Invariant algebras and geometric reasoning /:
The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics - among them, Grassmann-Cayley algebra and geometric algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other...
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1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Singarore ; Hackensack, N.J. :
World Scientific,
©2008.
|
Schlagworte: | |
Online-Zugang: | DE-862 DE-863 |
Zusammenfassung: | The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics - among them, Grassmann-Cayley algebra and geometric algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author's most recent, original development of Grassmann-Cayley algebra and geometric algebra and their applications in automated reasoning of classical geometries. It includes three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide. |
Beschreibung: | 1 online resource (xiv, 518 pages) : illustrations |
Bibliographie: | Includes bibliographical references (pages 495-504) and index. |
ISBN: | 9789812770110 9812770119 1281919004 9781281919007 9786611919009 6611919007 |
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245 | 1 | 0 | |a Invariant algebras and geometric reasoning / |c Hongbo Li. |
260 | |a Singarore ; |a Hackensack, N.J. : |b World Scientific, |c ©2008. | ||
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520 | |a The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics - among them, Grassmann-Cayley algebra and geometric algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author's most recent, original development of Grassmann-Cayley algebra and geometric algebra and their applications in automated reasoning of classical geometries. It includes three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide. | ||
505 | 0 | |a 1. Introduction. 1.1. Leibniz's dream. 1.2. Development of geometric algebras. 1.3. Conformal geometric algebra. 1.4. Geometric computing with invariant algebras. 1.5. From basic invariants to advanced invariants. 1.6. Geometric reasoning with advanced invariant algebras. 1.7. Highlights of the chapters -- 2. Projective space, bracket algebra and Grassmann-Cayley algebra. 2.1. Projective space and classical invariants. 2.2. Brackets from the symbolic point of view. 2.3. Covariants, duality and Grassmann-Cayley algebra. 2.4. Grassmann coalgebra. 2.5. Cayley expansion. 2.6. Grassmann factorization. 2.7. Advanced invariants and Cayley bracket algebra -- 3. Projective incidence geometry with Cayley bracket algebra. 3.1. Symbolic methods for projective incidence geometry. 3.2. Factorization techniques in bracket algebra. 3.3. Contraction techniques in bracket computing. 3.4. Exact division and pseudodivision. 3.5. Rational invariants. 3.6. Automated theorem proving. 3.7. Erdös' consistent 5-tuples -- 4. Projective conic geometry with bracket algebra and quadratic Grassmann-Cayley algebra. 4.1. Conics with bracket algebra, 4.2. Bracket-oriented representation. 4.3. Simplification techniques in conic computing. 4.4. Factorization techniques in conic computing. 4.5. Automated theorem proving. 4.6. Conics with quadratic Grassmann-Cayley algebra -- 5. Inner-product bracket algebra and Clifford algebra. 5.1. Inner-product bracket algebra. 5.2. Clifford algebra. 5.3. Representations of Clifford algebras. 5.4. Clifford expansion theory -- 6. Geometric algebra. 6.1. Major techniques in geometric algebra. 6.2. Versor compression. 6.3. Obstructions to versor compression. 6.4. Clifford coalgebra, Clifford summation and factorization. 6.5. Clifford bracket algebra -- 7. Euclidean geometry and conformal Grassmann-Cayley algebra. 7.1. Homogeneous coordinates and Cartesian coordinates. 7.2. The conformal model and the homogeneous model. 7.3. Positive-vector representations of spheres and hyperplanes. 7.4. Conformal Grassmann-Cayley algebra. 7.5. The Lie model of oriented spheres and hyperplanes. 7.6. Apollonian contact problem -- 8. Conformal Clifford algebra and classical geometries. 8.1. The geometry of positive monomials. 8.2. Cayley transform and exterior exponential. 8.3. Twisted Vahlen matrices and Vahlen matrices. 8.4. Affine geometry with dual Clifford algebra. 8.5. Spherical geometry and its conformal model. 8.6. Hyperbolic geometry and its conformal model. 8.7. Unifed algebraic framework for classical geometries. | |
