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Volumn , Issue , 2008, Pages 1-518

Invariant algebras and geometric reasoning

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EID: 85032069041     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6514     Document Type: Book
Times cited : (62)

References (211)
  • 3
    • 0042899463 scopus 로고
    • Invariant Theory and Enumerative Combinatorics of Young Tableaux
    • Mundy, J.L. and Zisserman, A. (eds.), MIT Press, Cambridge, Massachusetts
    • Abhyankar, S.S. Invariant Theory and Enumerative Combinatorics of Young Tableaux. In: Mundy, J.L. and Zisserman, A. (eds.) Geometric Invariance in Computer Vision. MIT Press, Cambridge, Massachusetts, pp. 45-76, 1992.
    • (1992) Geometric Invariance in Computer Vision , pp. 45-76
    • Abhyankar, S.S.1
  • 5
    • 0002083314 scopus 로고
    • Möbius Transformations and Clifford Numbers
    • Chavel, I. and Farkas, H.M. (eds.), Springer, Berlin, Heidelberg
    • Ahlfors, L.V. Möbius Transformations and Clifford Numbers. In: Chavel, I. and Farkas, H.M. (eds.), Differential Geometry and Complex Analysis, Springer, Berlin, Heidelberg, 1985.
    • (1985) Differential Geometry and Complex Analysis
    • Ahlfors, L.V.1
  • 6
    • 0038353657 scopus 로고
    • Möbius Transformations in Rn Expressed through 2 × 2 Matrices of Clifford Numbers
    • Ahlfors, L.V. Möbius Transformations in Rn Expressed through 2 × 2 Matrices of Clifford Numbers. Complex Variables 5: 215-224, 1986.
    • (1986) Complex Variables , vol.5 , pp. 215-224
    • Ahlfors, L.V.1
  • 9
    • 0025787424 scopus 로고
    • Higher-Order Syzygies for the Bracket Algebra and for the Ring of Coordinates of the Grassmannian
    • Anick, D. and Rota, G.-C. Higher-Order Syzygies for the Bracket Algebra and for the Ring of Coordinates of the Grassmannian. Proc. Nat. Acad. Sci. 88(18): 8087-8090, 1991.
    • (1991) Proc. Nat. Acad. Sci , vol.88 , Issue.18 , pp. 8087-8090
    • Anick, D.1    Rota, G.-C.2
  • 11
    • 0004281677 scopus 로고
    • Interscience, New York, 1957
    • Artin, E. Geometric Algebra. Interscience, New York, 1957, 1988.
    • (1988) Geometric Algebra
    • Artin, E.1
  • 14
    • 0000704940 scopus 로고
    • On the Exterior Calculus of Invariant Theory
    • Barnabei, M., Brini, A. and Rota, G.-C. On the Exterior Calculus of Invariant Theory. J. of Algebra 96: 120-160, 1985.
    • (1985) J. of Algebra , vol.96 , pp. 120-160
    • Barnabei, M.1    Brini, A.2    Rota, G.-C.3
  • 18
    • 33750099764 scopus 로고    scopus 로고
    • Omnidirectional Vision: Unified Model Using Conformal Geometry
    • Bayro-Corrochano, E. and López-Franco, C. Omnidirectional Vision: Unified Model Using Conformal Geometry. ECCV’04 (1): 536-548, 2004.
    • (2004) ECCV’04 , Issue.1 , pp. 536-548
    • Bayro-Corrochano, E.1    López-Franco, C.2
  • 19
    • 33745428402 scopus 로고    scopus 로고
    • Robot Perception and Action Using Conformal Geometric Algebra
    • Bayro-Corrochano, E. (ed.), Springer, Heidelberg
    • Bayro-Corrochano, E. Robot Perception and Action Using Conformal Geometric Algebra. In: Bayro-Corrochano, E. (ed.), Handbook of Geometric Computing, Springer, Heidelberg, pp. 405-458, 2005.
    • (2005) Handbook of Geometric Computing , pp. 405-458
    • Bayro-Corrochano, E.1
  • 20
    • 27744493780 scopus 로고    scopus 로고
    • Geometric Algebra of Points, Lines, Planes and Spheres for Computer Vision and Robotics
    • Bayro-Corrochano E. and Falcon, L. E. Geometric Algebra of Points, Lines, Planes and Spheres for Computer Vision and Robotics. Robotica 23: 755-770, 2005.
    • (2005) Robotica , vol.23 , pp. 755-770
    • Bayro-Corrochano, E.1    Falcon, L.E.2
  • 25
    • 0004280275 scopus 로고
    • VEB Deutscher Verlag der Wissenschaften, Berlin
    • Blaschke, W. Kinematik und Quaternionen. VEB Deutscher Verlag der Wissenschaften, Berlin, 1960.
