Use OMDoc Representing Geometric Algebra

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1 Use OMDoc Representing Geometric Algebra Author: Michael Watts Jr. and Ratish Shrestha Faculty Advisor: Dr. Kuo-pao Yang and Dr. Wendy Zhang Department: Computer Science and Industrial Technology INTRODUCTION OMDoc (Open Mathematical Document) is an XML based markup language used to represent mathematical documents and complex theory in a very easy and understandable manner. OMDoc has been developed by a German mathematician and computer scientist Michael Kohlhase since 1998 and has already released different versions of OMDoc specifications. OMDoc can be used to represent mathematical formulae and it supports content dictionaries containing the definitions of the symbols used in formulae. OMDoc provides an infrastructure for the communication and storage of mathematical knowledge. OMDoc extends OpenMath and MathML standard formats by creating markup for documents and theory level of mathematical documents. The document author can specify them in a formal way and publish it on the Web site and people using the document can take advantage of them. OMDoc uses three levels of modeling to represent a mathematical document. a) Mathematical Theory: At this level, OMDoc supplies original markup for clustering sets of statements into theories. b) Mathematical Statement: OMDoc provides original markup infrastructure for making the structure of mathematical statements explicit. c) Mathematical Formulae: At the level of mathematical formulae, OMDoc uses the established standards OpenMath [BCC+04] and Content-MathML [ABC+03]. Mathematical knowledge can be vary greatly in its presentation and its level of formality, but its semantic structure is common to all forms of mathematics. OMDoc

2 markup language can present the common semantic structure and exchange structured mathematical documents between different systems and software. PROPOSED RESEARCH The proposed research is to develop OMDoc format documents to represent mathematical expressions in the book Clifford Algebra to Geometric Calculus by David Hestenes and Garret Sobczyk. Clifford Algebra is an associative algebra that contains vector space with a quadratic form. Clifford Algebra can be used to generalize the representation of Complex numbers. In this research, we will be representing Geometric Algebra that is defined by a set of axioms that explain the definitions and identities of different properties. By this way, we can use OMDoc format XML documents to develop a content dictionary of definitions and their meaning to make it a versatile and efficient computational tool. METHOD We plan on using Cygwin and QMath to write most of the OMDoc and an editor such as Altova XMLSpy to edit the XML as needed. We will be using these tools to create informative examples and formulas to the user based on the information provided in the Clifford Algebra to Geometric Calculus book. COLLABORATION WITH FACULTY SPONSOR Dr. Wendy Zhang, Associate Professor, is the sponsor for this project together with cosponsor Dr. Kuo-pao Yang, Assistant Professor. They have provided all the necessary information about OMDoc, its documentations and examples. We will be working together in the representation of the Clifford Algebra into OMDoc format. Faculty sponsors and students will meet once a week to ensure the progress of the project. IMPACT OF PROJECT We are aiming to build a library of mathematical definitions of axioms used in Clifford Algebra. This library will be stored in a web repository that can be accessed by anyone in the Internet and use is to represent different mathematical expressions and definitions. We also plan to write a paper based on the research of this project and

3 submit it to Consortium for Computing Sciences in Colleges (CCSC) Conference 2009 for publication. OVERALL VALUE OF PROJECT TO STUDENT S LEARNING We will be learning a new type of XML based markup language called OMDoc. This markup language will provide us knowledge about how to express mathematical expressions as well as its different applications. We will also be familiar with different technologies used by developers around the world who are working in similar projects. Since OMDoc has been used in various projects and developers are continuously using it for new technologies, we will get ideas about the applications of OMDoc in other different field of mathematics. CAPABILITY OF STUDENTS TO COMPLETE PROJECT Michael Watts is a third year student at Southeastern Louisiana University. He s been involved in web development since a young age and has taken courses in Software Engineering and Web Development. His knowledge of XML markup will contribute to the project. Ratish Shrestha, a senior computer student, has taken computer science courses such as Theory of Numerical Methods, Web Programming, and Software Engineering that are helpful in the success of this project. Currently, he has been working for Southeastern Web Team as a Web Programmer Intern. He can use his experience as a Web Programmer and contribute his efforts to this project. FEASIBILITY OF PROJECT TO BE COMPLETED WITH AVAILABLE RESOURCES Our faculty sponsor will provide us space to work in the lab of Computer Science department. We do not need to travel places for this project. We will be using computers extensively that has access to the Internet. This project is based primarily on Open Source environment, so we do not need to buy most of the required software. We can download much of the software, including Cygwin, QMath, and some basic editors from the Internet for free. A more feature-filled editor will require more funding, which we believe will speed the project as well as increase the accuracy of our results.

4 BUDGET JUSTIFICATION The total funds requested for our project equal $1, Our project requires Operating Expenses include two copies of Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, by Hestenes and Garret Sobczyk are requested for purchase to use for the project ($ x 2 = $250). A copy of XML editor Altova XMLSpy is requested ($600). This software allows us to work with XML using the views and options that best suit our project needs and working preferences, increases productivity by allowing us to develop higher-quality, standardsconformant XML-based applications. Two flash drivers, Extreme Cruzer Contour 8GB USB Flash Drive, SDCZ A75 ($65 x 2 = $130). We also request printer paper ($20) for print out the results.

5 Literature Cited Kohlhase, Michael. "An Open Markup Format for Mathematical Documents." Springer APR Sep 2008 < Hestenes, David. Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Dordrecht: D. Reidel Publishing Company, 1984.

6 STAR Budget/Narrative Page Title of Project Use OMDoc Representing Geometric Algebra Please carefully consider your budget requests. If funded, you will be expected to spend grant dollars as indicated in your original budget. Any subsequent budget adjustments must be approved by the Dean s office and will result in funding delays. List all amounts beside the appropriate category and provided a brief, but specific justification for the request. *Exp. Budget Category Funds Reason for Request Code Requested Travel in LA Field Travel Out-of-LA, Conf.&Conv Travel Out of LA Field Printing $20.00 Paper for printing Xeroxing Postage Operating Supplies: Misc Office supplies $ x Extreme Cruzer Contour 8GB USB Flash Drive, SDCZ A Supplies Oper. Supplies - Software $ Altova XMLSpy Oper. Supplies - Computer Oper. Supplies - Ed. & Rec Oper. Supplies - Other Oper. Supplies - Books $ x Clifford Algebra to Geometric Calculus A Unified Language for Mathematics and Physics, by Hestenes and Garret Sobczyk Acquisitions: Acad. Computer Acquisitions: Ed. & Rec. Total Request $1, *For a detailed description of each expenditure code, please visit the Controller s website at: You are reminded that internal grant funds are public monies; therefore, they must be managed in accordance with State procedures. This means (1) processing funds through specific numbered budget categories; (2) completing the necessary purchase requisitions, travel authorizations, etc. IN ADVANCE of any expenditure; and (3) following requirements to use specific vendors (University Bookstore, state contractors, etc.) Remember that all materials and/or equipment purchased with these monies are the property of Southeastern Louisiana University. NOTE: All funds related to this grant must be expended/encumbered by May 30. All remaining funds will revert back to the College of Science and Technology budget on June 1.

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International Journal of Research in Advent Technology Available Online at: CONTENT DICTIONARIES FOR RELATIONAL ALGEBRA Kuo-pao Yang 1, Theresa Beaubouef 2 1 2 Department of Computer Science and Industrial Technology 12 Southeastern Louisiana University 1 kyang@selu.edu ABSTARCT: