Relevant bibliographies by topics / Geometric algebra for conics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Geometric algebra for conics'

Author: Grafiati
Published: 28 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Geometric algebra for conics"

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Dragovic, Vladimir. "Algebro-geometric approach to the Yang-Baxter equation and related topics." Publications de l'Institut Math?matique (Belgrade) 91, no. 105 (2012): 25–48. http://dx.doi.org/10.2298/pim1205025d.

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We review the results of algebro-geometric approach to 4 ? 4 solutions of the Yang-Baxter equation. We emphasis some further geometric properties, connected with the double-reflection theorem, the Poncelet porism and the Euler-Chasles correspondence. We present a list of classifications in Mathematical Physics with a similar geometric background, related to pencils of conics. In the conclusion, we introduce a notion of discriminantly factorizable polynomials as a result of a computational experiment with elementary n-valued groups.
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Halbeisen, Lorenz, and Norbert Hungerbühler. "The exponential pencil of conics." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 3 (2017): 549–71. http://dx.doi.org/10.1007/s13366-017-0375-1.

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RASHED, ROSHDI. "LES CONSTRUCTIONS GÉOMÉTRIQUES ENTRE GÉOMÉTRIE ET ALGÈBRE: L'ÉPÎTRE D'AB AL-JD À AL-BRN." Arabic Sciences and Philosophy 20, no. 1 (2010): 1–51. http://dx.doi.org/10.1017/s0957423909990075.

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AbstractAbū al-Jūd Muḥammad ibn al-Layth is one of the mathematicians of the 10th century who contributed most to the novel chapter on the geometric construction of the problems of solids and super-solids, and also to another chapter on solving cubic and bi-quadratic equations with the aid of conics. His works, which were significant in terms of the results they contained, are moreover important with regard to the new relations they established between algebra and geometry. Good fortune transmitted to us his correspondences with the mathematician and astronomer al-Bīrūnī. The questions they de
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Halbeisen, Lorenz, and Norbert Hungerbühler. "Closed chains of conics carrying poncelet triangles." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 58, no. 2 (2017): 277–302. http://dx.doi.org/10.1007/s13366-016-0327-1.

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Halbeisen, Lorenz, and Norbert Hungerbühler. "Generalized pencils of conics derived from cubics." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61, no. 4 (2020): 681–93. http://dx.doi.org/10.1007/s13366-020-00499-3.

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Mirman, Boris. "Short cycles of Poncelet’s conics." Linear Algebra and its Applications 432, no. 10 (2010): 2543–64. http://dx.doi.org/10.1016/j.laa.2009.11.032.

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Diemente, Damon. "Algebra in the Service of Geometry: Can Euler's Line Be Parallel to a Side of a Triangle?" Mathematics Teacher 93, no. 5 (2000): 428–31. http://dx.doi.org/10.5951/mt.93.5.0428.

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This investigation of Euler's line has become a regular and valued unit in my honors–geometry syllabus. It originated with an intelligent question from a curious student. Its geometric foundation comprises sophisticated Euclidean triangle geometry. Its solution requires plentiful but not excessively complicated algebra. It culminates in the discovery of a conic locus that can be verified by construction on a computer screen.
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Nievergelt, Yves. "Fitting conics of specific types to data." Linear Algebra and its Applications 378 (February 2004): 1–30. http://dx.doi.org/10.1016/j.laa.2003.08.022.

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Wu, Junhua. "Conics arising from internal points and their binary codes." Linear Algebra and its Applications 439, no. 2 (2013): 422–34. http://dx.doi.org/10.1016/j.laa.2013.04.004.

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Easter, Robert Benjamin, and Eckhard Hitzer. "Conic and cyclidic sections in double conformal geometric algebra G8,2 with computing and visualization using Gaalop." Mathematical Methods in the Applied Sciences 43, no. 1 (2019): 334–57. http://dx.doi.org/10.1002/mma.5887.

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Dissertations / Theses on the topic "Geometric algebra for conics"

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Machálek, Lukáš. "Aplikace geometrických algeber." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445454.

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Tato diplomová práce se zabývá využitím geometrické algebry pro kuželosečky (GAC) v autonomní navigaci, prezentované na pohybu robota v trubici. Nejprve jsou zavedeny teoretické pojmy z geometrických algeber. Následně jsou prezentovány kuželosečky v GAC. Dále je provedena implementace enginu, který je schopný provádět základní operace v GAC, včetně zobrazování kuželoseček zadaných v kontextu GAC. Nakonec je ukázán algoritmus, který odhadne osu trubice pomocí bodů, které umístí do prostoru pomocí středů elips, umístěných v obrazu, získaných obrazovým filtrem a fitovacím algoritmem.
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Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.

