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Power of Geometric Algebra Computing: For Engineering and Quantum Computing [Kõva köide]

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  • Formaat: Hardback, 178 pages, kõrgus x laius: 229x152 mm, kaal: 399 g, 21 Tables, black and white; 90 Line drawings, black and white; 90 Illustrations, black and white
  • Ilmumisaeg: 30-Sep-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367684586
  • ISBN-13: 9780367684587
Teised raamatud teemal:
Power of Geometric Algebra Computing: For Engineering and Quantum ComputingSuurem pilt
  • Formaat: Hardback, 178 pages, kõrgus x laius: 229x152 mm, kaal: 399 g, 21 Tables, black and white; 90 Line drawings, black and white; 90 Illustrations, black and white
  • Ilmumisaeg: 30-Sep-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367684586
  • ISBN-13: 9780367684587
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367684587.html
Märksõnad:
"The Power of Geometric Algebra Computing for Engineering and Quantum Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications. This book includes applications from the fields of computer graphics, robotics and quantum computing and will help students, engineers and researchers interested in really computing withGeometric Algebra"--

Geometric Algebra is a very powerful mathematical system for an easy and intuitive treatment of geometry, but the community working with it is still very small. The main goal of this book is to close this gap from a computing perspective in presenting the power of Geometric Algebra Computing for engineering applications and quantum computing.

The Power of Geometric Algebra Computing for Engineering and Quantum Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications.

Key Features:

  • Introduces a new web-based optimizer for Geometric algebra algorithms.
  • Supports many programming languages as well as hardware.
  • Covers the advantages of High-dimensional algebras.
  • Includes geometrically intuitive support of quantum computing.

This book includes applications from the fields of computer graphics, robotics and quantum computing and will help students, engineers and researchers interested in really computing with Geometric Algebra.



The Power of Geometric Algebra Computing for Engineering and Quantum Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications.

