Breuils, Stephane; Tachibana, Kanta; Hitzer, Eckhard New applications of Clifford’s geometric algebra. (English) Zbl 1490.15036 Adv. Appl. Clifford Algebr. 32, No. 2, Paper No. 17, 39 p. (2022). Reviewer: Morteza Shahpari (Adelaide) MSC: 15A67 15A66 68T01 68U05 11E88 70E60 94A12 PDFBibTeX XMLCite \textit{S. Breuils} et al., Adv. Appl. Clifford Algebr. 32, No. 2, Paper No. 17, 39 p. (2022; Zbl 1490.15036) Full Text: DOI
Dechant, Pierre-Philippe Clifford spinors and root system induction: \(H_4\) and the grand antiprism. (English) Zbl 1471.15019 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 57, 35 p. (2021). MSC: 15A66 15A67 20F55 17B22 20G41 52B15 52B11 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 57, 35 p. (2021; Zbl 1471.15019) Full Text: DOI arXiv
Dechant, Pierre-Philippe From the trinity \((A_3, B_3, H_3)\) to an ADE correspondence. (English) Zbl 1425.92225 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2220, Article ID 20180034, 19 p. (2018). MSC: 92E10 20F55 15A66 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2220, Article ID 20180034, 19 p. (2018; Zbl 1425.92225) Full Text: DOI arXiv
Eid, Ahmad Hosny An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature. (English) Zbl 1390.68776 Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 16, 32 p. (2018). MSC: 68W30 15A66 PDFBibTeX XMLCite \textit{A. H. Eid}, Adv. Appl. Clifford Algebr. 28, No. 1, Paper No. 16, 32 p. (2018; Zbl 1390.68776) Full Text: DOI
Hildenbrand, Dietmar; Franchini, Silvia; Gentile, Antonio; Vassallo, Giorgio; Vitabile, Salvatore GAPPCO: an easy to configure geometric algebra coprocessor based on GAPP programs. (English) Zbl 1415.68267 Adv. Appl. Clifford Algebr. 27, No. 3, 2115-2132 (2017). MSC: 68W30 15A66 PDFBibTeX XMLCite \textit{D. Hildenbrand} et al., Adv. Appl. Clifford Algebr. 27, No. 3, 2115--2132 (2017; Zbl 1415.68267) Full Text: DOI Link
Lopez Belon, Mauricio Cele; Hildenbrand, Dietmar Practical geometric modeling using geometric algebra motors. (English) Zbl 1425.68435 Adv. Appl. Clifford Algebr. 27, No. 3, 2019-2033 (2017). MSC: 68U05 15A66 65D18 PDFBibTeX XMLCite \textit{M. C. Lopez Belon} and \textit{D. Hildenbrand}, Adv. Appl. Clifford Algebr. 27, No. 3, 2019--2033 (2017; Zbl 1425.68435) Full Text: DOI
Tingelstad, Lars; Egeland, Olav Automatic multivector differentiation and optimization. (English) Zbl 1367.65034 Adv. Appl. Clifford Algebr. 27, No. 1, 707-731 (2017). MSC: 65D25 65K05 15A66 90C30 70E15 PDFBibTeX XMLCite \textit{L. Tingelstad} and \textit{O. Egeland}, Adv. Appl. Clifford Algebr. 27, No. 1, 707--731 (2017; Zbl 1367.65034) Full Text: DOI
Hrdina, J.; Návrat, A.; Vašík, P.; Matoušek, R. Geometric control of the trident snake robot based on CGA. (English) Zbl 1364.93149 Adv. Appl. Clifford Algebr. 27, No. 1, 633-645 (2017). MSC: 93B27 93C85 93C10 70F25 15A66 93B05 PDFBibTeX XMLCite \textit{J. Hrdina} et al., Adv. Appl. Clifford Algebr. 27, No. 1, 633--645 (2017; Zbl 1364.93149) Full Text: DOI
Hildenbrand, D.; Albert, J.; Charrier, P.; Steinmetz, Chr. Geometric algebra computing for heterogeneous systems. (English) Zbl 1367.65030 Adv. Appl. Clifford Algebr. 27, No. 1, 599-620 (2017). MSC: 65D18 15A66 65Y20 65Y04 PDFBibTeX XMLCite \textit{D. Hildenbrand} et al., Adv. Appl. Clifford Algebr. 27, No. 1, 599--620 (2017; Zbl 1367.65030) Full Text: DOI
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore Embedded coprocessors for native execution of geometric algebra operations. (English) Zbl 1367.15034 Adv. Appl. Clifford Algebr. 27, No. 1, 559-580 (2017). MSC: 15A66 68U05 68W30 PDFBibTeX XMLCite \textit{S. Franchini} et al., Adv. Appl. Clifford Algebr. 27, No. 1, 559--580 (2017; Zbl 1367.15034) Full Text: DOI