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Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.

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This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
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Lopes, Wilder Bezerra. "Geometric-algebra adaptive filters." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-22092016-143525/.

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This document introduces a new class of adaptive filters, namely Geometric- Algebra Adaptive Filters (GAAFs). Those are generated by formulating the underlying minimization problem (a least-squares cost function) from the perspective of Geometric Algebra (GA), a comprehensive mathematical language well-suited for the description of geometric transformations. Also, differently from the usual linear algebra approach, Geometric Calculus (the extension of Geometric Algebra to differential calculus) allows to apply the same derivation techniques regardless of the type (subalgebra) of the data, i.e.
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Kessaris, Haris. "Geometric algebra and applications." Thesis, University of Cambridge, 2001. https://www.repository.cam.ac.uk/handle/1810/251756.

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MOREIRA, JOHANN SENRA. "CONSTRUCTION OF THE CONICS USING THE GEOMETRIC DRAWING AND CONCRETE INSTRUMENTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33061@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL<br>O presente trabalho tem como objetivo facilitar o estudo das cônicas e ainda despertar o interesse do aluno para o desenho geométrico. Será apresentado que as curvas cônicas estão em nosso dia a dia, não só como beleza estética, mas também provocando fenômenos físicos amplamente utilizado pela arquitetura e engenharia civil, como acústica e reflexão da luz. Utilizaremos instrumentos para desenhar curvas que des
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Minh, Tuan Pham, Tomohiro Yoshikawa, Takeshi Furuhashi, and Kaita Tachibana. "Robust feature extractions from geometric data using geometric algebra." IEEE, 2009. http://hdl.handle.net/2237/13896.

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Khalfallah, Hazem. "Mordell-Weil theorem and the rank of elliptical curves." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3119.

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The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.
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Wu, Junhua. "Geometric structures and linear codes related to conics in classical projective planes of odd orders." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 105 p, 2009. http://proquest.umi.com/pqdweb?did=1654490971&sid=2&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Wareham, Richard James. "Computer graphics using conformal geometric algebra." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612753.

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Books on the topic "Geometric algebra for conics"

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Artin, E. Geometric Algebra. John Wiley & Sons, Inc., 1988. http://dx.doi.org/10.1002/9781118164518.

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Bayro-Corrochano, Eduardo, and Gerik Scheuermann, eds. Geometric Algebra Computing. Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-108-0.

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1832489.

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The monograph is devoted to the fundamental aspects of geometric algebra and closely related issues. The category of Clifford algebras is considered as the conjugate category of vector spaces with a quadratic form. Possible constructions in this category and internal algebraic operations of an algebra with a geometric interpretation are studied. An application to the differential geometry of a Euclidean manifold based on a shape tensor is included.&#x0D; We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Cliffor
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1960-, Zaslavskiĭ A. A., ed. Geometry of conics. American Mathematical Society, 2007.

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Li, Hongbo, Peter J. Olver, and Gerald Sommer, eds. Computer Algebra and Geometric Algebra with Applications. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/b137294.

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Shifrin, Theodore. Abstract algebra: A geometric approach. Prentice Hall, 1996.

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Geometric algebra for computer graphics. Springer, 2008.

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Hildenbrand, Dietmar. Foundations of Geometric Algebra Computing. Springer Berlin Heidelberg, 2013.

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Linear algebra: A geometric approach. Chapman & Hall, 1993.

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Fontijne, D. H. F. Efficient implementation of geometric algebra. s.n.], 2007.

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Book chapters on the topic "Geometric algebra for conics"

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Hildenbrand, Dietmar. "GAALOPWeb for Conics." In The Power of Geometric Algebra Computing. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003139003-10.

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Neri, Ferrante. "An Introduction to Geometric Algebra and Conics." In Linear Algebra for Computational Sciences and Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21321-3_6.

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Neri, Ferrante. "An Introduction to Geometric Algebra and Conics." In Linear Algebra for Computational Sciences and Engineering. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40341-0_6.

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Hitzer, Eckhard M. S. "Conic Sections and Meet Intersections in Geometric Algebra." In Computer Algebra and Geometric Algebra with Applications. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11499251_25.

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Serrano Rubio, Juan Pablo, Arturo Hernández Aguirre, and Rafael Herrera Guzmán. "A Conic Higher Order Neuron Based on Geometric Algebra and Its Implementation." In Advances in Computational Intelligence. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37798-3_20.

