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| 003 - CONTROL NUMBER IDENTIFIER |
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CITU |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20241021094647.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
241021b |||||o|||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781394173242 |
| Qualifying information |
hardcover |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781394173259 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1394173253 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781394173273 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
139417327X |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781394173266 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1394173261 |
| Qualifying information |
electronic book |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)1369031647 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
DLC |
| Language of cataloging |
eng |
| Description conventions |
rda |
| Transcribing agency |
DLC |
| Modifying agency |
OCLCF |
| -- |
YDX |
| -- |
N$T |
| -- |
YDX |
| -- |
DG1 |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
pcc |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA199 |
| Item number |
.S43 2023 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
512/.57 |
| Edition number |
23/eng20230203 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Preferred name for the person |
Seagar, Andrew, |
| Authority record control number |
https://id.loc.gov/authorities/names/no2016037150 |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Numerical calculations in Clifford algebra : |
| Remainder of title |
a practical guide for engineers and scientists / |
| Statement of responsibility, etc |
Andrew Seagar. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Hoboken, NJ : |
| Name of publisher, distributor, etc |
John Wiley & Sons, Inc., |
| Date of publication, distribution, etc |
2023. |
| 264 #4 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Date of publication, distribution, etc |
©2023. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 online resource (xxiv, 502 pages) : |
| Other physical details |
illustrations (some color) |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent. |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia. |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - CONTENTS |
|---|
| Formatted contents note |
Table of Contents<br/>List of Figures xv<br/><br/>List of Tables xix<br/><br/>Preface xxi<br/><br/>Part I Entities and Operations 1<br/><br/>1 Introduction 3<br/><br/>1.1 Operations 3<br/><br/>1.2 History 4<br/><br/>1.3 Alternative Forms 5<br/><br/>1.4 Naming 6<br/><br/>1.5 Structure 7<br/><br/>1.5.1 Algebraic 7<br/><br/>1.5.2 Numeric 8<br/><br/>1.6 Entities 11<br/><br/>References 12<br/><br/>2 Input 13<br/><br/>2.1 Syntax 13<br/><br/>2.2 Constants 14<br/><br/>2.2.1 Specific Types 14<br/><br/>2.2.2 General 16<br/><br/>2.3 Variables 19<br/><br/>2.3.1 Checking and Converting 19<br/><br/>Reference 23<br/><br/>3 Output 25<br/><br/>3.1 Tree Format 26<br/><br/>3.2 Numeric Formats 29<br/><br/>3.2.1 Default Format 29<br/><br/>3.2.2 Defined Format 31<br/><br/>3.3 Extended Formats 32<br/><br/>3.3.1 Rounding 32<br/><br/>3.3.2 Parts of Coefficients 33<br/><br/>3.4 Selected Components 35<br/><br/>3.5 Primitive Formats 36<br/><br/>3.6 Recovered Values 38<br/><br/>4 Unary Operations 41<br/><br/>4.1 Theory 41<br/><br/>4.1.1 Negation 41<br/><br/>4.1.2 Involution 41<br/><br/>4.1.3 Pair Exchange 42<br/><br/>4.1.4 Reversion 43<br/><br/>4.1.5 Clifford Conjugation 44<br/><br/>4.1.6 