Dechant, Pierre-Philippe The \(E_8\) geometry from a Clifford perspective. (English) Zbl 1368.52006 Adv. Appl. Clifford Algebr. 27, No. 1, 397-421 (2017). MSC: 52B10 52B12 52B15 15A66 20F55 17B22 14E16 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 27, No. 1, 397--421 (2017; Zbl 1368.52006) Full Text: DOI arXiv
Dechant, Pierre-Philippe Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups. (English) Zbl 1382.51009 Adv. Appl. Clifford Algebr. 27, No. 1, 17-31 (2017). MSC: 51F15 15A66 20F55 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 27, No. 1, 17--31 (2017; Zbl 1382.51009) Full Text: DOI arXiv
Zhang, Feng; Jiang, Xiaomin; Zhang, Xiaoyi; Wang, Yingzhi; Du, Zhenhong; Liu, Renyi Unified spatial intersection algorithms based on conformal geometric algebra. (English) Zbl 1400.68252 Math. Probl. Eng. 2016, Article ID 7412373, 10 p. (2016). MSC: 68U05 15A66 PDFBibTeX XMLCite \textit{F. Zhang} et al., Math. Probl. Eng. 2016, Article ID 7412373, 10 p. (2016; Zbl 1400.68252) Full Text: DOI
Ma, Sha; Shi, Zhiping; Shao, Zhenzhou; Guan, Yong; Li, Liming; Li, Yongdong Higher-order logic formalization of conformal geometric algebra and its application in verifying a robotic manipulation algorithm. (English) Zbl 1367.65032 Adv. Appl. Clifford Algebr. 26, No. 4, 1305-1330 (2016). MSC: 65D18 15A66 70E60 PDFBibTeX XMLCite \textit{S. Ma} et al., Adv. Appl. Clifford Algebr. 26, No. 4, 1305--1330 (2016; Zbl 1367.65032) Full Text: DOI
Hrdina, Jaroslav; Návrat, Aleš; Vašík, Petr Control of 3-link robotic snake based on conformal geometric algebra. (English) Zbl 1394.93209 Adv. Appl. Clifford Algebr. 26, No. 3, 1069-1080 (2016). MSC: 93C85 70E60 93C10 15A66 PDFBibTeX XMLCite \textit{J. Hrdina} et al., Adv. Appl. Clifford Algebr. 26, No. 3, 1069--1080 (2016; Zbl 1394.93209) Full Text: DOI
Rodríguez-Andrade, M. A.; Aragón-González, G.; Aragón, J. L.; Gómez-Rodríguez, A.; Romeu, D. The coincidence site lattices in 2D hexagonal lattices using Clifford algebra. (English) Zbl 1380.15020 Adv. Appl. Clifford Algebr. 25, No. 2, 425-440 (2015). Reviewer: Sirkka-Liisa Eriksson (Helsinki) MSC: 15A66 06C10 PDFBibTeX XMLCite \textit{M. A. Rodríguez-Andrade} et al., Adv. Appl. Clifford Algebr. 25, No. 2, 425--440 (2015; Zbl 1380.15020) Full Text: DOI
Charrier, Patrick; Klimek, Mariusz; Steinmetz, Christian; Hildenbrand, Dietmar Geometric algebra enhanced precompiler for C++, OpenCL and Mathematica’s OpenCLLink. (English) Zbl 1299.15001 Adv. Appl. Clifford Algebr. 24, No. 2, 613-630 (2014). MSC: 15-04 PDFBibTeX XMLCite \textit{P. Charrier} et al., Adv. Appl. Clifford Algebr. 24, No. 2, 613--630 (2014; Zbl 1299.15001) Full Text: DOI
Fuchs, Laurent; Théry, Laurent Implementing geometric algebra products with binary trees. (English) Zbl 1311.68147 Adv. Appl. Clifford Algebr. 24, No. 2, 589-611 (2014). MSC: 68T15 11E88 15A66 PDFBibTeX XMLCite \textit{L. Fuchs} and \textit{L. Théry}, Adv. Appl. Clifford Algebr. 24, No. 2, 589--611 (2014; Zbl 1311.68147) Full Text: DOI
González-Jiménez, L.; Carbajal-Espinosa, O.; Loukianov, A.; Bayro-Corrochano, E. Robust pose control of robot manipulators using conformal geometric algebra. (English) Zbl 1297.93119 Adv. Appl. Clifford Algebr. 24, No. 2, 533-552 (2014). MSC: 93C85 70E60 15A66 53A30 70G45 93B12 PDFBibTeX XMLCite \textit{L. González-Jiménez} et al., Adv. Appl. Clifford Algebr. 24, No. 2, 533--552 (2014; Zbl 1297.93119) Full Text: DOI
