| Preface |
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Beneath-and-Beyond Revisited |
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1 | (22) |
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1 | (1) |
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Definitions, an Algorithm, and a Classical Theorem |
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2 | (4) |
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Sizes of Triangulations and Algorithm Complexity |
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6 | (6) |
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12 | (1) |
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13 | (4) |
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17 | (6) |
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20 | (3) |
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Some Algorithmic Problems in Polytope Theory |
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23 | (26) |
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23 | (3) |
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26 | (5) |
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31 | (4) |
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35 | (2) |
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37 | (2) |
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39 | (1) |
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40 | (9) |
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45 | (4) |
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Computing Triangulations Using Oriented Matroids |
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49 | (28) |
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49 | (1) |
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The oriented matroid of a Point Configuration |
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50 | (6) |
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Applications of the Oriented Matroid: How to Find Triangulations |
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56 | (5) |
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Implementing the Ideas: TOPCOM |
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61 | (2) |
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Exploring Further Structures |
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63 | (6) |
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Implementing the Ideas: Software Integration with polymake |
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69 | (2) |
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71 | (6) |
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71 | (2) |
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A Equivariant BFS: An Example Run for the Six-gon |
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73 | (4) |
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Discrete Geometry for Algebraic Elimination |
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77 | (16) |
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77 | (1) |
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78 | (3) |
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81 | (3) |
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Algebraic Solving by Linear Algebra |
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84 | (4) |
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88 | (5) |
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90 | (3) |
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Sparse Resultant Perturbations |
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93 | (16) |
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93 | (2) |
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95 | (2) |
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Sparse Projection Operators |
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97 | (2) |
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99 | (2) |
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101 | (2) |
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103 | (6) |
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106 | (3) |
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Numerical Irreducible Decomposition Using PHCpack |
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109 | (22) |
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109 | (3) |
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Toolbox and Blackbox Design of PHCpack |
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112 | (1) |
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A Maple Interface to PHCpack |
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113 | (1) |
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Numerical Elimination Methods |
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114 | (3) |
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Factoring into Irreducible Components |
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117 | (2) |
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119 | (2) |
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A Numerical Blackbox Decomposer |
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121 | (1) |
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122 | (3) |
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125 | (6) |
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126 | (5) |
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Generating Kummer Type Formulas for Hypergeometric Functions |
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131 | (16) |
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131 | (1) |
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Hypergeometric Function Associated to Δk--1 x Δn--k--1 |
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132 | (2) |
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134 | (3) |
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137 | (2) |
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Deriving Kummer Type Formulas |
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139 | (8) |
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144 | (3) |
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A Computer Algebra System: Risa/Asir |
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147 | (16) |
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147 | (1) |
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148 | (2) |
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150 | (6) |
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Parallel and Distributed Computation |
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156 | (1) |
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157 | (3) |
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160 | (3) |
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161 | (2) |
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Singular in a Framework for Polynomial Computations |
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163 | (14) |
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163 | (1) |
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164 | (1) |
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Basic Polynomial Operations and Representations |
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164 | (6) |
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170 | (1) |
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Arithmetics for Polynomials: Refinement: Bucket Addition |
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171 | (1) |
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172 | (2) |
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A Proposal for Distributing Polynomials |
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174 | (3) |
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176 | (1) |
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Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms |
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177 | (30) |
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177 | (2) |
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Generating the Boundary Matrices |
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179 | (2) |
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The Elimination Algorithm |
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181 | (2) |
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183 | (10) |
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193 | (3) |
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196 | (5) |
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Other Invariants of Simplicial Complexes |
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201 | (6) |
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204 | (3) |
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The Geometry of Cn is Important for the Algebra of Elementary Functions |
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207 | (18) |
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207 | (2) |
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How to Handle Multi-valued Functions |
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209 | (3) |
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212 | (1) |
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Simplifying Equations (4) and (5) |
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213 | (1) |
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213 | (4) |
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Strategies for Simplifying Elementary Expressions |
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217 | (1) |
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Strategies to Algorithms? |
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218 | (4) |
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222 | (3) |
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224 | (1) |
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A Visual Introduction to Cubic Surfaces Using the Computer Software Spicy |
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225 | (14) |
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225 | (2) |
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Blowing-Up the Plane in Six Points |
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227 | (2) |
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Visualizing Cubic Surfaces Using SPICY |
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229 | (10) |
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235 | (1) |
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Clebsch's Explicit Equation for the Covariant of Order 9 that Meets the Cubic Surface in the 27 Lines |
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236 | (1) |
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Coble's Explicit Parametrization for the Cubic Surface and the 27 Lines on it |
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237 | (2) |
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A Client-Server System for the Visualisation of Algebraic Surfaces on the Web |
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239 | (16) |
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239 | (1) |
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240 | (1) |
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241 | (8) |
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Examples of Algebraic Surfaces |
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249 | (2) |
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251 | (4) |
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253 | (2) |
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Visualizing Maple Plots with JavaViewLib |
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255 | (22) |
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255 | (1) |
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Visualization in Maple and JavaView |
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256 | (2) |
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JavaViewLib - A New Maple Powertool |
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258 | (7) |
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Importing and Exporting Geometries |
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265 | (4) |
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269 | (5) |
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274 | (1) |
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275 | (2) |
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275 | (2) |
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Automated Generation of Diagrams with Maple and Java |
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277 | (12) |
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Introduction and Motivation |
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277 | (2) |
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279 | (2) |
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281 | (2) |
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283 | (2) |
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285 | (4) |
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287 | (2) |
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Interactive Mathematical Documents on the Web |
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289 | (20) |
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Ernesto Reinaldo Barreiro |
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289 | (1) |
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A Framework for Interactive Mathematics |
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290 | (5) |
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The Mathematical Document Server |
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295 | (3) |
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MathBook, Our Implementation |
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298 | (6) |
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304 | (5) |
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306 | (3) |
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Distributed Computing for Conglomerate Mathematical Systems |
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309 | (18) |
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309 | (1) |
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Current Techniques for Integration of Mathematical Systems |
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310 | (4) |
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A Synopsis of Distributed Computing |
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314 | (2) |
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A Distributed Framework for Mathematical Systems |
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316 | (1) |
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317 | (10) |
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318 | (2) |
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A Technical Concepts and Terminology |
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320 | (7) |
| Index |
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327 | (4) |
| Software Systems |
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331 | |