546 | |a English. | ||
650 | 0 | |a Clifford algebras. |0 http://id.loc.gov/authorities/subjects/sh85027030 | |
650 | 0 | |a Invariants. |0 http://id.loc.gov/authorities/subjects/sh85067665 | |
650 | 0 | |a Symmetry (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh2006001303 | |
650 | 6 | |a Algèbres de Clifford. | |
650 | 6 | |a Invariants. | |
650 | 6 | |a Symétrie (Mathématiques) | |
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650 | 7 | |a Clifford algebras |2 fast | |
650 | 7 | |a Invariants |2 fast | |
650 | 7 | |a Symmetry (Mathematics) |2 fast | |
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author | Li, Hongbo |
author_facet | Li, Hongbo |
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contents | 1. Introduction. 1.1. Leibniz's dream. 1.2. Development of geometric algebras. 1.3. Conformal geometric algebra. 1.4. Geometric computing with invariant algebras. 1.5. From basic invariants to advanced invariants. 1.6. Geometric reasoning with advanced invariant algebras. 1.7. Highlights of the chapters -- 2. Projective space, bracket algebra and Grassmann-Cayley algebra. 2.1. Projective space and classical invariants. 2.2. Brackets from the symbolic point of view. 2.3. Covariants, duality and Grassmann-Cayley algebra. 2.4. Grassmann coalgebra. 2.5. Cayley expansion. 2.6. Grassmann factorization. 2.7. Advanced invariants and Cayley bracket algebra -- 3. Projective incidence geometry with Cayley bracket algebra. 3.1. Symbolic methods for projective incidence geometry. 3.2. Factorization techniques in bracket algebra. 3.3. Contraction techniques in bracket computing. 3.4. Exact division and pseudodivision. 3.5. Rational invariants. 3.6. Automated theorem proving. 3.7. Erdös' consistent 5-tuples -- 4. Projective conic geometry with bracket algebra and quadratic Grassmann-Cayley algebra. 4.1. Conics with bracket algebra, 4.2. Bracket-oriented representation. 4.3. Simplification techniques in conic computing. 4.4. Factorization techniques in conic computing. 4.5. Automated theorem proving. 4.6. Conics with quadratic Grassmann-Cayley algebra -- 5. Inner-product bracket algebra and Clifford algebra. 5.1. Inner-product bracket algebra. 5.2. Clifford algebra. 5.3. Representations of Clifford algebras. 5.4. Clifford expansion theory -- 6. Geometric algebra. 6.1. Major techniques in geometric algebra. 6.2. Versor compression. 6.3. Obstructions to versor compression. 6.4. Clifford coalgebra, Clifford summation and factorization. 6.5. Clifford bracket algebra -- 7. Euclidean geometry and conformal Grassmann-Cayley algebra. 7.1. Homogeneous coordinates and Cartesian coordinates. 7.2. The conformal model and the homogeneous model. 7.3. Positive-vector representations of spheres and hyperplanes. 7.4. Conformal Grassmann-Cayley algebra. 7.5. The Lie model of oriented spheres and hyperplanes. 7.6. Apollonian contact problem -- 8. Conformal Clifford algebra and classical geometries. 8.1. The geometry of positive monomials. 8.2. Cayley transform and exterior exponential. 8.3. Twisted Vahlen matrices and Vahlen matrices. 8.4. Affine geometry with dual Clifford algebra. 8.5. Spherical geometry and its conformal model. 8.6. Hyperbolic geometry and its conformal model. 8.7. Unifed algebraic framework for classical geometries. |
ctrlnum | (OCoLC)560635800 |
dewey-full | 512/.57 |
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dewey-ones | 512 - Algebra |
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them, Grassmann-Cayley algebra and geometric algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author's most recent, original development of Grassmann-Cayley algebra and geometric algebra and their applications in automated reasoning of classical geometries. It includes three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Introduction. 1.1. Leibniz's dream. 1.2. Development of geometric algebras. 1.3. Conformal geometric algebra. 1.4. Geometric computing with invariant algebras. 1.5. From basic invariants to advanced invariants. 1.6. Geometric reasoning with advanced invariant algebras. 1.7. Highlights of the chapters -- 2. Projective space, bracket algebra and Grassmann-Cayley algebra. 2.1. Projective space and classical invariants. 2.2. Brackets from the symbolic point of view. 2.3. Covariants, duality and Grassmann-Cayley algebra. 