Numerical calculations in Clifford algebra : a practical guide for engineers and scientists

Numerical calculations in Clifford algebra a practical guide for engineers and scientists

Detalles Bibliográficos
Otros Autores: Seagar, Andrew, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, NJ : Wiley [2023]
Materias:
Algebra > Data processing.
Clifford algebras.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009828028806719
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • List of Figures
  • List of Tables
  • Preface
  • Part I Entities and Operations
  • Chapter 1 Introduction
  • 1.1 Operations
  • 1.2 History
  • 1.3 Alternative Forms
  • 1.4 Naming
  • 1.5 Structure
  • 1.5.1 Algebraic
  • 1.5.2 Numeric
  • 1.6 Entities
  • References
  • Chapter 2 Input
  • 2.1 Syntax
  • 2.2 Constants
  • 2.2.1 Specific Types
  • 2.2.2 General
  • 2.3 Variables
  • 2.3.1 Checking and Converting
  • Reference
  • Chapter 3 Output
  • 3.1 Tree Format
  • 3.2 Numeric Formats
  • 3.2.1 Default Format
  • 3.2.2 Defined Format
  • 3.3 Extended Formats
  • 3.3.1 Rounding
  • 3.3.2 Parts of Coefficients
  • 3.4 Selected Components
  • 3.5 Primitive Formats
  • 3.6 Recovered Values
  • Chapter 4 Unary Operations
  • 4.1 Theory
  • 4.1.1 Negation
  • 4.1.2 Involution
  • 4.1.3 Pair Exchange
  • 4.1.4 Reversion
  • 4.1.5 Clifford Conjugation
  • 4.1.6 Supplementation and Pseudo‐scalar
  • 4.2 Practice
  • 4.2.1 Example Code
  • 4.2.2 Example Output
  • Chapter 5 Binary Operations
  • 5.1 Geometric Origins
  • 5.1.1 Outer Multiplication
  • 5.1.2 Orthogonal Components
  • 5.1.3 Inner Multiplication
  • 5.1.4 Names
  • 5.2 Multiplication of Units
  • 5.2.1 Progressive and Regressive Multiplication
  • 5.2.2 Outer, Inner, and Central Multiplication
  • 5.2.3 Multiplication By Scalars
  • 5.3 Central Multiplication
  • 5.3.1 Primal Units
  • 5.3.2 Evolved and Other Units
  • 5.3.3 Numbers
  • 5.4 Practice
  • 5.4.1 Example Code
  • 5.4.2 Example Output
  • 5.4.3 Multiplication Tables
  • References
  • Chapter 6 Vectors and Geometry
  • 6.1 Theory
  • 6.1.1 Magnitude
  • 6.1.2 Inverse
  • 6.1.3 Reflection
  • 6.1.4 Projection
  • 6.1.5 Rotation
  • 6.2 Practice
  • 6.2.1 Example Code
  • 6.2.2 Example Output
  • Chapter 7 Quaternions
  • 7.1 Theory
  • 7.1.1 Magnitude
  • 7.1.2 Inverse
  • 7.1.3 Reflection and Projection
  • 7.1.4 Rotation
  • 7.1.5 Intersection.
  • 7.1.6 Factorisation
  • 7.2 Practice
  • 7.2.1 Example Code
  • 7.2.2 Example Output
  • References
  • Chapter 8 Pauli Matrices
  • 8.1 Theory
  • 8.1.1 Recovery of Components
  • 8.1.2 Magnitude
  • 8.1.3 Inverse
  • 8.1.4 Reflection, Projection, and Rotation
  • 8.2 Practice
  • 8.2.1 Example Code
  • 8.2.2 Example Output
  • Reference
  • Chapter 9 Bicomplex Numbers
  • 9.1 Theory
  • 9.1.1 Conjugate
  • 9.1.2 Magnitude
  • 9.1.3 Inverse
  • 9.1.4 Reflection, Projection, and Rotation
  • 9.2 Practice
  • 9.2.1 Example Code
  • 9.2.2 Example Output
  • Reference
  • Chapter 10 Electromagnetic Fields
  • 10.1 Theory
  • 10.1.1 Time and Frequency
  • 10.1.2 Electromagnetic Entities
  • 10.1.3 Dirac Operators
  • 10.1.4 Maxwell's Equations
  • 10.1.5 Simplified Notation
  • 10.1.6 Magnitude
  • 10.1.7 Inverse
  • 10.1.8 Reflection
  • 10.1.9 Projection
  • 10.1.10 Rotation
  • 10.2 Practice
  • 10.2.1 Example Code
  • 10.2.2 Example Output
  • 10.3 Field Arithmetic
  • 10.3.1 Extensions Based on Quaternions
  • 10.3.2 Inverses
  • 10.3.3 Example Code
  • 10.3.4 Example Output
  • References
  • Chapter 11 Arrays of Clifford Numbers
  • 11.1 Theory
  • 11.2 Practice
  • 11.2.1 Example Code
  • 11.2.2 Example Output
  • Reference
  • Chapter 12 Power Series
  • 12.1 Theory
  • 12.1.1 User Defined