    • (1960) Kinematik und Quaternionen
    • Blaschke, W.1
  • 28
    • 27644520205 scopus 로고    scopus 로고
    • Remarks on Invariant Geometric Calculus, Cayley-Grassmann Algebras and Geometric Clifford Algebras
    • Crapo, H. and Senato, D. (eds.), Springer, Milano
    • Bravi, P. and Brini, A. Remarks on Invariant Geometric Calculus, Cayley-Grassmann Algebras and Geometric Clifford Algebras. In: Crapo, H. and Senato, D. (eds.), Algebraic Combinatorics and Computer Science, Springer, Milano, pp. 129-150, 2001.
    • (2001) Algebraic Combinatorics and Computer Science , pp. 129-150
    • Bravi, P.1    Brini, A.2
  • 29
    • 82155200643 scopus 로고    scopus 로고
    • Grassmann Geometric Calculus, Invariant Theory and Superalgebras
    • Crapo, H. and Senato D. (eds.), Springer, Milano
    • Brini, A., Regonati, F. and Teolis, A.G.B. Grassmann Geometric Calculus, Invariant Theory and Superalgebras. In: Crapo, H. and Senato D. (eds.), Algebraic Combinatorics and Computer Science, Springer, Milano, pp. 151-196, 2001.
    • (2001) Algebraic Combinatorics and Computer Science , pp. 151-196
    • Brini, A.1    Regonati, F.2    Teolis, A.G.B.3
  • 31
    • 0037918608 scopus 로고
    • Application of Gröbner Basis in Non-linear Computational Geometry
    • Rice, J. (ed.), Springer, New York
    • Buchberger, B. Application of Gröbner Basis in Non-linear Computational Geometry. In: Rice, J. (ed.), Scientific Software. Springer, New York, 1988.
    • (1988) Scientific Software
    • Buchberger, B.1
  • 33
    • 0005871293 scopus 로고
    • Nombres Complexes
    • Molk, J. (red.), Tome I, Fasc. 4, art. I5
    • Cartan, É. Nombres Complexes. In: Molk, J. (red.), Encyclopédie des Sciences Mathématiques, Tome I, vol. 1, Fasc. 4, art. I5, pp. 329-468, 1908.
    • (1908) Encyclopédie des Sciences Mathématiques , vol.1 , pp. 329-468
    • Cartan, E.1
  • 36
    • 0004126712 scopus 로고
    • CollectedWorks, Volume 2. Editors: Cartier, P. and Chevalley, C. Springer, Berlin, Heidelberg, 1997. Originally published by Columbia University Press, New York
    • Chevalley, C. The Algebraic Theory of Spinors and Clifford Algebras, CollectedWorks, Volume 2. Editors: Cartier, P. and Chevalley, C. Springer, Berlin, Heidelberg, 1997. Originally published by Columbia University Press, New York, 1954.
    • (1954) The Algebraic Theory of Spinors and Clifford Algebras
    • Chevalley, C.1
  • 37
    • 0025872206 scopus 로고
    • Lie Algebras, Modules, Dual Quaternions, and Algebraic Methods in Kinematics
    • Chevallier, D.P. Lie Algebras, Modules, Dual Quaternions, and Algebraic Methods in Kinematics. Machine and Mechanical Theory 26: 613-627, 1991.
    • (1991) Machine and Mechanical Theory , vol.26 , pp. 613-627
    • Chevallier, D.P.1
  • 38
    • 1842558625 scopus 로고    scopus 로고
    • Clifford Algebra, Lorentzian Geometry, and Rational Parametrization of Canal Surfaces
    • Cho, H.C., Choi, H.I., Kwon, S.-H., Lee, D.-S., and Wee, N.-S. Clifford Algebra, Lorentzian Geometry, and Rational Parametrization of Canal Surfaces. Computer Aided Geometric Design 21: 327-339, 2004.
    • (2004) Computer Aided Geometric Design , vol.21 , pp. 327-339
    • Cho, H.C.1    Choi, H.I.2    Kwon, S.-H.3    Lee, D.-S.4    Wee, N.-S.5
  • 41
    • 0033704697 scopus 로고    scopus 로고
    • A Deductive Database Approach to Auto mated Geometry Theorem Proving and Discovering
    • Chou, S.C., Gao, X.S. and Zhang, J.Z. A Deductive Database Approach to Auto mated Geometry Theorem Proving and Discovering. J. Automated Reasoning 25(10): 219-246, 2000.
