried Out Attempt to add a Word file instead of a content dictionary Expected Result As the file is not a valid content dictionary an error should be returned Successful Yes see Figure 5 8 in Appendix B Test Carried Out Carry out a conversion between Metres and Pascal Expected Result The conversion is not possible so an error should be returned Successful Yes see Figure 5 9 in Appendix B Requirements 9 amp 10 Time to execute user commands amp Reliability 40 An OpenMath based Unit Converter Test Carried Out All of the above Expected Result All of the tests should be successful and the operation should have provided the user with the desired result within 2 seconds Successful Yes Requirement 11 Robustness Test Carried Out Keep the system running for 5 hours carrying out a number of different tests including failure cases Expected Result All of the tests should run successfully and in the failure case the system should recover and be operational within 15 seconds Successful Yes the only test that went wrong was when adding certain content dictionaries Although the dictionaries failed to add properly the system did
28. Usability Study Results User No 1 2 3 4 5 6 7 8 9 10 Front End 10 8 8 9 10 9 8 9 10 8 8 Usability 10 8 7 8 9 8 7 8 7 8 9 The final results were e How simple and easy to use the front end is 8 7 10 e How useable they felt the system is 7 9 10 Verbal discussions with the different users did not raise any major issues with the design and usability of the front end Most felt that the system itself was simple enough to navigate and given the user guide as a backup they couldn t foresee any major problems occurring The reason the usability had a slightly lower score compared with the actual design was because of the error reporting Not all of the content dictionaries are compatible with the system and when a non compatible content dictionary is added there was often some confusion because the user is not made aware of this 5 3 3 Testing Summary The original goal of this project was to create a system that would demonstrate OpenMath as a suitable foundation for a unit converter and in turn create an extensible unit converter the requirements specification firmly defined these parameters The majority of tests carried out on my functional requirements were a success the testing demonstrated that the system could carry out conversions and add content dictionaries hence increasing the number of conversion available Despite the fact that that the non functional requirements
29. ajor number is increased the revision number is normally reset to zero 6 Astatus which can be e Official approved by the OpenMath society e Experimental under development and thus liable to change e Private used by a private group of OpenMath users e Obsolete kept only for archival purposes 7 ACD base which when combined with the CD name forms a unique identifier for the Content Dictionary It may or may not refer to an actual location from which it can be retrieved 8 Aseries of one or more symbol definitions An OpenMath based Unit Converter 2 1 2 3 Writing Content Dictionaries The symbols contained in a content dictionary form the mechanism by which OpenMath achieves its goal of being an extensible framework for exchanging semantically rich representations of mathematical objects Davenport 2000 The motivation for writing a new CD would be that there are some semantics that one wishes to exchange When writing a new content dictionary you need to ensure that e There must be a new piece of semantic information to convey e It must be possible to informally write down the semantics that the author of the CD intends to convey e There must be a motivation for wishing to convey the information in a content dictionary An excellent example of this would be to define further units that could then be used in the unit converter A well written content dictionary should contain Examples Every symbol defined in a CD should h
30. arch is called again to try and find a conversion from N string to the original dstUnit double val search N string dstUnit newSrcVal visited if val 999 return val 67 An OpenMath based Unit Converter catch Exception e System err println e return 999 Do a check to see if the unit is in the visited array list This means it should be ignored public static boolean beenVisited ArrayList visited String unit for int k 0 k lt visited size k if visited get k equals unit return true return false read new Content Dictionaries into the converter public static void readCD String nameCD try Read in the file SAXBuilder parser new SAXBuilder Document cd parser build nameCD Extract the information from the correct path and add the names to the Arraylist XPath x XPath newInstance CD CDDefinition FMP OMOBJ OMA OMA OMS 2 Qname java util List nodes x selectNodes cd ArrayList allNodes ArrayList nodes Search through the list removing any duplicates for int k 0 k lt allNodes size k String name Attribute allNodes get k getValue for int d k 1 d lt allNodes size d String compare Attribute allNodes get d getValue if compare equals name allNodes remove d allNodes trimToSize convertFrom addItem name con
31. are harder to test than the functional requirements they were also deemed to have been met The usability study demonstrated that after a host of different users tested the system they felt that the front end and system usability were both more than adequate 42 An OpenMath based Unit Converter The main problem highlighted during both rounds of testing was the fact that not all content dictionaries are compatible with the system this is discussed further in the conclusion 43 An OpenMath based Unit Converter Conclusions 44 An OpenMath based Unit Converter 6 1 Project Critique At the beginning of this project the task set to me was to research the OpenMath language and investigate its suitability as the foundation for an extensible unit converter This broke down into two major sections the inclusion of content dictionaries into the system and evaluating the input to return the answer or an error I set out studying OpenMath as a language and given my lack of knowledge on OpenMath and XML followed what 1 deemed to be quite a sensible development process By carrying out my implementation in an evolutionary manner it meant that as I developed the system I could learn about some of the more advanced features and incorporate them in the system at a later date The main draw back of an evolutionary approach is that it can be very easy to lose control of the development process By carrying out quite an informal approach to evol