Supplementation and Pseudo-scalar 44<br/><br/>4.2 Practice 45<br/><br/>4.2.1 Example Code 45<br/><br/>4.2.2 Example Output 47<br/><br/>5 Binary Operations 49<br/><br/>5.1 Geometric Origins 49<br/><br/>5.1.1 Outer Multiplication 49<br/><br/>5.1.2 Orthogonal Components 52<br/><br/>5.1.3 Inner Multiplication 53<br/><br/>5.1.4 Names 54<br/><br/>5.2 Multiplication of Units 55<br/><br/>5.2.1 Progressive and Regressive Multiplication 55<br/><br/>5.2.2 Outer, Inner, and Central Multiplication 57<br/><br/>5.2.3 Multiplication By Scalars 58<br/><br/>5.3 Central Multiplication 59<br/><br/>5.3.1 Primal Units 60<br/><br/>5.3.2 Evolved and Other Units 61<br/><br/>5.3.3 Numbers 62<br/><br/>5.4 Practice 63<br/><br/>5.4.1 Example Code 63<br/><br/>5.4.2 Example Output 65<br/><br/>5.4.3 Multiplication Tables 65<br/><br/>References 70<br/><br/>6 Vectors and Geometry 71<br/><br/>6.1 Theory 71<br/><br/>6.1.1 Magnitude 71<br/><br/>6.1.2 Inverse 72<br/><br/>6.1.3 Reflection 72<br/><br/>6.1.4 Projection 73<br/><br/>6.1.5 Rotation 73<br/><br/>6.2 Practice 74<br/><br/>6.2.1 Example Code 74<br/><br/>6.2.2 Example Output 76<br/><br/>7 Quaternions 79<br/><br/>7.1 Theory 79<br/><br/>7.1.1 Magnitude 80<br/><br/>7.1.2 Inverse 80<br/><br/>7.1.3 Reflection and Projection 80<br/><br/>7.1.4 Rotation 81<br/><br/>7.1.5 Intersection 82<br/><br/>7.1.6 Factorisation 82<br/><br/>7.2 Practice 83<br/><br/>7.2.1 Example Code 83<br/><br/>7.2.2 Example Output 86<br/><br/>References 87<br/><br/>8 Pauli Matrices 89<br/><br/>8.1 Theory 89<br/><br/>8.1.1 Recovery of Components 90<br/><br/>8.1.2 Magnitude 90<br/><br/>8.1.3 Inverse 91<br/><br/>8.1.4 Reflection, Projection, and Rotation 91<br/><br/>8.2 Practice 91<br/><br/>8.2.1 Example Code 91<br/><br/>8.2.2 Example Output 94<br/><br/>Reference 95<br/><br/>9 Bicomplex Numbers 97<br/><br/>9.1 Theory 97<br/><br/>9.1.1 Conjugate 98<br/><br/>9.1.2 Magnitude 98<br/><br/>9.1.3 Inverse 98<br/><br/>9.1.4 Reflection, Projection, and Rotation 99<br/><br/>9.2 Practice 99<br/><br/>9.2.1 Example Code 99<br/><br/>9.2.2 Example Output 101<br/><br/>Reference 102<br/><br/>10 Electromagnetic Fields 103<br/><br/>10.1 Theory 103<br/><br/>10.1.1 Time and Frequency 103<br/><br/>10.1.2 Electromagnetic Entities 104<br/><br/>10.1.3 Dirac Operators 105<br/><br/>10.1.4 Maxwell’s Equations 105<br/><br/>10.1.5 Simplified Notation 105<br/><br/>10.1.6 Magnitude 106<br/><br/>10.1.7 Inverse 106<br/><br/>10.1.8 Reflection 107<br/><br/>10.1.9 Projection 107<br/><br/>10.1.10 Rotation 107<br/><br/>10.2 Practice 107<br/><br/>10.2.1 Example Code 107<br/><br/>10.2.2 Example Output 110<br/><br/>10.3 Field Arithmetic 112<br/><br/>10.3.1 Extensions Based on Quaternions 112<br/><br/>10.3.2 Inverses 113<br/><br/>10.3.3 Example Code 115<br/><br/>10.3.4 Example Output 117<br/><br/>References 118<br/><br/>11 Arrays of Clifford Numbers 119<br/><br/>11.1 Theory 119<br/><br/>11.2 Practice 120<br/><br/>11.2.1 Example Code 120<br/><br/>11.2.2 Example Output 123<br/><br/>Reference 125<br/><br/>12 Power Series 127<br/><br/>12.1 Theory 127<br/><br/>12.1.1 User Defined 127<br/><br/>12.1.2 Predefined 128<br/><br/>12.1.3 Convergence 129<br/><br/>12.1.4 Factorisation 130<br/><br/>12.1.5 Squaring 131<br/><br/>12.2 Practice 131<br/><br/>12.2.1 User Defined 131<br/><br/>12.2.2 Predefined 133<br/><br/>12.2.2.1 Standard Convergence 136<br/><br/>12.2.2.2 Extended Convergence 141<br/><br/>12.2.2.3 Doubly Extended Convergence 146<br/><br/>References 148<br/><br/>13 Matrices of Clifford Numbers 149<br/><br/>13.1 Background 149<br/><br/>13.2 Inversion 150<br/><br/>13.3 Practice 152<br/><br/>13.3.1 Example Code 152<br/><br/>13.3.2 Example