    • (2000) J. Automated Reasoning , vol.25 , Issue.10 , pp. 219-246
    • Chou, S.C.1    Gao, X.S.2    Zhang, J.Z.3
  • 42
    • 84960556043 scopus 로고
    • Preliminary Sketch of Bi-quaternions
    • Clifford, W.K. Preliminary Sketch of Bi-quaternions. Proc. London Math. Society 4: 381-395, 1873.
    • (1873) Proc. London Math. Society , vol.4 , pp. 381-395
    • Clifford, W.K.1
  • 43
    • 0000082109 scopus 로고
    • Application of Grassmann’s Extensive Algebra
    • Clifford, W.K. Application of Grassmann’s Extensive Algebra. American Journal of Mathematics I: 350-358, 1878.
    • (1878) American Journal of Mathematics , vol.1 , pp. 350-358
    • Clifford, W.K.1
  • 44
    • 0009220122 scopus 로고    scopus 로고
    • Vahlen Matrices for Non-definite Metrics
    • Ablamowicz, R. et al. (eds.), Birkhäuser, Boston
    • Cnops, J. Vahlen Matrices for Non-definite Metrics. In: Ablamowicz, R. et al. (eds.), Clifford Algebras with Numeric and Symbolic Computations, Birkhäuser, Boston, 1996.
    • (1996) Clifford Algebras with Numeric and Symbolic Computations
    • Cnops, J.1
  • 49
    • 0033099697 scopus 로고    scopus 로고
    • Hand-Eye calibration Using Dual Quaternions
    • Daniilidis, K. Hand-Eye calibration Using Dual Quaternions. International J. Robotics Research 18: 286-298, 1999.
    • (1999) International J. Robotics Research , vol.18 , pp. 286-298
    • Daniilidis, K.1
  • 50
    • 0000628354 scopus 로고
    • A Characteristic Free Approach to Invariant Theory
    • DeConcini, C. and Procesi C. A Characteristic Free Approach to Invariant Theory. Adv. in Math. 21: 330-354, 1976.
    • (1976) Adv. in Math , vol.21 , pp. 330-354
    • DeConcini, C.1    Procesi, C.2
  • 53
  • 54
    • 85032122505 scopus 로고    scopus 로고
    • Objects in Contact: Boundary Collisions as Geometric Wave Propagation
    • Bayro-Corrochano, E. and Sobczyk, G. (eds.), Birkhäuser, Boston
    • Dorst, L. Objects in Contact: Boundary Collisions as Geometric Wave Propagation. In: Bayro-Corrochano, E. and Sobczyk, G. (eds.) Geometric Algebra with Applications in Science and Engineering, Birkhäuser, Boston, pp. 349-390, 2001.
    • (2001) Geometric Algebra with Applications in Science and Engineering , pp. 349-390
    • Dorst, L.1
  • 57
    • 0002119120 scopus 로고
    • On the Foundations of Combinatorial Theory IX: Combinatorial Methods in Invariant Theory
    • Doubilet, P., Rota, G.-C. and Stein, J. On the Foundations of Combinatorial Theory IX: Combinatorial Methods in Invariant Theory. Stud. Appl. Math. 57: 185-216, 1974.
    • (1974) Stud. Appl. Math , vol.57 , pp. 185-216
    • Doubilet, P.1    Rota, G.-C.2    Stein, J.3
  • 58
    • 0001858460 scopus 로고
    • Grassmann-Plücker Relations and Matroids with Coefficients
    • Dress, A. and Wenzel, D. Grassmann-Plücker Relations and Matroids with Coefficients. Advances in Mathematics 86: 68-110, 1991.
    • (1991) Advances in Mathematics , vol.86 , pp. 68-110
    • Dress, A.1    Wenzel, D.2
  • 59
    • 0029227003 scopus 로고
    • On the Geometry and Algebra of the Point and Line Correspondences between n Images
    • Boston, IEEE Computer Society Press
    • Faugeras, O. and Mourrain, B. On the Geometry and Algebra of the Point and Line Correspondences between n Images. In: Proc. ICCV’95, Boston, IEEE Computer Society Press, pp. 951-956, 1995.
    • (1995) Proc. ICCV’95 , pp. 951-956
    • Faugeras, O.1    Mourrain, B.2
  • 60
    • 3242783927 scopus 로고    scopus 로고
    • Grassmann-Cayley Algebra for Modeling Systems of Cameras and the Algebraic Equations of the Manifold of Trifocal Tensors
    • Faugeras, O. and Papadopoulo, T. Grassmann-Cayley Algebra for Modeling Systems of Cameras and the Algebraic Equations of the Manifold of Trifocal Tensors. Phil. Trans. R. Soc. Lond. A 356(1740): 1123-1152, 1998.
