Numerical Calculations in Clifford Algebra

Andrew Seagar 지음

Wiley 2023년 05월 25일 출간

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책소개

NUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA An intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. Applications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of particular types, including scalars, bicomplex numbers, quaternions, Pauli matrices, and extended electromagnetic fields. Readers will find: A thorough introduction to Clifford algebra, with a combination of theory and practical implementation in a range of engineering problems Comprehensive explorations of a variety of worked and computed examples at various levels of complexity Practical discussions of the conceptual and computational tools for solving common engineering problems Detailed documentation on the deployment and application of the Clifford Numerical Suite Perfect for engineers, researchers, and academics with an interest in Clifford algebra, Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists will particularly benefit professionals in the areas of antenna design, digital image processing, theoretical physics, and geometry.

목차

Preface xix I Entities and Operations 1 Introduction 3 1.1 Operations 3 1.2 History 4 1.3 Alternative Forms 4 1.4 Naming 5 1.5 Structure 6 1.5.1 Algebraic 6 1.5.2 Numeric 6 1.6 Entities 9 2 Input 11 2.1 Syntax 11 2.2 Constants 12 2.2.1 Specific Types 12 2.2.2 General 13 2.3 Variables 15 2.3.1 Checking and Converting 15 3 Output 21 3.1 Tree Format 21 3.2 Numeric Formats 24 3.2.1 Default Format 24 3.2.2 Defined Format 25 3.3 Extended Formats 26 3.3.1 Rounding 26 v vi c Seagar/Wiley, September 16, 2022 Contents 3.3.2 Parts of Coefficients 27 3.4 Selected Components 28 3.5 Primitive Formats 29 3.6 Recovered Values 30 4 Unary Operations 33 4.1 Theory 33 4.1.1 Negation 33 4.1.2 Involution 34 4.1.3 Pair Exchange 34 4.1.4 Reversion 35 4.1.5 Clifford Conjugation 36 4.1.6 Supplementation and Pseudoscalar 36 4.2 Practice 37 4.2.1 Example Code 37 4.2.2 Example Output 38 5 Binary Operations 41 5.1 Geometric Origins 41 5.1.1 Outer Multiplication 41 5.1.2 Orthogonal Components 43 5.1.3 Inner Multiplication 44 5.1.4 Names 45 5.2 Multiplication of Units 46 5.2.1 Progressive and Regressive Multiplication 46 5.2.2 Outer, Inner and Central Multiplication 47 5.2.3 Multiplication by Scalars 49 5.3 Central Multiplication 49 5.3.1 Primal Units 50 5.3.2 Evolved and Other Units 51 5.3.3 Numbers 52 5.4 Practice 53 5.4.1 Example Code 53 5.4.2 Example Output 54 5.4.3 Multiplication Tables 54 Contents c Seagar/Wiley, September 16, 2022 vii 6 Vectors and Geometry 59 6.1 Theory 59 6.1.1 Magnitude 59 6.1.2 Inverse 60 6.1.3 Reflection 60 6.1.4

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저자(글) Andrew Seagar