Output 155<br/><br/>Reference 159<br/><br/>Part II Customisation 161<br/><br/>14 Memory 163<br/><br/>14.1 Memory Usage 163<br/><br/>14.2 Examples 165<br/><br/>14.2.1 Memory Tree Sparsity 165<br/><br/>14.2.2 Memory Expansion 170<br/><br/>14.2.3 Memory Recycling 171<br/><br/>14.2.3.1 Explicit and Implicit 171<br/><br/>14.2.3.2 Implicit and Nested 173<br/><br/>Reference 175<br/><br/>15 Errors 177<br/><br/>15.1 User Errors 177<br/><br/>15.1.1 Syntax Errors and Messages 180<br/><br/>15.2 System Errors 181<br/><br/>15.3 Recovery 182<br/><br/>15.4 Beneficial Usage 185<br/><br/>Reference 191<br/><br/>16 Extension 193<br/><br/>16.1 Accumulation 193<br/><br/>16.2 Multiplication 195<br/><br/>16.3 Transformation 197<br/><br/>16.4 Filtration 198<br/><br/>Part III Application 203<br/><br/>17 Verification 205<br/><br/>17.1 Identities 205<br/><br/>17.2 Tests 205<br/><br/>17.2.1 Example Code 205<br/><br/>17.2.2 Example Output 208<br/><br/>Reference 214<br/><br/>18 Lines Not Parallel 215<br/><br/>18.1 Theory 215<br/><br/>18.1.1 Common Plane 215<br/><br/>18.1.1.1 Inner Product 216<br/><br/>18.1.1.2 Outer Product 217<br/><br/>18.1.1.3 Geometrical Interpretation 217<br/><br/>18.1.2 No Plane in Common 218<br/><br/>18.1.2.1 Inner Product 219<br/><br/>18.1.2.2 Solution 219<br/><br/>18.2 Practice 220<br/><br/>18.2.1 Example Code 220<br/><br/>18.2.2 Example Output 223<br/><br/>Reference 224<br/><br/>19 Perspective Projection 225<br/><br/>19.1 Theory 225<br/><br/>19.2 Practice 225<br/><br/>19.2.1 Example Code 225<br/><br/>19.2.2 Example Output 229<br/><br/>Reference 230<br/><br/>20 Linear Systems 231<br/><br/>20.1 Theory 231<br/><br/>20.2 Practice 233<br/><br/>20.2.1 Example Code 233<br/><br/>20.2.2 Example Output 235<br/><br/>References 235<br/><br/>21 Fast Fourier Transform 237<br/><br/>21.1 Theory 237<br/><br/>21.2 Practice 238<br/><br/>21.2.1 Example Code 238<br/><br/>21.2.2 Example Output 243<br/><br/>References 244<br/><br/>22 Hertzian Dipole 245<br/><br/>22.1 Theory 245<br/><br/>22.2 Practice 246<br/><br/>22.2.1 Example Code 246<br/><br/>22.2.2 Example Output 251<br/><br/>Reference 253<br/><br/>23 Finite Difference Time Domain 255<br/><br/>23.1 Theory 255<br/><br/>23.1.1 Analytical Solution 255<br/><br/>23.1.2 Series Solution 256<br/><br/>23.1.3 Analytical Example 257<br/><br/>23.1.4 Numerical Derivatives 257<br/><br/>23.2 Practice 259<br/><br/>23.2.1 Example Code 259<br/><br/>23.2.2 Example Output 265<br/><br/>References 270<br/><br/>24 Cauchy Extension 271<br/><br/>24.1 Background 271<br/><br/>24.2 Theory 272<br/><br/>24.2.1 Two Dimensions 272<br/><br/>24.2.2 Three Dimensions 272<br/><br/>24.2.3 Singularity 273<br/><br/>24.2.4 The Taming Function 273<br/><br/>24.2.5 Construction 274<br/><br/>24.3 Practice 276<br/><br/>24.3.1 Example Code 276<br/><br/>24.3.2 Example Output 281<br/><br/>References 284<br/><br/>25 Electromagnetic Scattering 285<br/><br/>25.1 Background 285<br/><br/>25.2 Theory 286<br/><br/>25.3 Practice 288<br/><br/>25.3.1 Example Code 288<br/><br/>25.3.2 Example Output 289<br/><br/>References 293<br/><br/>Part IV Programming 295<br/><br/>26 Interfaces 297<br/><br/>26.1 Configuration and Observation 297<br/><br/>26.1.1 Management 297<br/><br/>26.1.2 Printing 298<br/><br/>26.2 Simple Entities 300<br/><br/>26.2.1 Units 300<br/><br/>26.2.2 Components 300<br/><br/>26.2.3 Numbers 302<br/><br/>26.2.3.1 Establishing and Recovering Values 302<br/><br/>26.2.3.2 Functions 303<br/><br/>26.2.3.3 Addition and Subtraction 304<br/><br/>26.2.3.4 Multiplication 304<br/><br/>26.2.3.5 Geometric 305<br/><br/>26.2.3.6 Filtering 305<br/><br/>26.3 Higher Entities 306<br/><br/>26.3.1 Vectors 