    • (1998) Phil. Trans. R. Soc. Lond. A , vol.356 , Issue.1740 , pp. 1123-1152
    • Faugeras, O.1    Papadopoulo, T.2
  • 63
    • 17544404472 scopus 로고    scopus 로고
    • Combining Clifford Algebraic Computing and Term-Rewriting for Geometric Theorem Proving
    • Fevre, S. andWang, D. Combining Clifford Algebraic Computing and Term-Rewriting for Geometric Theorem Proving. Fundamenta Informaticae 39(1-2): 85-104, 1999.
    • (1999) Fundamenta Informaticae , vol.39 , Issue.1-2 , pp. 85-104
    • Fevre, S.1    Wang, D.2
  • 64
    • 0040144397 scopus 로고
    • Möbius Groups over General Fields Using Clifford Algebras Associated with Spheres
    • Fillmore, J.P. and Springer, A. Möbius Groups over General Fields Using Clifford Algebras Associated with Spheres. International J. Theoretical Phys. 29: 225-246, 1990.
    • (1990) International J. Theoretical Phys , vol.29 , pp. 225-246
    • Fillmore, J.P.1    Springer, A.2
  • 65
    • 0037341609 scopus 로고    scopus 로고
    • Modeling 3D Euclidean Geometry - Performance and Elegance of Five Models of 3D Euclidean Geometry in a Ray Tracing Application
    • Fontijne, D. and Dorst, L. Modeling 3D Euclidean Geometry - Performance and Elegance of Five Models of 3D Euclidean Geometry in a Ray Tracing Application. Computer Graphics and Applications 23(2): 68-78, 2003.
    • (2003) Computer Graphics and Applications , vol.23 , Issue.2 , pp. 68-78
    • Fontijne, D.1    Dorst, L.2
  • 67
    • 85084726815 scopus 로고
    • Quaternions and the Algebra of Vectors
    • Gibbs, J.M. Quaternions and the Algebra of Vectors. Nature 47: 463-464, 1893.
    • (1893) Nature , vol.47 , pp. 463-464
    • Gibbs, J.M.1
  • 68
    • 84967517168 scopus 로고
    • Translated by Kannenberg, L.C. in The Ausdehnungslehre of 1844 and Other Works, Chicago, La Salle: Open Court Publ., 1995
    • Grassmann, H. Linear Extension Theory (Die Lineale Ausdehnungslehre), 1844. Translated by Kannenberg, L.C. in The Ausdehnungslehre of 1844 and Other Works, Chicago, La Salle: Open Court Publ., 1995.
    • (1844) Linear Extension Theory (Die Lineale Ausdehnungslehre)
    • Grassmann, H.1
  • 70
    • 0011306552 scopus 로고
    • Some Examples of the Use of Distances as Coordinates for Euclidean Geometry
    • Havel, T.F. Some Examples of the Use of Distances as Coordinates for Euclidean Geometry. J. Symb. Comp. 11: 579-594, 1991.
    • (1991) J. Symb. Comp , vol.11 , pp. 579-594
    • Havel, T.F.1
  • 71
    • 0343402093 scopus 로고
    • Distance Geometry and Geometric Algebra
    • Havel, T.F. and Dress, A. Distance Geometry and Geometric Algebra, Found. Phys. 23: 1357-1374, 1993.
    • (1993) Found. Phys , vol.23 , pp. 1357-1374
    • Havel, T.F.1    Dress, A.2
  • 72
    • 0009231143 scopus 로고
    • Geometric Algebra and Möbius Sphere Geometry as a Basis for Euclidean Invariant Theory
    • White, N. (ed.), D. Reidel, Dordrecht
    • Havel, T.F. Geometric Algebra and Möbius Sphere Geometry as a Basis for Euclidean Invariant Theory. In: White, N. (ed.), Invariant Methods in Discrete and Computational Geometry, D. Reidel, Dordrecht, pp. 245-256, 1995.
    • (1995) Invariant Methods in Discrete and Computational Geometry , pp. 245-256
    • Havel, T.F.1
  • 73
    • 84949488506 scopus 로고    scopus 로고
    • Qubit Logic, Algebra and Geometry
    • Richter-Gebert, J. andWang, D. (eds.), LNAI 2061, Springer, Berlin, Heidelberg
    • Havel, T.F. Qubit Logic, Algebra and Geometry. In: Richter-Gebert, J. andWang, D. (eds.), Automated Deduction in Geometry, LNAI 2061, Springer, Berlin, Heidelberg, pp. 228-245, 2001.