2.4. Grassmann coalgebra. 2.5. Cayley expansion. 2.6. Grassmann factorization. 2.7. Advanced invariants and Cayley bracket algebra -- 3. Projective incidence geometry with Cayley bracket algebra. 3.1. Symbolic methods for projective incidence geometry. 3.2. Factorization techniques in bracket algebra. 3.3. Contraction techniques in bracket computing. 3.4. Exact division and pseudodivision. 3.5. Rational invariants. 3.6. Automated theorem proving. 3.7. Erdös' consistent 5-tuples -- 4. Projective conic geometry with bracket algebra and quadratic Grassmann-Cayley algebra. 4.1. Conics with bracket algebra, 4.2. Bracket-oriented representation. 4.3. Simplification techniques in conic computing. 4.4. Factorization techniques in conic computing. 4.5. Automated theorem proving. 4.6. Conics with quadratic Grassmann-Cayley algebra -- 5. Inner-product bracket algebra and Clifford algebra. 5.1. Inner-product bracket algebra. 5.2. Clifford algebra. 5.3. Representations of Clifford algebras. 5.4. Clifford expansion theory -- 6. Geometric algebra. 6.1. Major techniques in geometric algebra. 6.2. Versor compression. 6.3. Obstructions to versor compression. 6.4. Clifford coalgebra, Clifford summation and factorization. 6.5. Clifford bracket algebra -- 7. Euclidean geometry and conformal Grassmann-Cayley algebra. 7.1. Homogeneous coordinates and Cartesian coordinates. 7.2. The conformal model and the homogeneous model. 7.3. Positive-vector representations of spheres and hyperplanes. 7.4. Conformal Grassmann-Cayley algebra. 7.5. The Lie model of oriented spheres and hyperplanes. 7.6. Apollonian contact problem -- 8. Conformal Clifford algebra and classical geometries. 8.1. The geometry of positive monomials. 8.2. Cayley transform and exterior exponential. 8.3. Twisted Vahlen matrices and Vahlen matrices. 8.4. Affine geometry with dual Clifford algebra. 8.5. Spherical geometry and its conformal model. 8.6. Hyperbolic geometry and its conformal model. 8.7. Unifed algebraic framework for classical geometries.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Clifford algebras.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85027030</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Invariants.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85067665</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Symmetry (Mathematics)</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh2006001303</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Algèbres de Clifford.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Invariants.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Symétrie (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Linear.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematics.</subfield><subfield code="2">eflch</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Clifford algebras</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Invariants</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Symmetry (Mathematics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Li, Hongbo.</subfield><subfield code="t">Invariant algebras and geometric reasoning.</subfield><subfield code="d">Singarore ; Hackensack, N.J. : World Scientific, ©2008</subfield><subfield code="w">(DLC) 2008297934</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-862</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236092</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-863</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236092</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">cloudLibrary</subfield><subfield code="b">CLDL</subfield><subfield code="n">9789812770110</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24684228</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">9460131</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681616</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255404</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">236092</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">191900</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2891929</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-862</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
id | ZDB-4-EBA-ocn560635800 |
illustrated | Illustrated |
indexdate | 2025-04-11T08:36:34Z |
