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 (December 21, 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 (March 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 debated, and the answers they yielded, all offer us multiple in vivo perspectives on the research that was undertaken in that period. The reader would find in this article a critical edition and French translation of this correspondence, with historical and mathematical commentaries.
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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 (January 18, 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 (April 15, 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 (May 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 (May 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 (July 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 (September 9, 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., real, complex-numbers, quaternions etc. Exploiting those characteristics, among others, a general leastsquares cost function is posed, from which two types of GAAFs are designed. The first one, called standard, provides a generalization of regular adaptive filters for any subalgebra of GA. From the obtained update rule, it is shown how to recover the following least-mean squares (LMS) adaptive filter variants: real-entries LMS, complex LMS, and quaternions LMS. Mean-square analysis and simulations in a system identification scenario are provided, showing almost perfect agreement for different levels of measurement noise. The second type, called pose estimation, is designed to estimate rigid transformations { rotation and translation - in n-dimensional spaces. The GA-LMS performance is assessed in a 3-dimensional registration problem, in which it is able to estimate the rigid transformation that aligns two point clouds that share common parts.
Este documento introduz uma nova classe de filtros adaptativos, entitulados Geometric-Algebra Adaptive Filters (GAAFs). Eles s~ao projetados via formulação do problema de minimização (uma função custo de mínimos quadrados) do ponto de vista de álgebra geométrica (GA), uma abrangente linguagem matemática apropriada para a descrição de transformações geométricas. Adicionalmente, diferente do que ocorre na formulação com álgebra linear, cálculo geométrico (a extensão de álgebra geométrica que possibilita o uso de cálculo diferencial) permite aplicar as mesmas técnicas de derivação independentemente do tipo de dados (subálgebra), isto é, números reais, números complexos, quaternions etc. Usando essas e outras características, uma função custo geral de mínimos quadrados é proposta, da qual dois tipos de GAAFs são gerados. O primeiro, chamado standard, generaliza filtros adaptativos da literatura concebidos sob a perspectiva de subálgebras de GA. As seguintes variantes do filtro least-mean squares (LMS) s~ao obtidas como casos particulares: LMS real, LMS complexo e LMS quaternions. Uma análise mean-square é desenvolvida e corroborada por simulações para diferentes níveis de ruído de medição em um cenário de identificação de sistemas. O segundo tipo, chamado pose estimation, é projetado para estimar transformações rígidas - rotação e translação { em espaços n-dimensionais. A performance do filtro GA-LMS é avaliada em uma aplicação de alinhamento tridimensional na qual ele estima a tranformação rígida que alinha duas nuvens de pontos com partes em comum.
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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
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL
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 despertem a curiosidade dos alunos e faremos uso das equações e lugares geométricos a fim de demostrar tais recursos. Pretende-se assim que ao adquirir tais conhecimentos o aluno aprimore seu entendimento matemático e amplie seu horizonte cultural.
The present research aims to facilitate the study of the conics and also to arouse the interest of the student for the geometric drawing. The conic curves will be presented not only as they are in our day to day as aesthetic beauty but also as responsible for the physical phenomena widely used by architecture and civil engineering as well as acoustics and reflection of light. We will use instruments to draw curves that arouse the curiosity of the students, making use of the equations and locus in order to demonstrate such resources. It is intended that the student acquire this knowledge, improving his mathematical understanding and broadening his cultural horizon.
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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. Hoboken, NJ, USA: 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. London: Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-108-0.

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. ru: 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. We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Clifford algebras into simple components. Spinors are introduced. Methods of matrix representation of the Clifford algebra are studied. It may be of interest to students, postgraduates and specialists in the field of mathematics, physics and cybernetics.
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1960-, Zaslavskiĭ A. A., ed. Geometry of conics. Providence, R.I: American Mathematical Society, 2007.

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

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Shifrin, Theodore. Abstract algebra: A geometric approach. Englewood Cliffs, N.J: Prentice Hall, 1996.

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Geometric algebra for computer graphics. London: Springer, 2008.

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

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

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Fontijne, D. H. F. Efficient implementation of geometric algebra. [S.l: 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, 87–100. Boca Raton: 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, 203–49. Cham: 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, 159–207. Cham: 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, 350–62. Berlin, Heidelberg: 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, 223–35. Berlin, Heidelberg: 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, 81–83. Boston, MA: 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, 134–36. Boston, MA: 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, 337–72. London: 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, 329–33. Boston, MA: 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, 41–61. Cham: 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. This work also attempts Taylor Series approximation of basic trigonometric and inverse trigonometric series. The advantage of this proposed power series approximation technique is that it provides a lower absolute mean error difference in comparison to previously existing approximation techniques.
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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&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 accessible motions are obtained readily. The inverse and forward position solutions are obtained easily utilizing special geometric relations of 3-RSR&SS parallel positioning mechanism, which are proven by calculating relations among point, line and plane in virtue of CGA operation rules. Two indices of singularity are defined to identify singular configurations of 3-RSR&SS parallel positioning mechanism in the light of the shuffle and outer products. The work of this paper lay a solid theoretical and technical foundation for the prototype design and manufacture of 3-RSR&SS parallel positioning mechanism.
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Li, Hongbo. "Automated Geometric Reasoning with Geometric Algebra." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: 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. New York, New York, USA: 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. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3305366.3328099.

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Reisossadat, S. H. R., F. Kheirandish, H. Pahlavani, S. Salehi, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "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. Fort Belvoir, VA: Defense Technical Information Center, May 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), May 1997. http://dx.doi.org/10.2172/468621.

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Meisel, L. V. A Mathematica Formulation of Geometric Algebra in 3-Space. Fort Belvoir, VA: Defense Technical Information Center, March 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), May 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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