    • (2001) Automated Deduction in Geometry , pp. 228-245
    • Havel, T.F.1
  • 74
    • 18444381258 scopus 로고    scopus 로고
    • Geometric Algebra in Quantum Information Processing by Nuclear Magnetic Resonance
    • Bayro-Corrochano, E. and Sobczyk, G. (eds.), Birkhäuser, Boston
    • Havel, T.F., Cory, D.G., Somaroo, S.S. and Tseng, C.H. Geometric Algebra in Quantum Information Processing by Nuclear Magnetic Resonance. In: Bayro-Corrochano, E. and Sobczyk, G. (eds.) Geometric Algebra with Applications in Science and Engineering, Birkhäuser, Boston, pp. 281-308, 2001.
    • (2001) Geometric Algebra with Applications in Science and Engineering , pp. 281-308
    • Havel, T.F.1    Cory, D.G.2    Somaroo, S.S.3    Tseng, C.H.4
  • 75
    • 33748929455 scopus 로고
    • Algebres de Clifford et algebres de Weyl
    • Montpellier
    • Helmstetter, J. Algebres de Clifford et algebres de Weyl. Cahiers Math. 25, Montpellier, 1982.
    • (1982) Cahiers Math , vol.25
    • Helmstetter, J.1
  • 78
    • 0004322106 scopus 로고
    • A Unified Language for Mathematics and Physics
    • Chisholm, J.S.R. and Common A.K. (eds.), Kluwer Academic Publishers, Dordrecht
    • Hestenes, D. A Unified Language for Mathematics and Physics. In: Chisholm, J.S.R. and Common A.K. (eds.), Clifford Algebras and their Applications in Mathematical Physics, Kluwer Academic Publishers, Dordrecht, pp. 1-23, 1986.
    • (1986) Clifford Algebras and their Applications in Mathematical Physics , pp. 1-23
    • Hestenes, D.1
  • 79
    • 0002256263 scopus 로고
    • Projective Geometry with Clifford Algebra
    • Hestenes, D. and Ziegler, R. Projective Geometry with Clifford Algebra, Acta Appl. Math. 23: 25-63, 1991.
    • (1991) Acta Appl. Math , vol.23 , pp. 25-63
    • Hestenes, D.1    Ziegler, R.2
  • 80
    • 0002585378 scopus 로고
    • The Design of Linear Algebra and Geometry
    • Hestenes, D. The Design of Linear Algebra and Geometry, Acta Appl. Math. 23: 65-93, 1991.
    • (1991) Acta Appl. Math , vol.23 , pp. 65-93
    • Hestenes, D.1
  • 81
    • 0027975632 scopus 로고
    • Invariant Body Kinematics I, II
    • Hestenes, D. Invariant Body Kinematics I, II. Neural Networks 7: 65-77, 79-88, 1994.
    • (1994) Neural Networks , vol.7
    • Hestenes, D.1
  • 84
    • 3042516351 scopus 로고    scopus 로고
    • New algebraic tools for classical geometry
    • Sommer, G. (ed.), Springer, Heidelberg
    • Hestenes, D., Li, H. and Rockwood, A. New algebraic tools for classical geometry. In: Sommer, G. (ed.), Geometric Computing with Clifford Algebra, Springer, Heidelberg, pp. 3-26, 2001.
    • (2001) Geometric Computing with Clifford Algebra , pp. 3-26
    • Hestenes, D.1    Li, H.2    Rockwood, A.3
  • 85
    • 3242720233 scopus 로고    scopus 로고
    • Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry
    • Bayro-Corrochano, E. and Sobczyk, G. (eds.), Birkhäuser, Boston
    • Hestenes, D. Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry. In: Bayro-Corrochano, E. and Sobczyk, G. (eds.), Geometric Algebra with Applications in Science and Engineering, Birkhäuser, Boston, pp. 3-17, 2001.
    • (2001) Geometric Algebra with Applications in Science and Engineering , pp. 3-17
    • Hestenes, D.1
  • 86
    • 33847616943 scopus 로고    scopus 로고
    • The Crystallographic Space Groups in Geometric Algebra
    • Hestenes, D. and Holt, J. The Crystallographic Space Groups in Geometric Algebra. Journal of Mathematical Physics 48, 023514, 2007.
