Biasbas 2005 A Clifford algebra calculator for multivector multiplication

Christopher B. Biasbas, “A Clifford algebra calculator for multivector multiplication,” Undergraduate thesis, Physics Department (Ateneo de Manila University, Quezon City, Philippines, 2005), 38 pages.

Abstract
Clifford Algebra is considered by its proponents to be the unification of mathematical and physical knowledge. The Calculator produced in this project is the first step towards a Clifford Algebra software that can symbolically perform operations between multivectors of arbitrary dimension using the linked-list data structure, and can be use an instructional or verification tool. It is constructed using the parser-generation tools Flex and Bison, which makes it very upgradeable.

CONTENTS

1.  Introduction
1.1 Background of the Study
1.1.1 Clifford Algebra
1.1.2 Multivectors
1.1.3 Multiplication Calculator
1.2 Statement of the Problem
1.3 Objectives
1.4 Scope and Limitations
1.5 Significance of the Study

2. Review of Related Literature
2.1 Other Clifford Algebra Packages
2.2 Multivector Multiplication Methods
2.2.1 Walsh Function Approach
2.2.2 Linked-List Multiplication Approach
2.3 Parser Design Tools: Flex and Bison<

3. Theoretical Framework: Clifford Algebra
3.1 Orthonormality Axiom
3.2 Multivector Multiplication

4. Methodology
4.1 Conceptual Framework
4.2 Input String
4.3 Lexical Analyzer
4.4 Syntax Analyzer/Processor
4.5 Multiplication and Output

5. Results and Discussion
5.1 Sample Run
5.2 Clifford Algebra Group Tables

6. Conclusion

7. Recommendations

References
Appendix
A. Flex Source Code
B. Bison Source Code
C. C Functions