Dechant, Pierre-Philippe A Clifford algebraic framework for Coxeter group theoretic computations. (English) Zbl 1301.20030 Adv. Appl. Clifford Algebr. 24, No. 1, 89-108 (2014). MSC: 20F55 15A66 17B22 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 24, No. 1, 89--108 (2014; Zbl 1301.20030) Full Text: DOI arXiv Link
Hitzer, Eckhard; Ichikawa, Daisuke Representation of crystallographic subperiodic groups in Clifford’s geometric algebra. (English) Zbl 1292.20057 Adv. Appl. Clifford Algebr. 23, No. 4, 887-906 (2013). MSC: 20H15 15A66 20C15 82D25 PDFBibTeX XMLCite \textit{E. Hitzer} and \textit{D. Ichikawa}, Adv. Appl. Clifford Algebr. 23, No. 4, 887--906 (2013; Zbl 1292.20057) Full Text: DOI arXiv
Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki Applications of Clifford’s geometric algebra. (English) Zbl 1269.15022 Adv. Appl. Clifford Algebr. 23, No. 2, 377-404 (2013). MSC: 15A66 15-02 PDFBibTeX XMLCite \textit{E. Hitzer} et al., Adv. Appl. Clifford Algebr. 23, No. 2, 377--404 (2013; Zbl 1269.15022) Full Text: DOI arXiv
Dechant, Pierre-Philippe Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups. (English) Zbl 1273.15021 Adv. Appl. Clifford Algebr. 23, No. 2, 301-321 (2013). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A66 15B33 PDFBibTeX XMLCite \textit{P.-P. Dechant}, Adv. Appl. Clifford Algebr. 23, No. 2, 301--321 (2013; Zbl 1273.15021) Full Text: DOI arXiv Link
Hildenbrand, Dietmar Foundations of geometric algebra computing. (English) Zbl 1268.65038 Geometry and Computing 8. Berlin: Springer (ISBN 978-3-642-31793-4/hbk; 978-3-642-31794-1/ebook). xxvii, 196 p. (2013). Reviewer: Raffaella Pavani (Milano) MSC: 65Fxx 65-01 15A66 65Y15 PDFBibTeX XMLCite \textit{D. Hildenbrand}, Foundations of geometric algebra computing. Berlin: Springer (2013; Zbl 1268.65038) Full Text: DOI
Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore Fixed-size quadruples for a new, hardware-oriented representation of the 4D Clifford algebra. (English) Zbl 1251.15028 Adv. Appl. Clifford Algebr. 21, No. 2, 315-340 (2011). MSC: 15A66 65D18 68U05 68W30 PDFBibTeX XMLCite \textit{S. Franchini} et al., Adv. Appl. Clifford Algebr. 21, No. 2, 315--340 (2011; Zbl 1251.15028) Full Text: DOI
Hitzer, E. Crystal planes and reciprocal space in Clifford geometric algebra. (English) Zbl 1219.74009 Math. Methods Appl. Sci. 34, No. 12, 1421-1429 (2011). MSC: 74E15 15A66 PDFBibTeX XMLCite \textit{E. Hitzer}, Math. Methods Appl. Sci. 34, No. 12, 1421--1429 (2011; Zbl 1219.74009) Full Text: DOI arXiv
Hitzer, Eckhard; Perwass, Christian Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups. (English) Zbl 1242.20060 Adv. Appl. Clifford Algebr. 20, No. 3-4, 631-658 (2010). MSC: 20H15 15A66 68U05 82D25 51F15 PDFBibTeX XMLCite \textit{E. Hitzer} and \textit{C. Perwass}, Adv. Appl. Clifford Algebr. 20, No. 3--4, 631--658 (2010; Zbl 1242.20060) Full Text: DOI
Perwass, Christian Geometric algebra with applications in engineering. (English) Zbl 1179.15025 Geometry and Computing 4. Berlin: Springer (ISBN 978-3-540-89067-6/hbk). xiv, 385 p. (2009). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 15A66 51-01 68-01 70E60 68U05 65D19 15-02 51-04 PDFBibTeX XMLCite \textit{C. Perwass}, Geometric algebra with applications in engineering. Berlin: Springer (2009; Zbl 1179.15025)
Abłamowicz, Rafał (ed.); Sobczyk, Garret (ed.) [Baylis, William E.; Branson, Thomas; Lounesto, Pertti; Porteous, Ian; Ryan, John; Selig, J. M.; Ablamowicz, R.; Sobczyk, G.] Lectures on Clifford (geometric) algebras and applications. (English) Zbl 1058.15033 Boston, MA: Birkhäuser. (ISBN 0-8176-3257-3/pbk). xvii, 221 p. (2004). Reviewer: Waldyr A. Rodrigues (Campinas) MSC: 15A66 11E88 15-06 30G35 83C60 15A75 15-02 PDFBibTeX XML