    • (2007) Journal of Mathematical Physics , vol.48 , pp. 023514
    • Hestenes, D.1    Holt, J.2
  • 87
    • 33846158949 scopus 로고    scopus 로고
    • Geometric Algebra and Its Application to Computer Graphics
    • published by INRIA and Eurographics Assoc., Grenoble
    • Hildenbrand, D., Fontijne, D., Perwass, C. and Dorst, L. Geometric Algebra and Its Application to Computer Graphics. Tutorial of Eurographics 2004, published by INRIA and Eurographics Assoc., Grenoble, 2004.
    • (2004) Tutorial of Eurographics 2004
    • Hildenbrand, D.1    Fontijne, D.2    Perwass, C.3    Dorst, L.4
  • 88
    • 27444443869 scopus 로고    scopus 로고
    • Geometric Computing in Computer Graphics Using Conformal Geometric Algebra
    • Hildenbrand, D. Geometric Computing in Computer Graphics Using Conformal Geometric Algebra. Computers and Graphics 29(5): 795-803, 2005.
    • (2005) Computers and Graphics , vol.29 , Issue.5 , pp. 795-803
    • Hildenbrand, D.1
  • 89
    • 0000596483 scopus 로고
    • Über die Theorie der Algebraischen Formen
    • Hilbert, D. Über die Theorie der Algebraischen Formen. Mathematische Ann. 36: 473-534, 1890.
    • (1890) Mathematische Ann , vol.36 , pp. 473-534
    • Hilbert, D.1
  • 90
    • 0039060770 scopus 로고
    • Über die vollen Invariantensysteme
    • Hilbert, D. Über die vollen Invariantensysteme. Mathematische Ann. 42: 313-373, 1893.
    • (1893) Mathematische Ann , vol.42 , pp. 313-373
    • Hilbert, D.1
  • 91
    • 17044405190 scopus 로고    scopus 로고
    • Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}
    • Hitzer, E.M.S. Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}. Simon Stevin 11(5): 653-662, 2004.
    • (2004) Simon Stevin , vol.11 , Issue.5 , pp. 653-662
    • Hitzer, E.M.S.1
  • 92
    • 0035624782 scopus 로고    scopus 로고
    • Russian Killer" № 2: A Challenging Geometric Theorem with Machine vs. Human Proofs
    • Hou, X., Li, H., Wang, D. and Yang, L. "Russian Killer" № 2: a Challenging Geometric Theorem with Machine vs. Human Proofs. Math. Intelligencer 23(1): 9-15, 2001.
    • (2001) Math. Intelligencer , vol.23 , Issue.1 , pp. 9-15
    • Hou, X.1    Li, H.2    Wang, D.3    Yang, L.4
  • 94
    • 0141974031 scopus 로고
    • Supersymmetric Bracket Algebra and Invariant Theory
    • Huang, R.Q., Rota, G.-C. and Stein, J. Supersymmetric Bracket Algebra and Invariant Theory, Acta Appl. Math. 21: 193-246, 1990.
    • (1990) Acta Appl. Math , vol.21 , pp. 193-246
    • Huang, R.Q.1    Rota, G.-C.2    Stein, J.3
  • 95
    • 0004256209 scopus 로고
    • Cambridge University Press, Cambridge
    • Iversen, B. Hyperbolic Geometry. Cambridge University Press, Cambridge, 1992.
    • (1992) Hyperbolic Geometry
    • Iversen, B.1
  • 96
    • 0347419901 scopus 로고    scopus 로고
    • Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases and Characteristic Sets
    • Wang, D. (ed.), LNAI 1360, Springer, Berlin, Heidelberg
    • Kapur, D. Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases and Characteristic Sets. In: Wang, D. (ed.), Automated Deduction in Geometry, LNAI 1360, Springer, Berlin, Heidelberg, pp. 1-36, 1998.
    • (1998) Automated Deduction in Geometry , pp. 1-36
    • Kapur, D.1
  • 98
    • 25144484254 scopus 로고    scopus 로고
    • Surface Evolution and Representation Using Geometric Algebra
    • Cipolla, R. and Martin, R. (eds.), Springer, London
    • Lasenby, A. and Lasenby, J. Surface Evolution and Representation Using Geometric Algebra. In: Cipolla, R. and Martin, R. (eds.), The Mathematics of Surfaces IX, Springer, London, pp. 144-168, 2000.
    • (2000) The Mathematics of Surfaces IX , pp. 144-168
    • Lasenby, A.1    Lasenby, J.2
  • 100
    • 8344244854 scopus 로고    scopus 로고
    • Conformal Geometry and the Universe
    • submitted to
    • Lasenby, A. Conformal Geometry and the Universe, submitted to Phil. Trans. R. Soc. Lond. A, 2004.
