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The Power of Geometric Algebra Computing For Engineering and Quantum Computing 1st Edition by Dietmar Hildenbrand ISBN 9780367684587 0367684586

Name: The Power of Geometric Algebra Computing For Engineering and Quantum Computing 1st Edition by Dietmar Hildenbrand ISBN 9780367684587 0367684586
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The Power of Geometric Algebra Computing: For Engineering and Quantum Computing 1st Edition Dietmar Hildenbrand Digital Instant Download

Author(s): Dietmar Hildenbrand

ISBN(s): 9780367684587, 0367684586

Edition: 1

File Details: PDF, 13.09 MB

Year: 2021

Language: English

SKU: EB-34416490 Category: Computers - Computer Science Tag: Dietmar Hildenbrand

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The Power of Geometric Algebra Computing For Engineering and Quantum Computing 1st Edition by Dietmar Hildenbrand – Ebook PDF Instant Download/Delivery: 9780367684587 ,0367684586
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ISBN 10: 0367684586
ISBN 13: 9780367684587
Author: Dietmar Hildenbrand

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 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 1st Edition Table of contents:

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

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Tags: Dietmar Hildenbrand, Geometric Algebra Computing, Engineering, Quantum Computing