32. ath OpenMath avoids defining what the right behaviour is in a given circumstance and leaves that up to the phrase book writer it is also possible that a piece of software could have multiple phrase books associated with it for different purposes The OpenMath Society 2006 This means that a whole host of different systems can be produced that utilize a mixture of content dictionaries There are a number of different content dictionaries already written and available on the Internet that cover a variety of topics A good example of this is the dimensioni content dictionary This content dictionary defines units such as length area velocity time speed etc These content dictionaries really highlight the advantages of OpenMath using a phrase book that can interpret these content dictionaries a mathematical tutor or teaching aid could be produced A mathematical tutor would be able to read the content dictionaries and return the relations in a more legible manner furthermore the content dictionaries can be used to work out the result of equations for the user For Example given the length and time travelled the system can work out the acceleration 6 4 Summary OpenMath as a language is highly underutilised it is an excellent way of formally defining the semantics of and relations between mathematical objects and as a result I can see the use of the language increasing greatly over the coming years Due to the way that OpenMath is formalise
33. atic boolean beenVisited ArrayList visited String unit for int k 0 k visited size k if visited get k equals unit return true return false i For this process to work successfully before the search method calls itself to start another iteration the source unit needs to be added to the visited array 32 An OpenMath based Unit Converter 4 4 2 Developing a GUI Having reviewed some of the existing unit converters in the marketplace I was not going to spend a great deal of time producing the GUI The GUI has a few basic requirements e Must be able to enter a number e Must be able to select a source and destination unit to convert e Must have a button for carrying out the conversion e Must have a button to add content dictionaries e Must have a way of presenting the conversion answer Figure 4 Main system GUI PENNE nm Convert A Unit The OpenMath Way Convert From DIE Add A New Library public static JTextField convertAmount new JTextField 1 public static JComboBox convertFrom new JComboBox public static JComboBox convertTo new JComboBox public static JButton processButton new JButton Add public static JButton convertButton new JButton Convert I toyed with a variety of approaches for the GUI but felt the best approach would be to keep it as simple as possible The processes of carrying out a conversion could 33 An OpenMath based Unit Converter no be easie
34. ave at least one example either as such i e Example or via an FMP which uses it In general FMPs are more useful because formal systems can also read the FMP whereas examples provide no further semantics As examples illustrate uses unlike FMPs a combination of the two is usually compromised upon If an FMP is given then the equivalent CMP should also be given and if possible the conversion should be done as well CMPs should be written in English and in full no abbreviations FMPs should be as comprehensive as sensibly possible whereas examples are generally a lot more concise The CDUses field which lists all of the other CDs which have symbols occurring in this CD should be correct It is naive to expect a CD to be completely self contained so restraint is necessary Particularly a CD should not be using other CDs which are less official that itself The corresponding STS file should be written these signatures should be as helpful as possible An OpenMath based Unit Converter 2 1 2 4 Phrasebooks The Phrasebook is an internal interface that carries out the conversion of an OpenMath object to from the internal representation in a software application It is envisioned that a software application dealing with a specific area of mathematics declares which content dictionaries it understands this means the translation can be governed by the content dictionaries and specifics of the application Essentially the Phraseboo
35. ctionaries carry out conversions 45 An OpenMath based Unit Converter 6 2 The Future The Unit Converter 6 2 1 Writing Content Dictionaries One of the main disadvantages of OpenMath is that as yet is does not have mass appeal and as a result there is not wide spread understand of the language The unique selling point behind an OpenMath based unit converter is that it is extensible However at this moment in time the only way users can add content dictionaries to the system is to search through the list of dictionaries gather the required information and add the dictionary that relates to the conversion they want to perform Although the content dictionaries are written in XML and that is designed to be both machine and human readable this is not a particularly practical approach for non computer literate users To ensure all types of users fully utilise the system a sensible addition would be a section of the program that can write content dictionaries for the user Phrase books are available to convert other languages to OpenMath for example OMA gt OMS cd Basic name segment gt 1 2 lt OMA gt Is written by OMApplication om new OMApplication functor1 params1 Vector params2 new Vector params2 addElement new OMInteger 1 params2 addElement new OMInteger 3 This means that if a conversion is not already available the user could enter the two units they want to convert between as well as some of
36. d Destination Units if event getSource processButton new FileChoose launchFrame public static void main String args Unit Converter uc new Unit Converter 70
37. d MathML using OpenMath to define the semantics OpenMath during the course of its development has matured and found a natural role as the encoding of Mathematics in situations where more An OpenMath based Unit Converter precision or richness is required than may easily be obtained by using MathML The preciseness of OpenMath will be required ahead of MathML for the unit converter as it will enable more advanced and obscure conversions This fixed range and default presentation makes it more suitable for being embedded in web browsers than OpenMath For further detail about the conversion between OpenMath and MathML see Conversion between MathML and OpenMath Carlisle 2001 2 1 2 8 eXtensible Markup Language XML OpenMath defines two ways to encode its objects XML and binary encoding To support the computers mathematic interaction XML encoding is necessary When XML was first introduced it was hailed as the cornerstone of a new kind of technology that would permit interoperable Web services XML provides a standardized way to represent structured and typed data XML has been incorporated into every aspect of application and enterprise development It is now a part of networking protocols Web servers operating systems programming languages application servers etc XML is a markup language for documents containing structured information A markup language is a mechanism to identify structures in a document XML defines a generic syntax