institution | BVB |
isbn | 9789812770110 9812770119 1281919004 9781281919007 9786611919009 6611919007 |
language | English |
oclc_num | 560635800 |
open_access_boolean | |
owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
physical | 1 online resource (xiv, 518 pages) : illustrations |
psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
publishDate | 2008 |
publishDateSearch | 2008 |
publishDateSort | 2008 |
publisher | World Scientific, |
record_format | marc |
spelling | Li, Hongbo. Invariant algebras and geometric reasoning / Hongbo Li. Singarore ; Hackensack, N.J. : World Scientific, ©2008. 1 online resource (xiv, 518 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 495-504) and index. Print version record. The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics - among them, Grassmann-Cayley algebra and geometric algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author's most recent, original development of Grassmann-Cayley algebra and geometric algebra and their applications in automated reasoning of classical geometries. It includes three advanced invariant algebras - Cayley bracket algebra, conformal geometric algebra, and null bracket algebra - for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide. 1. Introduction. 1.1. Leibniz's dream. 1.2. Development of geometric algebras. 1.3. Conformal geometric algebra. 1.4. Geometric computing with invariant algebras. 1.5. From basic invariants to advanced invariants. 1.6. Geometric reasoning with advanced invariant algebras. 1.7. Highlights of the chapters -- 2. Projective space, bracket algebra and Grassmann-Cayley algebra. 2.1. Projective space and classical invariants. 2.2. Brackets from the symbolic point of view. 2.3. Covariants, duality and Grassmann-Cayley algebra. 2.4. Grassmann coalgebra. 2.5. Cayley expansion. 2.6. Grassmann factorization. 2.7. Advanced invariants and Cayley bracket algebra -- 3. Projective incidence geometry with Cayley bracket algebra. 3.1. Symbolic methods for projective incidence geometry. 3.2. Factorization techniques in bracket algebra. 3.3. Contraction techniques in bracket computing. 3.4. Exact division and pseudodivision. 3.5. Rational invariants. 3.6. Automated theorem proving. 3.7. Erdös' consistent 5-tuples -- 4. Projective conic geometry with bracket algebra and quadratic Grassmann-Cayley algebra. 4.1. Conics with bracket algebra, 4.2. Bracket-oriented representation. 4.3. Simplification techniques in conic computing. 4.4. Factorization techniques in conic computing. 4.5. Automated theorem proving. 4.6. Conics with quadratic Grassmann-Cayley algebra -- 5. Inner-product bracket algebra and Clifford algebra. 5.1. Inner-product bracket algebra. 5.2. Clifford algebra. 5.3. Representations of Clifford algebras. 5.4. Clifford expansion theory -- 6. Geometric algebra. 6.1. Major techniques in geometric algebra. 6.2. Versor compression. 6.3. Obstructions to versor compression. 6.4. Clifford coalgebra, Clifford summation and factorization. 6.5. Clifford bracket algebra -- 7. Euclidean geometry and conformal Grassmann-Cayley algebra. 7.1. Homogeneous coordinates and Cartesian coordinates. 7.2. The conformal model and the homogeneous model. 7.3. Positive-vector representations of spheres and hyperplanes. 7.4. Conformal Grassmann-Cayley algebra. 7.5. The Lie model of oriented spheres and hyperplanes. 7.6. Apollonian contact problem -- 8. Conformal Clifford algebra and classical geometries. 8.1. The geometry of positive monomials. 8.2. Cayley transform and exterior exponential. 8.3. Twisted Vahlen matrices and Vahlen matrices. 8.4. Affine geometry with dual Clifford algebra. 8.5. Spherical geometry and its conformal model. 8.6. Hyperbolic geometry and its conformal model. 8.7. Unifed algebraic framework for classical geometries. English. Clifford algebras. http://id.loc.gov/authorities/subjects/sh85027030 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Symmetry (Mathematics) http://id.loc.gov/authorities/subjects/sh2006001303 Algèbres de Clifford. Invariants. Symétrie (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Mathematics. eflch Clifford algebras fast Invariants fast Symmetry (Mathematics) fast Print version: Li, Hongbo. Invariant algebras and geometric reasoning. Singarore ; Hackensack, N.J. : World Scientific, ©2008 (DLC) 2008297934 |
