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| geometric_algebra [2020/07/19 17:34] – [Articles] pbk | geometric_algebra [2020/09/07 19:40] – [Computing frameworks] pbk |
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| * [[https://en.wikipedia.org/wiki/Vector_space|Vector space]] | * [[https://en.wikipedia.org/wiki/Vector_space|Vector space]] |
| * [[https://en.wikipedia.org/wiki/Quaternion|Quaternion]] | * [[https://en.wikipedia.org/wiki/Quaternion|Quaternion]] |
| | * [[https://en.wikipedia.org/wiki/Biquaternion|Biquaternion]] |
| * [[https://en.wikipedia.org/wiki/Octonion|Octonion]] | * [[https://en.wikipedia.org/wiki/Octonion|Octonion]] |
| * [[https://en.wikipedia.org/wiki/Spinor|Spinor]] | * [[https://en.wikipedia.org/wiki/Spinor|Spinor]] |
| * [[http://www.siue.edu/~sstaple/index_files/research.html|CliffMath]] - Clifford algebra computations, including zeon, sym-Clifford, and idem-Clifford subalgebras, //George Stacey Staples//. | * [[http://www.siue.edu/~sstaple/index_files/research.html|CliffMath]] - Clifford algebra computations, including zeon, sym-Clifford, and idem-Clifford subalgebras, //George Stacey Staples//. |
| * [[https://github.com/Prograf-UFF/TbGAL|TbGAL]] - Tensor-Based Geometric Algebra C++/Python Library, //Eduardo Vera Sousa, Leandro A. F. Fernandes//. | * [[https://github.com/Prograf-UFF/TbGAL|TbGAL]] - Tensor-Based Geometric Algebra C++/Python Library, //Eduardo Vera Sousa, Leandro A. F. Fernandes//. |
| | * [[https://github.com/vincentnozick/garamon|Garamon Generator]] - Geometric Algebra Recursive and Adaptative Monster is a generator of C++ libraries dedicated to Geometric Algebra., //Vincent Nozick, Stephane Breuils//. |
| ===== Articles ===== | ===== Articles ===== |
| * [[http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes// | * [[http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes// |
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| * [[https://www.researchgate.net/publication/264423339_An_invitation_to_Clifford_Analysis|Una Invitación al Análisis de Clifford]] (2003) - //Richard Delanghe, Juan Bory-Reyes// | * [[https://www.researchgate.net/publication/264423339_An_invitation_to_Clifford_Analysis|Una Invitación al Análisis de Clifford]] (2003) - //Richard Delanghe, Juan Bory-Reyes// |
| Una panorámica de los tópicos principales y herramientas básicas del Análisis de Clifford se presenta en este artículo, al mismo tiempo, las principales fórmulas integrales relacionadas con la integral tipo Cauchy -- y su versión singular -- son analizadas en un contexto multidimensional, con el uso de las técnicas de álgebras de Clifford. Se incluyen también algunas notas históricas sobre el desarrollo de este campo de investigación. | Una panorámica de los tópicos principales y herramientas básicas del Análisis de Clifford se presenta en este artículo, al mismo tiempo, las principales fórmulas integrales relacionadas con la integral tipo Cauchy --- y su versión singular --- son analizadas en un contexto multidimensional, con el uso de las técnicas de álgebras de Clifford. Se incluyen también algunas notas históricas sobre el desarrollo de este campo de investigación. |
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| * [[http://downloads.hindawi.com/journals/abb/2007/502679.pdf|Surface Approximation using Growing Self-Organizing Nets and Gradient Information]] (2007) - //Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano// | * [[http://downloads.hindawi.com/journals/abb/2007/502679.pdf|Surface Approximation using Growing Self-Organizing Nets and Gradient Information]] (2007) - //Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano// |
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| * [[http://www.cs.ox.ac.uk/people/david.reutter/AtiyahSinger_Essay.pdf|The Heat Equation and the Atiyah-Singer Index Theorem]] (2015) - //David Reutter// | * [[http://www.cs.ox.ac.uk/people/david.reutter/AtiyahSinger_Essay.pdf|The Heat Equation and the Atiyah-Singer Index Theorem]] (2015) - //David Reutter// |
| The Atiyah-Singer index theorem is a milestone of twentieth century mathematics. Roughly speaking, it relates a global analytical datum of a manifold -- the number of solutions of a certain linear PDE -- to an integral of local topological expressions over this manifold. The index theorem provided a link between analysis, geometry and topology, paving the way for many further applications along these lines. | The Atiyah-Singer index theorem is a milestone of twentieth century mathematics. Roughly speaking, it relates a global analytical datum of a manifold --- the number of solutions of a certain linear PDE --- to an integral of local topological expressions over this manifold. The index theorem provided a link between analysis, geometry and topology, paving the way for many further applications along these lines. |
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| * [[http://www.siue.edu/~sstaple/index_files/CODecompAccepted2015.pdf|Clifford algebra decompositions of conformal orthogonal group elements]] (2015) - //G. Stacey Staples, David Wylie// | * [[http://www.siue.edu/~sstaple/index_files/CODecompAccepted2015.pdf|Clifford algebra decompositions of conformal orthogonal group elements]] (2015) - //G. Stacey Staples, David Wylie// |