38. d it provides the perfect foundation for a mathematical system to build on As more OpenMath based applications are being produced it means there will be more content dictionaries and phrase books being built This in turn will increase the understanding functionality and usability of the language greatly increasing its popularity 47 An OpenMath based Unit Converter Bibliography e Bray T Paoli J 1998 Extensible Markup Language XML 1 0 Available at http www w3 org TR 1998 REC xml 19980210 pdf e Buswell S Caprotti O Carlisle D P Dewar M C Ga tano M and Kohlhase M 2004 The OpenMath Standard Available at http www openmath org standard om20 2004 06 30 omstd20 pdf e Carlisle D Davenport J Dewar M Hur N Naylor W 2001 Conversion between MathML and OpenMath Available at http www openmath org documents om mml pdf e Cohen M A Cuypers H Sterk H Algebra Interactive Available at http www win tue nl ida home html e Davenport J 1999 A Small OpenMath Type System Available at http www openmath org standard sts pdf e Davenport J 2000 On Writing OpenMath Content Dictionaries Available at http www openmath org documents writingCDs pdf e Davenport J Naylor W 2003 Units and Dimensions in OpenMath Available at http www openmath org documents Units pdf e Harold E R Means W S 2001 XML In a Nutshell United States O Reilly amp Associates Inc e
39. does fail then it needs to be able to be reset and quickly become functional to the user again in order to cause minimum annoyance 19 An OpenMath based Unit Converter 3 2 2 Non Functional requirements The non functional requirements specify those requirements that cannot be precisely measured by success or failure they are subjective They are 1 The front end should be simple and easy to use It should respond fast enough that it is usable 2 Future improvements should be catered for in the design 2 1 New operations and modifications to improve efficiency should be easy to add to the system 3 The user manual should provide the user with clear and simple instructions on the functionality of the system including illustrations of its use 3 3 Requirements Validation The goal of the requirements validation is to attempt to confirm the correctness and completeness of the requirements specification The tools for carrying out this process are usually a structured or informal walk through Once I had drawn up my requirements I carried out an informal walk through with Professor Davenport essentially this involved me and Professor Davenport running through a summary of my completed requirements The purpose of the informal walk through was firstly for Professor Davenport to highlight and remove any glaring errors in the specification and from there he could then confirm that 1 am heading in the right direction and highlight any fu
40. dstOma Element XPath selectSingleNode el OMA OMS name destinationUnit Focuses on the source unit Call the invertOp method reverse the operation thats applied to the source unit String invOp invertOp Attribute XPath selectSingleNode srcOma OMS name get Value Make srcBase a double double dblBase getValue srcOma double Integer parselnt srcBase Carry out the normalise method double norm normalise value dblBase invOp Retrieve the destination value from the content dictionary String dstOp Attribute XPath selectSingleNode dstOma OMS name getValue Make dstBase a double dblBase getValue dstOma double Integer parselnt dstBase Carry out the apply method result apply norm dblBase dstOp catch Exception e System err println e e printStackTrace return result Search for the correct conversion public static double search String srcUnit String dstUnit double srcVal ArrayList visited This loop ensures the method searches through all of the content dictionaries in the system for int y 0 y lt files size y try SAXBuilder parser new SAXBuilder Document response parser build String files get y sourceNodes lookup source unit Extract all sections that focus on the srcUnit add them to a list 66 An OpenMat
41. e host of unit converters already available on the internet that have all been written in a number of different languages As the back end of my system will be centred on OpenMath a review of how existing systems carry out conversions is not necessary however it is important to highlight some of the similarities and strength of the front ends There tends to be a given format amongst the unit converters available on the internet e A text box is usually used to enter the amount you would like to convert into the system e The source and destination units are typically stored in lists or drop down boxes e The design of the system is usually kept very simple with minimal distraction or confusion for the user 13 An OpenMath based Unit Converter 3 Requirements An OpenMath based Unit Converter This project has two key goals 1 To be able to read new Content Dictionaries into the system 2 To be able to read and utilize the information available in the content dictionaries to carry out conversions The requirements process will begin with the requirements elicitation and analysis all of the requirements highlighted will be gathered from the analysis of previous OpenMath projects and existing unit converters Once the requirements elicitation has been carried out I will draw up both the functional and non functional requirements as well as any optional requirements that are not core to the system but would add value To finish
42. esults Convert A Unit The OpenMath Way Convert From Convert To o xl un ETE Add A New Library T ea y pressure ocd y References doc y Unit Converter without the count java y Unitc class y unit Converter class 5 Unitc java File Name pressure ocd Figure 8 Test 3 Results O 1 0 pascal 1 0 newton_per_sqr_metre OK 55 An OpenMath based Unit Converter Figure 9 Test 4 Results O 1 0 pascal 0 224804981678394 pound_per_sqr_metre Figure 10 Test 5 Results Message 1 0 pascal 0 0208854 16340332037 pound_per_sqr_foot Figure 11 Test 6 Results Message 101 xi 1 0 mile 1609 344 metre 56 An OpenMath based Unit Converter Figure 12 Test 7 Results Convert A Unit The OpenMath Way Add A New Library Figure 13 Test 8 Results Message 15 xi Please make sure you have entered a value for the Amount to Convert and both the Source and Destination Units Figure 14 Test 9 Results Sorry that conversion is not mathematically possible OK 57 An OpenMath based Unit Converter Figure 15 Test 10 Results A las NUM un Se Convert A Unit The Openl y contentDictionary ocd xml 5 FileChoose java Comwert From 3 Convert MF Implementation Notes doc 3 Converter jar Java Compiling etc rtf Convert To D D doc D Lanky1 class Add A New Library 58 An OpenMath based Unit Converter Appendix C Code
