| Description |
1 online resource (645 pages) |
| Series |
Discrete Mathematics and Its Applications Ser |
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Discrete Mathematics and Its Applications Ser
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| Contents |
Intro; Halftitle Page; Title Page; Copyright; Table of Contents; Foreword; Preface; Contributors; 1 Overview and Preliminaries; 1.1 Introduction; 1.1.1 Specifying a GCS; 1.1.2 Fundamental GCS Questions; 1.1.3 Tractability and Computational Complexity; 1.2 Parts and Chapters of the Handbook; 1.2.1 Part I: Geometric Reasoning Techniques; 1.2.2 Part II: Distance Geometry, Configuration Space, and Real Algebraic Geometry Techniques; 1.2.3 Part III: Geometric Rigidity Techniques; 1.2.4 Part IV: Combinatorial Rigidity Techniques; 1.2.4.1 Inductive Constructions; 1.2.4.2 Body Frameworks |
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1.2.4.3 Body-Cad, and Point-Line Frameworks1.2.4.4 Symmetric and Periodic Frameworks and Frameworks under Polyhedral Norms; 1.2.5 Missing Topics and Chapters; 1.3 Terminology Reconciliation and Basic Concepts; 1.3.1 Constrainedness; 1.3.2 Rigidity of Frameworks; 1.3.3 Generic Rigidity of Frameworks; 1.3.4 Approximate Degree-of-Freedom and Sparsity; 1.4 Alternative Pathway through the Book; I Geometric Reasoning, Factorization and Decomposition; 2 Computer-Assisted Theorem Proving in Synthetic Geometry; 2.1 Introduction; 2.2 Automated Theorem Proving; 2.2.1 Foundations |
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2.2.2 Nondegenerate Conditions2.2.3 Purely Synthetic Methods; 2.2.3.1 Early Systems; 2.2.3.2 Deductive Database Method, GRAMY, and iGeoTutor; 2.2.3.3 Logic-Based Approaches; 2.2.4 Semisynthetic Methods; 2.2.4.1 Area Method; 2.2.4.2 Full-Angle Method; 2.2.4.3 Vector-Based Method; 2.2.4.4 Mass-Point Method; 2.2.5 Provers Implementations and Repositories of Theorems; 2.3 Interactive Theorem Proving; 2.3.1 Formalization of Foundations of Geometry; 2.3.1.1 Hilbert's Geometry; 2.3.1.2 Tarski's Geometry; 2.3.1.3 Axiom Systems and Continuity Properties; 2.3.1.4 Other Axiom Systems and Geometries |
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2.3.1.5 Meta-Theory2.3.2 Higher Level Results; 2.3.3 Other Formalizations Related to Geometry; 2.3.4 Verified Automated Reasoning; 3 Coordinate-Free Theorem Proving in Incidence Geometry; 3.1 Incidence Geometry; 3.1.1 Incidence Geometry in the Plane; 3.1.2 Other Primitive Operations; 3.1.3 Projective Invariance; 3.2 Bracket Algebra: Straightening, Division, and Final Polynomials; 3.2.1 Bracket Algebra and Straightening; 3.2.2 Division; 3.2.3 Final Polynomials; 3.3 Cayley Expansion and Factorization; 3.3.1 Cayley Expansion; 3.3.2 Cayley Factorization |
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3.3.3 Cayley Expansion and Factorization in Geometric Theorem Proving3.3.4 Rational Invariants and Antisymmetrization; 3.4 Bracket Algebra for Euclidean Geometry; 3.4.1 The Points I and J; 3.4.2 Proving Euclidean Theorems; 4 Special Positions of Frameworks and the Grassmann-Cayley Algebra; 4.1 Introduction: the Grassmann-Cayley Algebra and Frameworks; 4.2 Projective Space; 4.2.1 Motivation; 4.2.2 Homogeneous Coordinates and Points at Infinity; 4.2.3 Equations on Projective Space; 4.2.4 Duality Between Lines and Points in; 4.2.5 Grassmannians and Plücker Coordinates |
| Notes |
4.2.6 More About Lines in 3-space |
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Print version record |
| Form |
Electronic book
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| Author |
St. John, Audrey
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Sidman, Jessica
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| ISBN |
9781351647434 |
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1351647431 |
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9781498738927 |
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1498738923 |
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