  • 12.1.2 Predefined
  • 12.1.3 Convergence
  • 12.1.4 Factorisation
  • 12.1.5 Squaring
  • 12.2 Practice
  • 12.2.1 User Defined
  • 12.2.2 Predefined
  • 12.2.2.1 Standard Convergence
  • 12.2.2.2 Extended Convergence
  • 12.2.2.3 Doubly Extended Convergence
  • References
  • Chapter 13 Matrices of Clifford Numbers
  • 13.1 Background
  • 13.2 Inversion
  • 13.3 Practice
  • 13.3.1 Example Code
  • 13.3.2 Example Output
  • Reference
  • Part II Customisation
  • Chapter 14 Memory
  • 14.1 Memory Usage
  • 14.2 Examples
  • 14.2.1 Memory Tree Sparsity
  • 14.2.2 Memory Expansion
  • 14.2.3 Memory Recycling.
  • 14.2.3.1 Explicit and Implicit
  • 14.2.3.2 Implicit and Nested
  • Reference
  • Chapter 15 Errors
  • 15.1 User Errors
  • 15.1.1 Syntax Errors and Messages
  • 15.2 System Errors
  • 15.3 Recovery
  • 15.4 Beneficial Usage
  • Reference
  • Chapter 16 Extension
  • 16.1 Accumulation
  • 16.2 Multiplication
  • 16.3 Transformation
  • 16.4 Filtration
  • Part III Application
  • Chapter 17 Verification
  • 17.1 Identities
  • 17.2 Tests
  • 17.2.1 Example Code
  • 17.2.2 Example Output
  • Reference
  • Chapter 18 Lines Not Parallel
  • 18.1 Theory
  • 18.1.1 Common Plane
  • 18.1.1.1 Inner Product
  • 18.1.1.2 Outer Product
  • 18.1.1.3 Geometrical Interpretation
  • 18.1.2 No Plane in Common
  • 18.1.2.1 Inner Product
  • 18.1.2.2 Solution
  • 18.2 Practice
  • 18.2.1 Example Code
  • 18.2.2 Example Output
  • Reference
  • Chapter 19 Perspective Projection
  • 19.1 Theory
  • 19.2 Practice
  • 19.2.1 Example Code
  • 19.2.2 Example Output
  • Reference
  • Chapter 20 Linear Systems
  • 20.1 Theory
  • 20.2 Practice
  • 20.2.1 Example Code
  • 20.2.2 Example Output
  • References
  • Chapter 21 Fast Fourier Transform
  • 21.1 Theory
  • 21.2 Practice
  • 21.2.1 Example Code
  • 21.2.2 Example Output
  • References
  • Chapter 22 Hertzian Dipole
  • 22.1 Theory
  • 22.2 Practice
  • 22.2.1 Example Code
  • 22.2.2 Example Output
  • Reference
  • Chapter 23 Finite Difference Time Domain
  • 23.1 Theory
  • 23.1.1 Analytical Solution
  • 23.1.2 Series Solution
  • 23.1.3 Analytical Example
  • 23.1.4 Numerical Derivatives
  • 23.2 Practice
  • 23.2.1 Example Code
  • 23.2.2 Example Output
  • References
  • Chapter 24 Cauchy Extension
  • 24.1 Background
  • 24.2 Theory
  • 24.2.1 Two Dimensions
  • 24.2.2 Three Dimensions
  • 24.2.3 Singularity
  • 24.2.4 The Taming Function
  • 24.2.5 Construction
  • 24.3 Practice
  • 24.3.1 Example Code
  • 24.3.2 Example Output
  • References
  • Chapter 25 Electromagnetic Scattering.
  • 25.1 Background
  • 25.2 Theory
  • 25.3 Practice
  • 25.3.1 Example Code
  • 25.3.2 Example Output
  • References
  • Part IV Programming
  • Chapter 26 Interfaces
  • 26.1 Configuration and Observation
  • 26.1.1 Management
  • 26.1.2 Printing
  • 26.2 Simple Entities
  • 26.2.1 Units
  • 26.2.2 Components
  • 26.2.3 Numbers
  • 26.2.3.1 Establishing and Recovering Values
  • 26.2.3.2 Functions
  • 26.2.3.3 Addition and Subtraction
  • 26.2.3.4 Multiplication
  • 26.2.3.5 Geometric
  • 26.2.3.6 Filtering
  • 26.3 Higher Entities
  • 26.3.1 Vectors
  • 26.3.2 Bicomplex Numbers
  • 26.3.3 Quaternions
  • 26.3.4 Pauli Matrices
  • 26.3.5 Electromagnetic Fields
  • 26.4 Multiple Entities
  • 26.4.1 Arrays
  • 26.4.2 Fast Fourier Transforms
  • 26.4.3 Series
  • 26.4.4 Matrices
  • Reference
  • Chapter 27 Descriptions
  • 27.1 Arguments
  • 27.2 Data types
  • 27.3 Formats
  • 27.4 Manual Pages
  • 27.4.1 A-E
  • 27.4.2 F-J
  • 27.4.3 K-O
  • 27.4.4 P-T
  • 27.4.5 U-Z
  • 27.5 Quick Reference
  • Reference
  • A Key to Example Code and Results
  • Index
  • EULA.

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