43. example if application A is talking to application 5 and sends say an equation involving multiplication of matrices then A and 8 must agree on what a matrix is and on what matrix multiplication is and even on what constitutes an equation Buswell 2004 A content dictionary holds the meanings of various mathematical words it is not content dictionaries themselves which are being transmitted but some mathematics whose definitions are held independent to the application within the content dictionaries with a set of symbol definitions A and B can now talk in a common language In many cases the content dictionaries that an application understands will be constant and be built in to the application s mathematical use However applications can be developed that can handle every content dictionary or a changeable number of content dictionaries perhaps after being sent content dictionaries in some way A Content Dictionary consists of the following mandatory pieces of information 1 Aname 2 Adescription of the Content Dictionary 3 Arevision date the date of the last change to the Content Dictionary Dates should be stored in the ISO compliant format YYYY MM DD e g 1985 03 15 4 A review date a date until which the content dictionary is guaranteed to remain unchanged 5 A version number which consists of a major and revision part If the status is not experimental the version number should be a positive integer When the m
44. h based Unit Converter XPath x XPath newInstance CD CDDefinition FMP OMOBJ OMA OMA OMS name s rcUnit java util List sourceNodes x selectNodes response ArrayList srcNodes ArrayList sourceNodes loop over all source units in list for all nodes in sourceNodes for int i 0 i lt srcNodes size i Search the list to find the section that focuses on the srcUnit amp dstUnit XPath Element el Element srcNodes get i Element dstOma Element selectSingleNode el OMA OMS name dstUnit if dstOma null If there is a match for the dstUnit Carry out the conversion method return convert el srcUnit dstUnit srcVal for all nodes N in sourceNodes for int j 0 j lt srcNodes size j if srcUnit is not in visited if beenVisited visited srcUnit Return the attribute in the element that isn t the source unit Element N Element srcNodes get j Attribute a Attribute XPath selectSingleNode N OMA OMS 2 name srcUnit name N_string is out new element it becomes the new dstUnit String N string a getValue A conversion is carried out from the srcUnit to N string double newSrcVal convert N srcUnit N string srcVal Every srcUnit is added to a list of all units visited to no conversions are repeated visited add srcUnit N string is now the srcUnit Se
45. h based Unit Converter 4 4 1 Carrying out longer transformations Currently the system searches through all of the possible conversions to try and find an exact match with the source and destination units however it could be the case that a conversion is only possible with an intermediate step For example using the imperial content dictionary a conversion from metres to yards would have to go through feet The most suitable way of demonstrating this would be with an example Search A D amount2conv visitedlist 0 Lookup A D Not Found B and E Returned Search B D convert amount2conv A B visitedlist A Lookup B D Not Found A and C Returned Ignore A Search C D Convert Pre value B C visitedlist A B Lookup C D Found Return Convert Pre value C D This method carries out a conversion from A to D Initially it searches from a conversion directly from A to D if that is not possible it will look to see what other conversions are possible in this case B and E It then converts from A to B and adds A to the list of units that have already been used The cycle then continues with an attempt to convert from B to D If a direct conversion is not possible then the Search method will enter into another for loop this will enable us to iterate over all of the conversions that involve the source unit Although we do not know what the destination unit will be for each intermediate conversion we can extract it using the XPath A
46. ittee was elected to management the OpenMath development This project ran for 2 years and produced OpenMath v1 0 with prototype Phrasebooks The Esprit project was funded by the European Union between 1997 and 2000 this project carried on with the further development of the language and was in turn replaced by the OpenMath Thematic Network This ran from July 2001 until June 2004 and was also sponsored by the European Union it was a logical follow on from the Esprit project The projects main aims were to organise workshops bringing together people working on OpenMath from around the world provide a continued focus point for the development of the OpenMath Standard and Content Dictionaries coordinate the development of OpenMath and MathML tools and applications and to disseminate information about OpenMath and MathML the projects produced the OpenMath standard we use today v2 0 An OpenMath based Unit Converter 2 1 2 OpenMath The Specifics OpenMaths is a relatively new field of research it is emerging as a standard for encoding the meaning of a mathematical object rather than just creating a visual representation OpenMath allows the free exchange of mathematical objects between software systems and human beings it enables the manipulation and computing of mathematical expressions embedded in web pages and is designed to be machine generated and machine readable Typical uses include e displaying in a browser exchanging between software
47. k of the application is able to translate OpenMath objects built using symbols from these content dictionaries to from the internal mathematical objects of the application 2 1 2 5 Objects OpenMath uses objects as a representation of mathematical entities The objects can then be communicated among various software applications whilst preserving their semantics Basic OpenMath objects are one of the following e Integer No predefined range IEE Floating point number Double precision floating point numbers Character String Corresponds to Characters in XML Bytearray Sequence of Bytes Symbols Encodes three fields of information o Symbol name Sequence of Characters o Content Dictionary name the location of the symbol definition o Content Dictionary base URI or cdbase used to disambiguate multiple Content Dictionaries The URI usually follows the standard URI cdbase value cdvalue name value Example Symbol sin in cd transcl and cdbase http openmath org cd http openmath org cd transcl sin Objects can also be derived e Foreign Used to import a non OpenMath object into an OpenMath application e Application Constructs an object from a sequence of one or more OpenMath objects The first child of an application is referred to as it s head while the remaining objects are called its arguments Example application sin x corresponds to sin x application Rational 1
48. nsscssarssssencacnssasscecessacsseasacscssacoseasarscessacoees V INTRODUCTION te ree E UE ER nete e ae nenne re Peau e EAS RR ARR 1 LITERATURE SURVEY 5 5 init s interi it iio 3 2 1 AN INTRODUCTION TO OPENMATH sess nennen nennen nennen 4 2 1 1 OpenMath The Background 4 2 1 2 OpenMath The Specifics eere 5 2 2 PARSER APIS n ERR GUT ERR E UE nein menge 11 221 SAX sisse e testet trt tdt ti sc t drittes ae tes deste e Rea 11 222 DOM T Tasha Su Men M PDAS 11 2 2 3 IDOM rea DI nno uie n t eee E ds 11 2 3 EXISTING PROJECTS e a cs es 12 2 3 1 E NAAA ttd ettet ui dre len walls 12 2 3 2 OpenMath Web Service Package 12 23 3 Algebra Interactive amp ActiveMath seese re ereen 13 2 3 4 EXISUNG UNIE COOTER S 5 eit it ettet replies legerent 13 REQUIREMENTS E 14 3 1 REQUIREMENTS ELICITATION AND ANALYSIS 15 3 1 1 Methodology coc tatio UN e A nde 15 3 1 2 Hardware and Software Considerations 15 3 1 3 Carrying out Conversions esse 16 3 1 4 Searching Content Dictionaries 16 3 1 5 Adding NEW LIDIATIOS sens An en nn tent 16 3 1 6 User Interface ER RER RE abet e e eae 16 3 2 REQUIREMENTS SPECIFICATION una ire dic 18 3 2 1 Functional requirements 18 3 2 2 Non Functional requirements 20 3 3 REQUIREMENTS VALIDATION uuunsseesnsesensensnsensensnsensensnsnsensnsennensnnnnensnsnnensnnnsensn nennen 20 DESIGN amp IMPLEMENTATION