    • (2004) Phil. Trans. R. Soc. Lond. A
    • Lasenby, A.1
  • 101
    • 25144509533 scopus 로고    scopus 로고
    • Recent Applications of Conformal Geometric Algebra
    • Li, H. et al. (eds.), LNCS 3519, Springer, Berlin, Heidelberg
    • Lasenby, A. Recent Applications of Conformal Geometric Algebra. In: Li, H. et al. (eds.), Computer Algebra and Geometric Algebra with Applications, LNCS 3519, Springer, Berlin, Heidelberg, pp. 298-328, 2005.
    • (2005) Computer Algebra and Geometric Algebra with Applications , pp. 298-328
    • Lasenby, A.1
  • 104
    • 0342532622 scopus 로고    scopus 로고
    • Hyperbolic Geometry with Clifford Algebra
    • Li, H. Hyperbolic Geometry with Clifford Algebra, Acta Appl. Math. 48(3): 317-358, 1997.
    • (1997) Acta Appl. Math , vol.48 , Issue.3 , pp. 317-358
    • Li, H.1
  • 105
    • 84865573425 scopus 로고    scopus 로고
    • On Erdös’ Ten-Point Problem
    • Li, H. and Shi, H. On Erdös’ Ten-Point Problem, Acta Mathematica Sinica New Series, 13(2): 221-230, 1997.
    • (1997) Acta Mathematica Sinica New Series , vol.13 , Issue.2 , pp. 221-230
    • Li, H.1    Shi, H.2
  • 106
    • 84865561016 scopus 로고    scopus 로고
    • Some Applications of Clifford Algebra to Geometries
    • Gao, X.S. et al. (eds.), LNAI 1669, Springer, Berlin, Heidelberg
    • Li, H. Some Applications of Clifford Algebra to Geometries. In: Gao, X.S. et al. (eds.), Automated Deduction in Geometry, LNAI 1669, Springer, Berlin, Heidelberg, pp. 156-179, 1998.
    • (1998) Automated Deduction in Geometry , pp. 156-179
    • Li, H.1
  • 107
    • 0033686004 scopus 로고    scopus 로고
    • Vectorial Equation-Solving for Mechanical Geometry Theorem Proving
    • Li, H. Vectorial Equation-Solving for Mechanical Geometry Theorem Proving. J. Automated Reasoning 25: 83-121, 2000.
    • (2000) J. Automated Reasoning , vol.25 , pp. 83-121
    • Li, H.1
  • 108
    • 84937413266 scopus 로고    scopus 로고
    • The Lie Model for Euclidean Geometry
    • Sommer, G. and Zeevi, Y. (eds.), LNCS 1888, Springer, Berlin
    • Li, H. The Lie Model for Euclidean Geometry. In: Sommer, G. and Zeevi, Y. (eds.), Algebraic Frames for the Perception-Action Cycle, LNCS 1888, Springer, Berlin, pp. 115-133, 2000.
    • (2000) Algebraic Frames for the Perception-Action Cycle , pp. 115-133
    • Li, H.1
  • 109
    • 3543114972 scopus 로고    scopus 로고
    • Clifford Algebra Approaches to Automated Geometry Theorem Proving
    • Gao, X.S. and Wang, D. (eds.), Academic Press, London
    • Li, H. Clifford Algebra Approaches to Automated Geometry Theorem Proving. In: Gao, X.S. and Wang, D. (eds.), Mathematics Mechanization and Applications, Academic Press, London, pp. 205-230, 2000.
    • (2000) Mathematics Mechanization and Applications , pp. 205-230
    • Li, H.1
  • 110
    • 0141741054 scopus 로고    scopus 로고
    • Generalized Homogeneous Coordinates for Computational Geometry
    • Sommer, G. (ed.), Springer, Heidelberg
    • Li, H., Hestenes, D. and Rockwood, A. Generalized Homogeneous Coordinates for Computational Geometry. In: Sommer, G. (ed.), Geometric Computing with Clifford Algebras, Springer, Heidelberg, pp. 27-60, 2001.
    • (2001) Geometric Computing with Clifford Algebras , pp. 27-60
    • Li, H.1    Hestenes, D.2    Rockwood, A.3
  • 111
    • 25144441590 scopus 로고    scopus 로고
    • Spherical Conformal Geometry with Geometric Algebra
    • Sommer, G. (ed.), Springer, Heidelberg
    • Li, H., Hestenes, D. and Rockwood, A. Spherical Conformal Geometry with Geometric Algebra. In: Sommer, G. (ed.), Geometric Computing with Clifford Algebras, Springer, Heidelberg, pp. 61-76, 2001.