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Gelfand, Israel M., and Alexander Shen. "Geometric progressions." In Algebra. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_41.

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Gelfand, Israel M., and Alexander Shen. "Geometric illustrations." In Algebra. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_69.

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Vince, John. "Geometric Algebra." In Mathematics for Computer Graphics. Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7336-6_14.

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Dorst, Leo. "Geometric Algebra." In Computer Vision. Springer US, 2014. http://dx.doi.org/10.1007/978-0-387-31439-6_656.

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Xambó-Descamps, Sebastià. "Geometric Algebra." In SpringerBriefs in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00404-0_3.

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Conference papers on the topic "Geometric algebra for conics"

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Matos, S. A., C. R. Paiva, and A. M. Barbosa. "Conical refraction in generalized biaxial media: A geometric algebra approach." In IEEE EUROCON 2011 - International Conference on Computer as a Tool. IEEE, 2011. http://dx.doi.org/10.1109/eurocon.2011.5929176.

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Bajaj, Jasmine, and Babita Jajodia. "Squaring Technique using Vedic Mathematics." In International Conference on Women Researchers in Electronics and Computing. AIJR Publisher, 2021. http://dx.doi.org/10.21467/proceedings.114.75.

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Vedic Mathematics provides an interesting approach to modern computing applications by offering an edge of time and space complexities over conventional techniques. Vedic Mathematics consists of sixteen sutras and thirteen sub-sutras, to calculate problems revolving around arithmetic, algebra, geometry, calculus and conics. These sutras are specific to the decimal number system, but this can be easily applied to binary computations. This paper presented an optimised squaring technique using Karatsuba-Ofman Algorithm, and without the use of Duplex property for reduced algorithmic complexity. Th
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Li, Wanzhen, Tao Sun, Xinming Huo, and Yimin Song. "CGA Approach to Kinematic Analysis of a 2-DoF Parallel Positioning Mechanism." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60529.

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This paper proposes CGA based approach to determine motions and constraints, analyze mobility, identify singularity of parallel mechanisms, which is perfectly demonstrated by taking 3-RSR&amp;SS parallel positioning mechanism as an example. By introducing CGA, which combining elements of geometry and algebra, the motions and constraints are expressed as simple formulas and their relations are calculated by means of outer product with clear physical meaning, these lead to the motions and constraints are determined in a visual, concise and efficient way, and the number and type of DoF and access
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Li, Hongbo. "Automated Geometric Reasoning with Geometric Algebra." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. ACM, 2017. http://dx.doi.org/10.1145/3087604.3087663.

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Zambo, Samantha. "Defining geometric algebra semantics." In the 48th Annual Southeast Regional Conference. ACM Press, 2010. http://dx.doi.org/10.1145/1900008.1900157.

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Hildenbrand, Dietmar. "Foundations of Geometric Algebra computing." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756054.

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Qing, Ni, and Wang Zhengzhi. "Geometric invariants using geometry algebra." In 2011 IEEE 2nd International Conference on Computing, Control and Industrial Engineering (CCIE 2011). IEEE, 2011. http://dx.doi.org/10.1109/ccieng.2011.6008094.

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Gunn, Charles G., and Steven De Keninck. "Geometric algebra and computer graphics." In SIGGRAPH '19: Special Interest Group on Computer Graphics and Interactive Techniques Conference. ACM, 2019. http://dx.doi.org/10.1145/3305366.3328099.

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Reisossadat, S. H. R., F. Kheirandish, H. Pahlavani, et al. "Realization of a deformed parafermionic algebra." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043848.

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Altamirano-Gomez, Gerardo, and Eduardo Bayro-Corrochano. "Conformal Geometric Algebra method for detection of geometric primitives." In 2016 23rd International Conference on Pattern Recognition (ICPR). IEEE, 2016. http://dx.doi.org/10.1109/icpr.2016.7900291.

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Reports on the topic "Geometric algebra for conics"

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Bashelor, Andrew Clark. Enumerative Algebraic Geometry: Counting Conics. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada437184.

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Hanlon, J., and H. Ziock. Using geometric algebra to study optical aberrations. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/468621.

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Meisel, L. V. A Mathematica Formulation of Geometric Algebra in 3-Space. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada295512.

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Hanlon, J., and H. Ziock. Using geometric algebra to understand pattern rotations in multiple mirror optical systems. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/468622.

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Yanovski, Alexandar B. Geometric Interpretation of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Lie Algebra $A_2$. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-23-2011-97-111.

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