49. nversion and starting point would be to pass the initial system e The amount to convert 1 e The unit to convert from Source Unit Foot e The unit to convert to Destination Unit Metre Given these details the system should then e Read in one content dictionary o units_imperiall ocd as it contains the required conversion from feet to metres e Search through the content dictionary extracting a list of all the conversions that involve the source unit e Search the list of conversions to find the conversion that involves both the source and destination unit e Extract the required details and carry out the conversion 4 3 1 Reading in a Content Dictionary Reading in the content dictionaries is the job of the SAXBuilder The SAXBuilder builds a JDOM document from files streams readers URLs or a SAX InputSource instance using a SAX parser As it is only reading in a single file stored in a 25 An OpenMath based Unit Converter convenient location it was just a case of initialising a new SAXBuilder and building a document using the build method shown below SAXBuilder parser new SAXBuilder Document response parser build units imperial1 ocd 4 3 2 Extracting a list of relevant Conversions XPath is a W3C defined language and an official W3C recommendation The XPath language provides a simple concise syntax for selecting nodes from an XML document Using XPath I was able to search through the XML document pr
50. object i e the key in a key value pair The role of an OpenMath symbol is the restriction on how it may be used to construct a compound OpenMath object A symbol cannot have more than one role and cannot be used to construct a compound object in a way which requires a different role The possible roles are e Binder first child of a binding object e Attribution used as key in an attribution object i e the first element of a key value pair This can be used as a clarification of how the attribution should be interpreted e Semantic attribution This is the same as attribution except that it modifies the meaning of the attributed OpenMath object and thus cannot be ignored by an application without changing the meaning e Error first child of an error object e Application first child of an application object e Constant The symbol cannot be used to construct a compound object 2 1 2 7 OpenMath Vs MathML MathML and the OpenMath development cycles have been strongly linked there is an obvious overlap in both the people researching and developing the languages as well as the actual logic itself MathML has been developed to provide both content and presentation mechanisms it is a fixed set of mathematical operators that define a default presentation The mathematical range of MathML can be extended by attaching semantic meanings to expressions These external semantics may be in any form but one obvious contender is to exten
51. oduced by the SAXBuilder to extract all nodes that match the source unit in this case foot as each node was found it was added to a List Finally the list was cast to an ArrayList for easier manipulation XPath x XPath newInstance CD CDDefinition FMP OMOBJ OMA OMA OMS name src Unit List srcNodesList x selectNodes response ArrayList srcNodes ArrayList srcNodesList As you can see from the code above using XPath is just a case of entering the correct path so you can match the source unit to the predicate expression OMA OMS name srcUnit In this case I want to add the OMA where the name within the OMS is equal to the srcUnit or Foot 4 3 3 Searching the List of Nodes Within our ArrayList we now contain a number of nodes these correspond to all of the conversions within the content dictionary that involve the source unit The next step is to iterate through the ArrayList to match both the source and destination units with a node This will confirm that a conversion is possible and enable us to extract the corresponding details As the nodes within the List are in fact elements when iterating through the ArrayList we must first cast each node to an element Element el Element srcNodes get i 26 An OpenMath based Unit Converter By using XPath again we are able to match the source and destination units with the names within each element and start to extract the required conversion details
52. onverter transformation between the OpenMath representation and their corresponding representation within an application As a result of this project the robustness of OpenMath was increased and it has now become more diverse to fit different kinds of mathematical software The purpose of these projects was to increase the robustness of OpenMath and make it more available to different kinds of mathematical software and projects being developed In both systems there were issues with speed reliability security and error handling but on the whole they were deemed a success 2 3 3 Algebra Interactive amp ActiveMath Algebra Interactive and ActiveMath are two pioneering systems that use OpenMath as a semantic foundation They focus on web learning HTML based books for undergraduate students in all fields of science e g mathematics computer science physics and engineering The main themes throughout both systems range from the elementary structures of the integers polynomial rings in one variable to the abstract notions of groups rings and fields the systems tend to focus on an algorithmic approach to these algebraic structures The books provide the required knowledge for users of any aptitude as well as numerous exercises to work through The programs also provide further more novel features these include interactive examples and tools such as a Concept Map Tool or Plotting Tools 2 3 4 Existing Unit Converters There are a whol
53. ow Figure 2 Evolutionary Design Model Requirements Analysis amp Design Implementation Planning Deployment Initial Planning Evaluation Testing 4 2 Creating an OpenMath Content Dictionary Having explored the content dictionaries online I felt the best approach to fully understand the task I am undertaking would be to design my own content dictionary As it was a topic that has not been covered yet I produced a Pressure content dictionary 22 An OpenMath based Unit Converter 4 2 1 Anatomy of a Content Dictionary As previously mentioned in section 1 1 1 1 there is a standard motivation and process when designing content dictionaries Below I am going to highlight some of the key areas of a content dictionary that I will need to manipulate in my system The following example shows the body of a conversion between feet and metres lt CDDefinition gt lt Name gt foot lt Name gt lt Description gt This symbol represents the measure of one foot This is the standard imperial measure for distance lt Description gt lt CMP gt 1 foot 0 3048 metres lt CMP gt lt FMP gt lt OMOBJ gt lt OMA gt lt OMS name eq cd relationl gt lt OMA gt OMS name times cd arith1 gt lt OMI gt 1 lt OMI gt OMS name foot cd units imperiall gt lt OMA gt lt OMA gt OMS name times cd arith1 gt lt OMF gt 0 3048 lt OMF gt OMS name metre cd units metricl gt lt OMA gt