spellingShingle | Li, Hongbo Invariant algebras and geometric reasoning / 1. Introduction. 1.1. Leibniz's dream. 1.2. Development of geometric algebras. 1.3. Conformal geometric algebra. 1.4. Geometric computing with invariant algebras. 1.5. From basic invariants to advanced invariants. 1.6. Geometric reasoning with advanced invariant algebras. 1.7. Highlights of the chapters -- 2. Projective space, bracket algebra and Grassmann-Cayley algebra. 2.1. Projective space and classical invariants. 2.2. Brackets from the symbolic point of view. 2.3. Covariants, duality and Grassmann-Cayley algebra. 2.4. Grassmann coalgebra. 2.5. Cayley expansion. 2.6. Grassmann factorization. 2.7. Advanced invariants and Cayley bracket algebra -- 3. Projective incidence geometry with Cayley bracket algebra. 3.1. Symbolic methods for projective incidence geometry. 3.2. Factorization techniques in bracket algebra. 3.3. Contraction techniques in bracket computing. 3.4. Exact division and pseudodivision. 3.5. Rational invariants. 3.6. Automated theorem proving. 3.7. Erdös' consistent 5-tuples -- 4. Projective conic geometry with bracket algebra and quadratic Grassmann-Cayley algebra. 4.1. Conics with bracket algebra, 4.2. Bracket-oriented representation. 4.3. Simplification techniques in conic computing. 4.4. Factorization techniques in conic computing. 4.5. Automated theorem proving. 4.6. Conics with quadratic Grassmann-Cayley algebra -- 5. Inner-product bracket algebra and Clifford algebra. 5.1. Inner-product bracket algebra. 5.2. Clifford algebra. 5.3. Representations of Clifford algebras. 5.4. Clifford expansion theory -- 6. Geometric algebra. 6.1. Major techniques in geometric algebra. 6.2. Versor compression. 6.3. Obstructions to versor compression. 6.4. Clifford coalgebra, Clifford summation and factorization. 6.5. Clifford bracket algebra -- 7. Euclidean geometry and conformal Grassmann-Cayley algebra. 7.1. Homogeneous coordinates and Cartesian coordinates. 7.2. The conformal model and the homogeneous model. 7.3. Positive-vector representations of spheres and hyperplanes. 7.4. Conformal Grassmann-Cayley algebra. 7.5. The Lie model of oriented spheres and hyperplanes. 7.6. Apollonian contact problem -- 8. Conformal Clifford algebra and classical geometries. 8.1. The geometry of positive monomials. 8.2. Cayley transform and exterior exponential. 8.3. Twisted Vahlen matrices and Vahlen matrices. 8.4. Affine geometry with dual Clifford algebra. 8.5. Spherical geometry and its conformal model. 8.6. Hyperbolic geometry and its conformal model. 8.7. Unifed algebraic framework for classical geometries. Clifford algebras. http://id.loc.gov/authorities/subjects/sh85027030 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Symmetry (Mathematics) http://id.loc.gov/authorities/subjects/sh2006001303 Algèbres de Clifford. Invariants. Symétrie (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Mathematics. eflch Clifford algebras fast Invariants fast Symmetry (Mathematics) fast |
subject_GND | http://id.loc.gov/authorities/subjects/sh85027030 http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh2006001303 |
title | Invariant algebras and geometric reasoning / |
title_auth | Invariant algebras and geometric reasoning / |
title_exact_search | Invariant algebras and geometric reasoning / |
title_full | Invariant algebras and geometric reasoning / Hongbo Li. |
title_fullStr | Invariant algebras and geometric reasoning / Hongbo Li. |
title_full_unstemmed | Invariant algebras and geometric reasoning / Hongbo Li. |
title_short | Invariant algebras and geometric reasoning / |
title_sort | invariant algebras and geometric reasoning |
topic | Clifford algebras. http://id.loc.gov/authorities/subjects/sh85027030 Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Symmetry (Mathematics) http://id.loc.gov/authorities/subjects/sh2006001303 Algèbres de Clifford. Invariants. Symétrie (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Mathematics. eflch Clifford algebras fast Invariants fast Symmetry (Mathematics) fast |
topic_facet | Clifford algebras. Invariants. Symmetry (Mathematics) Algèbres de Clifford. Symétrie (Mathématiques) MATHEMATICS Algebra Linear. Mathematics. Clifford algebras Invariants |
work_keys_str_mv | AT lihongbo invariantalgebrasandgeometricreasoning |