306<br/><br/>26.3.2 Bicomplex Numbers 307<br/><br/>26.3.3 Quaternions 307<br/><br/>26.3.4 Pauli Matrices 308<br/><br/>26.3.5 Electromagnetic Fields 308<br/><br/>26.4 Multiple Entities 309<br/><br/>26.4.1 Arrays 309<br/><br/>26.4.2 Fast Fourier Transforms 309<br/><br/>26.4.3 Series 310<br/><br/>26.4.4 Matrices 310<br/><br/>Reference 311<br/><br/>27 Descriptions 313<br/><br/>27.1 Arguments 313<br/><br/>27.2 Data types 313<br/><br/>27.3 Formats 315<br/><br/>27.4 Manual Pages 316<br/><br/>27.4.1 A–e 316<br/><br/>27.4.2 F–j 342<br/><br/>27.4.3 K–o 369<br/><br/>27.4.4 P–t 387<br/><br/>27.4.5 U–z 468<br/><br/>27.5 Quick Reference 477<br/><br/>Reference 487<br/><br/>A Key to Example Code and Results 489<br/><br/>Index 493 |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
"The purpose of the suite of routines described here, the Clifford Numerical Suite (CNS), is to provide a platform for the implementation of applications which require numerical evaluation of the various mathematical operations offered within the context of Clifford algebra. The routines are designed to allow the user to ignore most of the internal details of data structures and memory management if so desired. The suite is constructed using the 'C' computer programming language (Kernighan & Ritchie 1978, King 2008) so that it can be embedded into, compiled with, and invoked directly from the user's code. This avoids the overheads of copying data associated with the call mechanisms involved in implementations underneath interpretive meta-languages 1 and consequently offers an overall higher speed of code execution. That in turn admits the possibility of solving problems which are more realistic and less trivial. The intention is to provide most users with a viable environment for the development of their own applications. Providing the source code also allows the user to enhance and tailor it to best suit their own purposes. In cases where ultimate speed and memory efficiency is required, the suite can be used in the formative development phase, and substituted with the user's own hard-coded replacements in the end application phase"-- |
| Assigning source |
Provided by publisher. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
|---|
| Biographical or historical note |
About the Author<br/>Andrew Seagar, PhD, is Director for the Bachelor of Engineering Programs at the Gold Coast Campus of the School of Engineering at Griffith University in Australia. He has experience in a variety of research, commercial development, and academic positions around the world, primarily in the areas of electrical or biomedical engineering. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Clifford algebras. |
| Authority record control number |
https://id.loc.gov/authorities/subjects/sh85027030. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Algebra |
| General subdivision |
Data processing. |
| Authority record control number |
https://id.loc.gov/authorities/subjects/sh2007100982. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Print version: |
| Main entry heading |
Seagar, Andrew. |
| Title |
Numerical calculations in Clifford algebra |
| Place, publisher, and date of publication |
Hoboken, NJ : Wiley, 2023 |
| International Standard Book Number |
9781394173242 |
| Record control number |
(DLC) 2022053609. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
https://onlinelibrary.wiley.com/doi/book/10.1002/9781394173273 |
| Link text |
Full text available at Wiley Online Library Click here to view |
| 942 ## - ADDED ENTRY ELEMENTS |
|---|
| Source of classification or shelving scheme |
|
| Item type |
EBOOK |