54. r enter the amount you would like to convert select the unit you would like to convert from and to and press the convert button Once the convert button has been pressed the system implements an ActionListener and selects the conversion amount from the JTextField which is then cast to a double As well as that the AcvtionListener gathers the source and destination units from their Combo Boxes each of them then being cast to a string The search method is then called to start the conversion process if event getSource convertButton ArrayList visited new ArrayList String srcUnit String convertFrom getSelectedItem double srcVal Double parseDouble convertAmount getText trim String dstUnit String convertTo getSelectedItem double result search srcUnit dstUnit srcVal visited If a solution is found a new JOptionPane is shown with the solution otherwise an error message will appear informing the user that the conversion they are attempting is not possible Figure 5 GUI to displaying the result iix de i 1 0 pascal 1 0 newton per sqr metre 34 An OpenMath based Unit Converter 4 4 3 Adding Multiple Dictionaries Figure 6 Adding a Content Dictionary Click Add CD button Select file Is selected file a directory Open Directory Is selected file a content dictionarv Return Error Add CD to the list of available CD s in the system
55. rther work or ideas that are worth exploring The validation process was fairly successful Professor Davenport was happy with the direction that I was taking and the work that I had already implement however there were a few extra points that Professor Davenport felt were worth addressing e I should explore how content dictionaries are written and ensure that my system can add a content dictionary written by myself e Try to explore some more complex conversions and incorporate them into the system 20 An OpenMath based Unit Converter 4 Design Implementation 21 An OpenMath based Unit Converter 4 1 Design amp Implementation Process Having researched OpenMath and drawn up the requirements of my project I now moved onto the design and implementation stage Having not worked with OpenMath before I felt it would be best to adopt almost an iterative or evolutionary development processes The basic idea behind iterative enhancement is to develop a software system incrementally This would then allow me to take advantage of the skills learnt during the development and testing of earlier deliverables of the system Key steps in the process were to start with a simple implementation of the software requirements and iteratively enhance the sequence of versions until the full system is implemented At each iteration design modifications are made and new functional capabilities are added This is demonstrated in the diagram bel
56. s variables or symbols lt OMA gt Element OMA is an application element It is an element that contains a sub tree of elements and allows you to add additional information to an object OMS Element The OMS element defines an OpenMath Symbol These are interesting because they consist of a name and a reference to a definition in an external content dictionary Using XML notation where the element name OMS indicates an OpenMath symbol the above example lt OMS name eq cd relation1 gt represents the standard equals function as defined in the content dictionary relation1 lt OMI gt Element The OMI is an OpenMath Integer the OMI element encapsulates the value of the Integer lt OMF gt Element 24 An OpenMath based Unit Converter The OMF is an OpenMath Float the OMF element encapsulates the value of the Float lt OMV gt Element The OMV is an OpenMath Variable the OMV element encapsulates the value of the Integer Following the guidelines set out in On Writing OpenMath Content Dictionaries Davenport 2000 I have produced my own content dictionary that outlines some pressure conversions these includes Pascal Newton s per square Metre Pounds per square Metre and Pounds per square Foot See Appendix D 4 3 The Simple Case The initial step in the design process is to interpret the content dictionaries and attempt to carry out a simple conversion After review the content dictionaries the simplest co
57. s by 0 6096 in the final method Resulting in the same answer 28 An OpenMath based Unit Converter 4 3 5 Carry out the Conversion By normalising the amount you want to convert it means the apply method is very simple It takes in the normalised amount you want to convert the destination conversion value and the destination operator and returns the answer public static double apply double arg1 double arg2 String operator if operator equals times return arg1 arg2 return 0 4 4 High Level Design With the simple case completed it gave me a chance to have a better look at the real structure of the system At which time I decided there were four key areas that I should focus on e Carrying out longer transformations e Developing a GUI e Adding content dictionaries e Reading Searching multiple dictionaries The main body of the system will follow the structure of the follow chart over page 29 An OpenMath based Unit Converter Figure 3 Main System Structure Input Number and Units Is a direct conversion possible from the source to the destination Yes Carry out Conversion Restart process at next iteration Yes Take the next available destination unit from the current source unit Has unit been used already Carry out conversion No Destination unit reached Yes No Destination unit Return Result becomes new source unit 30 An OpenMat
58. s were then designed to share the same core implementation based on DOM 2 3 2 OpenMath Web Service Package This was development in 2003 and had three main goals e Add functionality to the interface between the mathematical software applications and content dictionaries The interface should be able to extract information from the content dictionaries and respond to the applications The applications can then use the information and create new content dictionaries automatically e Build a user interface between human beings and content dictionaries hence the user can retrieve information they want from content dictionaries This was meant as an aid to people who are interested in building some kind of OpenMath tool For Example a designer of a Phrasebook to obtain information about content dictionaries more easily e Web services are still evolving there is an overwhelmingly long list of proposed standards and the complex interactions between each of them The final goal of the project was to try to implement these proposed standards and provide a successful practical example for the industry This project comprised of two parts the first component handled user s requests on the Web via HTTP and the second handled requests from applications connected through the Internet The purpose of the project was to allow mathematical software to create new content dictionaries automatically this would facilitate the 12 An OpenMath based Unit C
