The Power of Geometric Algebra Computing: For Engineering and Quantum Computing

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Foreword
Preface
CHAPTER 1: Introduction
	1.1. GEOMETRIC ALGEBRA
	1.2. GEOMETRIC ALGEBRA COMPUTING
	1.3. OUTLINE
CHAPTER 2: Geometric Algebras for Engineering
	2.1. THE BASICS OF GEOMETRIC ALGEBRA
	2.2. CONFORMAL GEOMETRIC ALGEBRA (CGA)
		2.2.1. Geometric Objects of Conformal Geometric Algebra
		2.2.2. Angles and Distances in 3D
		2.2.3. 3D Transformations
	2.3. COMPASS RULER ALGEBRA (CRA)
		2.3.1. Geometric Objects
		2.3.2. Angles and Distances
		2.3.3. Transformations
	2.4. PROJECTIVE GEOMETRIC ALGEBRA (PGA) WITH GANJA
		2.4.1. 2D PGA
		2.4.2. 3D PGA
CHAPTER 3: GAALOP
	3.1. INSTALLATION
	3.2. GAALOPSCRIPT
		3.2.1. The Main Notations
		3.2.2. Macros and Pragmas
		3.2.3. Bisector Example
		3.2.4. Line-Sphere Example
CHAPTER 4: GAALOPWeb
	4.1. THE WEB INTERFACE
	4.2. THE WORKFLOW
	4.3. GAALOPWEB VISUALIZATIONS
		4.3.1. Visualization of the Bisector Example
		4.3.2. Visualization of the Rotation of a Circle
		4.3.3. Visualization of the Line-Sphere Example
		4.3.4. Visualization of a Sphere of Four Points
		4.3.5. Sliders
CHAPTER 5: GAALOPWeb for C/C++
	5.1. GAALOPWEB HANDLING
	5.2. CODE GENERATION AND RUNTIME PERFORMANCE BASED ON GAALOPWEB
CHAPTER 6: GAALOPWeb for Python
	6.1. THE WEB INTERFACE
	6.2. THE PYTHON CONNECTOR FOR GAALOPWEB
	6.3. CLIFFORD/PYGANJA
	6.4. GAALOPWeb INTEGRATION INTO CLIFFORD/PYGANJA
	6.5. USING PYTHON TO GENERATE CODE NOT SUPPORTED BY GAALOPWEB
CHAPTER 7: Molecular Distance Application Using GAALOPWeb for Mathematica
	7.1. DISTANCE GEOMETRY EXAMPLE
	7.2. GAALOPWEB FOR MATHEMATICA
		7.2.1. Mathematica Code Generation
		7.2.2. The Web-Interface
	7.3. COMPUTATIONAL RESULTS
CHAPTER 8: Robot Kinematics Based on GAALOPWeb for MATLAB
	8.1. THE MANIPULATOR MODEL
	8.2. KINEMATICS OF A SERIAL ROBOT ARM
	8.3. MATLAB TOOLBOX IMPLEMENTATION
	8.4. THE GAALOP IMPLEMENTATION
	8.5. GAALOPWEB FOR MATLAB
	8.6. COMPARISON OF RUN-TIME PERFORMANCE
CHAPTER 9: The Power of High-Dimensional Geometric Algebras
	9.1. GAALOP DEFINITION
	9.2. VISUALIZATION
CHAPTER 10: GAALOPWeb for Conics
	10.1. GAALOP DEFINITION
		10.1.1. definition.csv
		10.1.2. macros.clu
	10.2. GAC OBJECTS
	10.3. GAC TRANSFORMATIONS
	10.4. INTERSECTIONS
CHAPTER 11: Double Conformal Geometric Algebra
	11.1. GAALOP DEFINITION OF DCGA
	11.2. THE DCGA OBJECTS
		11.2.1. Ellipsoid, Toroid and Sphere
		11.2.2. Planes and Lines
		11.2.3. Cylinders
		11.2.4. Cones
		11.2.5. Paraboloids
		11.2.6. Hyperboloids
		11.2.7. Parabolic and Hyperbolic Cylinders
		11.2.8. Specific Planes
		11.2.9. Cyclides
	11.3. THE DCGA TRANSFORMATIONS
	11.4. INTERSECTIONS
	11.5. REFLECTIONS AND PROJECTIONS
	11.6. INVERSIONS
CHAPTER 12: Geometric Algebra for Cubics
	12.1. GAALOP DEFINITION
	12.2. CUBIC CURVES
CHAPTER 13: GAALOPWeb for GAPP
	13.1. THE REFLECTOR EXAMPLE
	13.2. THE WEB INTERFACE
	13.3. GAPP CODE GENERATION
CHAPTER 14: GAALOPWeb for GAPPCO
	14.1. GAPPCO IN GENERAL
	14.2. GAPPCO I
		14.2.1. GAPPCO I Architecture
		14.2.2. The Compilation Process
		14.2.3. Configuration Phase
		14.2.4. Runtime Phase
	14.3. THE WEB INTERFACE
CHAPTER 15: GAPPCO II
	15.1. THE PRINCIPLE
	15.2. EXAMPLE
	15.3. IMPLEMENTATION ISSUES
CHAPTER 16: Introduction to Quantum Computing
	16.1. COMPARING CLASSIC COMPUTERS WITH QUANTUM COMPUTERS
	16.2. DESCRIPTION OF QUANTUM BITS
	16.3. QUANTUM REGISTER
	16.4. COMPUTING STEPS IN QUANTUM COMPUTING
		16.4.1. The NOT-Operation
		16.4.2. The Hadamard Transform
		16.4.3. The CNOT-Operation
CHAPTER 17: GAALOPWeb as a Qubit Calculator
	17.1. QUBIT ALGEBRA QBA
	17.2. GAALOPWEB FOR QUBITS
	17.3. THE NOT-OPERATION ON A QUBIT
	17.4. THE 2-QUBIT ALGEBRA QBA2
CHAPTER 18: Appendix
	18.1. APPENDIX A: PYTHON CODE FOR THE GENERATION OF OPTIMIZED MATHEMATICA CODE FROM GAALOP
Bibliography
Index