List of Figures
xiii
List of Tables
xvii
Foreword xix
Preface xxi
Chapter 1 Introduction
1(4)
1.1 Geometric Algebra
1(1)
1.2 Geometric Algebra Computing
2(1)
1.3 Outline
3(2)
Chapter 2 Geometric Algebras for Engineering
5(20)
2.1 The Basics Of Geometric Algebra
5(3)
2.2 Conformal Geometric Algebra (CGA)
8(5)
2.2.1 Geometric Objects of Conformal Geometric Algebra
9(1)
2.2.2 Angles and Distances in 3D
10(1)
2.2.3 3D Transformations
10(3)
2.3 Compass Ruler Algebra (CRA)
13(4)
2.3.1 Geometric Objects
13(3)
2.3.2 Angles and Distances
16(1)
2.3.3 Transformations
16(1)
2.4 Projective Geometric Algebra (PGA) with Ganja
17(8)
2.4.1 2D PGA
17(2)
2.4.2 3D PGA
19(6)
Chapter 3 Gaalop
25(8)
3.1 Installation
26(1)
3.2 Gaalopscript
27(6)
3.2.1 The Main Notations
29(1)
3.2.2 Macros and Pragmas
30(1)
3.2.3 Bisector Example
31(1)
3.2.4 Line-Sphere Example
31(2)
Chapter 4 GAALOPWeb
33(8)
4.1 The Web Interface
34(1)
4.2 The Workflow
34(1)
4.3 GAALOPWeb Visualizations
35(6)
4.3.1 Visualization of the Bisector Example
35(1)
4.3.2 Visualization of the Rotation of a Circle
36(2)
4.3.3 Visualization of the Line-Sphere Example
38(1)
4.3.4 Visualization of a Sphere of Four Points
38(1)
4.3.5 Sliders
39(2)
Chapter 5 GAALOPWeb for C/C+ +
41(8)
5.1 GAALOPWeb Handling
41(4)
5.2 Code Generation and Runtime Performance Based on GAALOPWeb
45(4)
Chapter 6 GAALOPWeb for Python
49(10)
6.1 The Web Interface
49(2)
6.2 The Python Connector for GAALOPWeb
51(2)
6.3 Clifford/Pyganja
53(2)
6.4 GAALOPWeb Integration Into Clifford/Pyganja
55(1)
6.5 Using Python To Generate Code Not Supported By GAALOPWeb
56(3)
Chapter 7 Molecular Distance Application Using GAALOP-Web for Mathematica
59(12)
7.1 Distance Geometry Example
60(2)
7.2 GAALOPWeb for Mathematica
62(3)
7.2.1 Mathematica Code Generation
62(2)
7.2.2 The Web-Interface
64(1)
7.3 Computational Results
65(6)
Chapter 8 Robot Kinematics Based on GAALOPWeb for MATLAB®
71(12)
8.1 THE Manipulator Model
72(1)
8.2 Kinematics of a Serial Robot ARM
72(3)
8.3 MATLAB® Toolbox Implementation
75(2)
8.4 The Gaalop Implementation
77(2)
8.5 GAALOPWeb for MATLAB®
79(1)
8.6 Comparison Of Run-Time Performance
80(3)
Chapter 9 The Power of High-Dimensional Geometric Al-gebras
83(4)
9.1 Gaalop Definition
83(2)
9.2 Visualization
85(2)
Chapter 10 GAALOPWeb for Conies
87(14)
10.1 Gaalop Definition
87(2)
10.1.1 definition.csv
87(1)
10.1.2 macros.clu
88(1)
10.2 GAC Objects
89(5)
10.3 GAC Transformations
94(3)
10.4 Intersections
97(4)
Chapter 11 Double Conformal Geometric Algebra
101(24)
11.1 Gaalop Definition of DCGA
101(2)
11.2 The DCGA Objects
103(16)
11.2.1 Ellipsoid, Toroid and Sphere
103(3)
11.2.2 Planes and Lines
106(2)
11.2.3 Cylinders
108(1)
11.2.4 Cones
109(2)
11.2.5 Paraboloids
111(2)
11.2.6 Hyperboloids
113(2)
11.2.7 Parabolic and Hyperbolic Cylinders
115(2)
11.2.8 Specific Planes
117(1)
11.2.9 Cyclides
118(1)
11.3 The DCGA Transformations
119(2)
11.4 Intersections
121(1)
11.5 Reflections and Projections
122(1)
11.6 Inversions
123(2)
Chapter 12 Geometric Algebra for Cubics
125(6)
12.1 Gaalop Definition
125(3)
12.2 Cubic Curves
128(3)
Chapter 13 GAALOPWeb for GAPP
131(4)
13.1 The Reflector Example
131(1)
13.2 The Web Interface
132(1)
13.3 Gapp Code Generation
133(2)
Chapter 14 GAALOPWeb for GAPPCO
135(12)
14.1 GAPPCO in General
136(2)
14.2 GAPPCO I
138(6)
14.2.1 GAPPCO I Architecture
138(1)
14.2.2 The Compilation Process
139(1)
14.2.3 Configuration Phase
140(3)
14.2.4 Runtime Phase
143(1)
14.3 THE WEB INTERFACE
144(3)
Chapter 15 GAPPCO II
147(6)
15.1 The Principle
147(1)
15.2 Example
148(1)
15.3 Implementation Issues
149(4)
Chapter 16 Introduction to Quantum Computing
153(10)
16.1 Comparing Classic Computers with Quantum Computers
153(1)
16.2 Description of Quantum Bits
154(2)
16.3 Quantum Register
156(1)
16.4 Computing Steps in Quantum Computing
157(6)
16.4.1 The NOT-Operation
157(2)
16.4.2 The Hadamard Transform
159(2)
16.4.3 The CNOT-Operation
161(2)
Chapter 17 GAALOPWeb as a Qubit Calculator
163(6)
17.1 Qubit Algebra QBA
163(1)
17.2 GAALOPWeb for Qubits
164(1)
17.3 The Not-Operation On A Qubit
165(1)
17.4 The 2-Qubit Algebra QBA2
165(4)
Chapter 18 Appendix
169(4)
18.1 Appendix A: Python Code for the Generation of Optimized Mathematica Code from Gaalop
169(4)
Bibliography 173(4)
Index 177
Dietmar Hildenbrand is a lecturer in Geometric Algebra at TU Darmstadt.