59. sageDialog null Error Please add a valid Content Dictionary else Unit_Converter addcd getSelectedFile chooser dispose When the correct file has been opened the system will pass the content dictionary into the addcd method in the Unit Converter class and close the JPanel The addcd method then adds the new content dictionary to the list of content dictionaries already in the system and passes the content dictionary into the readCD method The purpose of the readCD method is to update the combo boxes on the GUI the content dictionary is passed into the method and parsed by the SAXBuilder XPath is used to extract the names of all of the available units in that content dictionary and they re added to a list of nodes The list is checked for any duplicates and the resulting list is added to the combo boxes on the GUI this now makes the new conversions available to the user 4 4 4 Reading Searching multiple dictionaries Now there are multiple dictionaries in the system the search method needs to be edited to ensure all of the content dictionaries are being checked for relevant conversions The content dictionaries are stored in a list so a loop is necessary at the start of the searching method so that the existing search process can be carried out on every content dictionary As well as that the SAXBuilder code needs to be edited so that a different content dictionary is parsed during each iteration this is done by
60. selecting the content dictionary at the location corresponding to the for loop and casting it to a string for int y 0 y lt files size y SAXBuilder parser new SAXBuilder Document response parser build String files get y 37 An OpenMath based Unit Converter 5 Testing amp Results 38 An OpenMath based Unit Converter 5 1 Test Plan The testing document aims to show that each of outlined requirements have been met successfully this is going to be split into two parts Initially 1 am going to test that my system has met the functional requirements highlighted in the specification stage I am then going to carry out a usability study with some possible users to analyse the design and usability of the front end 5 2 Testing Functional Requirements The functional requirements are a specification stating what the system will and won t do they are generally yes or no answers so I designed a number of tests to see if the system can carry them out the results are as follows Tests 1 amp 2 Requirements 1 amp 5 Adding new content dictionaries to the system Test Carried Out Add the Pressure content dictionary via the front end Expected Result The content dictionary should be added to the system so the units Pascal Newton s per square Metre Pound s per square Metre and Pound s per square Foot should all be made available for conversions Successful Yes see Figure 5 1 in Appendix B Test Carried Out
61. t lt OMOBJ gt 60 An OpenMath based Unit Converter lt OMA gt OMS name eq cd relationl gt lt OMA gt OMS name times cd arithl gt lt OMI gt 1 lt OMI gt OMS name pound per sqr metre cd pressure lt OMA gt lt OMA gt OMS name times cd arithl gt lt OMF gt 4 4483 lt OMF gt OMS name pascal cd pressure gt lt OMA gt lt OMA gt lt OMOBJ gt lt FMP gt lt CDDefinition gt lt CDDefinition gt lt Name gt pound_per sqr foot lt Name gt lt Description gt This symbol represents the measure of one Pound per square foot This is the standard SI measure for pressure lt Description gt lt CMP gt 1 pound per sqr foot 47 8803 pascal lt CMP gt lt FMP gt lt OMOBJ gt lt OMA gt OMS name eq cd relationl gt lt OMA gt OMS name times cd arithl gt lt oMI gt 1 lt OMI gt OMS name pound per sqr foot cd pressure gt lt OMA gt lt OMA gt OMS name times cd arith1 lt OMF gt 47 8803 lt OMF gt OMS name pascal cd pressure gt lt OMA gt lt OMA gt lt OMOBJ gt lt FMP gt lt CDDefinition gt lt CD gt 61 An OpenMath based Unit Converter FileChoose java import java awt import java awt event import java io import javax swing public class FileChoose extends JFrame public FileChoose super JPanel pane new
62. t itself in any programs that can truly demonstrate the advantages OpenMath describes the logical structure of mathematical formula and concepts The OpenMath Society 2006 It is widely accepted as a basic protocol for mathematical interaction and communication It provides semantic rich mathematical symbols through constructing a set of content dictionaries content dictionaries are central to the OpenMath philosophy of transmitting mathematical information It is the OpenMath content dictionaries which actually hold the meanings of the objects being transmitted Buswell et al 2004 Page 34 The content dictionaries are defined in two different ways XML or binary encoding To support the computers mathematic interaction XML encoding is necessary XML The Extensible Markup Language is a W3C endorsed standard for document markup It is a markup language for documents containing structured information in essence it defines a generic syntax used to mark up data with simple human readable tags O Reilly 2001 Page 1 When XML was first introduced it was hailed as the cornerstone of a new kind of technology that would permit interoperable Web services this means you can write your own program that will interact with message and manipulate data in XML documents To summaries mathematical conversions can be formally defined in XML encoded content dictionaries I am going to investigate the possibility of designing a system that can read and
63. ttribute a Attribute XPath selectSingleNode N OMA OMSI2 name srcUnit name String N_string a getValue 31 An OpenMath based Unit Converter By making an arbitrary variable N_string the new destination unit the conversion method can now be called for a conversion from the source unit to the N_string The search method will then call itself with the newly worked out amount to convert and the current destination unit N_string as the new source unit The cycle continues until the conversion is carried out or there are no more conversions available hence it is not possible with the given content dictionaries There is some administration that needs to take place before this method will work In the previous example there was a been visited list This is essential because without checking that a unit has already been used at an intermediate stage it could loop endlessly over the same units The beenVisited method is called before any intermediate steps are taken it takes the list of units that have been visited and compares the contents with the N_string or new destination unit If the unit has already been visited the method returns false and the loop in the search method starts its next iteration The loop in search then finds another possible destination unit which is again checked by beenVisited this cycle continues until a suitable destination unit is found or the conversion is just not possible public st
64. used directly for presentation although tools exist to facilitate this OpenMath originated from the Computer Algebra community and since 1997 its development has been partially funded by the European Union under a multimedia ESPRIT project Computer Algebra packages were getting bigger and more unwieldy and it seemed reasonable to adopt a generic plug and play architecture to allow specialised programs to be used from general purpose environments There were plenty of mechanisms for connecting software components together but no common format for representing the underlying data objects It quickly became clear that any standard had to be vendor neutral and that objects encoded in OpenMath should not be too verbose In 1998 the Worldwide Web Consortium W3C produced its first recommendation for the Extensible Mark up Language XML intended to be a universal format for representing structured information on the worldwide web It was swiftly followed by the first MathML recommendation which is an XML application oriented mainly towards the presentation of mathematical expressions OpenMath was then derived from these developments To date there have been three main projects focused on the development of OpenMath as a language in 1995 the Editing and Computing Project was launched This was the organisation of five workshops open to all that have been interested in the project These initial meetings were mainly of a political nature a steering comm
65. used to mark up data with simple human tags It provides a standard format for computer documents This format is flexible enough to be customised for domains as diverse as web sites electronic data interchange software configuration remote procedure calls and more Since XML was first introduced it has been involved nearly everywhere information is managed XML is intended to be understandable by both humans and applications Therefore the syntax for XML is very simple and can be understood easily by humans At the same time the XML document is strictly formed with absolute minimum optional features so that the application can read it as well 10 An OpenMath based Unit Converter 2 2 Parser APIs A parser is essential to an XML aware application It takes the XML document as an input and generates data which can then be manipulated and handled by other XML tools or APIs The three APIs I explored were SAX DOM and JDOM 2 2 1 SAX SAX is an event driven API for XML it provides a set of classes for inserting and manipulating Put simply when an XML document is in the process of parsing events occur These events then provide the points that application code can insert into and manipulate Its sequential parsing process does not allow for random access to an XML document so forward and backward movement among elements is difficult The OpenMath content dictionaries are small XML documents although SAX requires a lot less memory than DOM
66. utionary design and implementation it has had a negative affect on my coding Java programs by definition are generally highly modularised with clear class diagrams and code layout Unfortunately this is not the case within my system a number of the methods within the main body of the system should really be separated into different classes the program as a whole could really do with being modularised Due to my coding it could mean that future development of the system could well be slowed Not only will it make it a lot harder for other programmers to read through and understand the processes I ve implemented thus far but future changes will also be more difficult to incorporate One of my non functional requirements was to ensure that future improvements were catered for in the design hence new operations and modifications to improve efficiency should be easy to add to the system Although I feel a better system was produced due to my implementation style it has resulted in this requirement not really being met I enjoyed researching and implementing this project OpenMath is a fascinating language and it was refreshing to work in a field that still has scope for development To critique myself I would say that I have achieved my primary objectives Although the system is limited by the number of content dictionaries it is compatible with it is capable of reading in a variety of content dictionaries and based on the details stored in those di
67. vertAmount Screen add convertFrom Screen add convertT Screen add convertTo screen add spacer Screen add convertButton screen add addNewL screen add processButton AAA frame setTitle frame show frame setLocation 400 200 69 An OpenMath based Unit Converter frame setContentPane screen frame setDefaultCloseOperation JFrame EXIT ON CLOSE frame pack Add action listeners to the relevant parts of the GUI convertFrom addActionListener this convertButton addActionListener this processButton addActionListener this public void actionPerformed ActionEvent event if event getSource convertButton try Read in the details and start the conversion process ArrayList visited new Arraylist String srcUnit String convertFrom getSelectedItem double srcVal Double parseDouble convertAmount getText trim String dstUnit String convertTo getSelectedItem double result search srcUnit dstUnit srcVal visited Return the result if result 999 JOoptionPane showMessageDialog null srcVal srcUnit result dstUntt else JOptionPane showMessageDialog null Sorry that conversion is not mathematically possible catch Exception e JOptionPane showMessageDialog null Please make sure you have entered a value for the Amount to Convert and both the Source an
68. vertTo addItem name 68 An OpenMath based Unit Converter catch Exception e System err println e public Unit Converter Initialise the Instance Variables JPanel screen new JPanel new FlowLayout JLabel title new JLabel Convert A Unit The OpenMath Way JLabel convertF new JLabel Convert From JLabel convertT new JLabel Convert To JLabel addNewL new JLabel Add A New Library JLabel spacer new JLabel Set the sizes of the variables screen setPreferredSize new Dimension 500 240 title setPreferredSize new Dimension 255 40 convertF setPreferredSize new Dimension 245 30 convertAmount setPreferredSize new Dimension 50 20 convertFrom setPreferredSize new Dimension 150 20 convertT setPreferredSize new Dimension 300 30 convertTo setPreferredSize new Dimension 150 20 addNewL setPreferredSize new Dimension 450 40 spacer setPreferredSize new Dimension 350 40 processButton setPreferredSize new Dimension 75 20 convertButton setPreferredSize new Dimension 100 30 Set borders on the TextPanes convertAmount setBorder new LineBorder Color black convertFrom setBorder new LineBorder Color black convertTo setBorder new LineBorder Color black Add the elements to the Screen screen add title Screen add convertF Screen add con

Prangle-D-Dissertati.. - Department of Computer Science

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