    • (2001) Geometric Computing with Clifford Algebras , pp. 61-76
    • Li, H.1    Hestenes, D.2    Rockwood, A.3
  • 112
    • 25144441590 scopus 로고    scopus 로고
    • A Universal Model for Conformal Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces
    • Sommer, G. (ed.), Springer, Heidelberg
    • Li, H., Hestenes, D. and Rockwood, A. A Universal Model for Conformal Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces. In: Sommer, G. (ed.), Geometric Computing with Clifford Algebras, Springer, Heidelberg, pp. 77-104, 2001.
    • (2001) Geometric Computing with Clifford Algebras , pp. 77-104
    • Li, H.1    Hestenes, D.2    Rockwood, A.3
  • 113
    • 25144438438 scopus 로고    scopus 로고
    • Hyperbolic Conformal Geometry with Clifford Algebra
    • Li, H. Hyperbolic Conformal Geometry with Clifford Algebra. International Journal of Theoretical Physics 40(1): 79-91, 2001.
    • (2001) International Journal of Theoretical Physics , vol.40 , Issue.1 , pp. 79-91
    • Li, H.1
  • 114
    • 33745314002 scopus 로고    scopus 로고
    • Coordinate-free Projective Geometry for Computer Vision
    • Sommer, G. (ed.), Springer, Heidelberg
    • Li, H. and Sommer, G. Coordinate-free Projective Geometry for Computer Vision. In: Sommer, G. (ed.), Geometric Computing with Clifford Algebras, Springer, Heidelberg, pp. 415-454, 2001.
    • (2001) Geometric Computing with Clifford Algebras , pp. 415-454
    • Li, H.1    Sommer, G.2
  • 115
    • 25144500927 scopus 로고    scopus 로고
    • Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra
    • Dorst, L. et al. (eds.), Birkhäuser, Boston
    • Li, H. Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra. In: Dorst, L. et al. (eds.), Applications of Geometric Algebra in Computer Science and Engineering, Birkhäuser, Boston, pp. 69-78, 2002.
    • (2002) Applications of Geometric Algebra in Computer Science and Engineering , pp. 69-78
    • Li, H.1
  • 116
    • 25144453695 scopus 로고    scopus 로고
    • Clifford Expansions and Summations
    • Li, H. Clifford Expansions and Summations. MM Research Preprints 21: 112-154, 2002.
    • (2002) MM Research Preprints , vol.21 , pp. 112-154
    • Li, H.1
  • 117
    • 0242593247 scopus 로고    scopus 로고
    • Automated Short Proof Generation in Projective Geometry with Cayley and Bracket Algebras I, II
    • Li, H. and Wu, Y. Automated Short Proof Generation in Projective Geometry with Cayley and Bracket Algebras I, II. J. Symb. Comput. 36(5): 717-762, 763-809, 2003.
    • (2003) J. Symb. Comput , vol.36 , Issue.5
    • Li, H.1    Wu, Y.2
  • 118
    • 25144495065 scopus 로고    scopus 로고
    • Clifford Algebras and Geometric Computation
    • Chen, F. and Wang, D. (eds.), World Scientific, Singapore
    • Li, H. Clifford Algebras and Geometric Computation. In: Chen, F. and Wang, D. (eds.), Geometric Computation, World Scientific, Singapore, pp. 221-247, 2004.
    • (2004) Geometric Computation , pp. 221-247
    • Li, H.1
  • 119
    • 25144503745 scopus 로고    scopus 로고
    • Automated Geometric Theorem Proving, Clifford Bracket Algebra and Clifford Expansions
    • Qian, T. et al. (eds.), Birkhäuser, Basel
    • Li, H. Automated Geometric Theorem Proving, Clifford Bracket Algebra and Clifford Expansions. In: Qian, T. et al. (eds.), Trends in Mathematics: Advances in Analysis and Geometry, Birkhäuser, Basel, pp. 345-363, 2004.
    • (2004) Trends in Mathematics: Advances in Analysis and Geometry , pp. 345-363
    • Li, H.1
  • 121
    • 25144482762 scopus 로고    scopus 로고
    • Symbolic Computation in the Homogeneous Geometric Model with Clifford Algebra
    • Gutierrez, J. (ed.), ACM Press, New York
    • Li, H. Symbolic Computation in the Homogeneous Geometric Model with Clifford Algebra. In: Gutierrez, J. (ed.), Proc. ISSAC 2004, ACM Press, New York, pp. 221-228, 2004.
    • (2004) Proc. ISSAC 2004 , pp. 221-228
    • Li, H.1
  • 122
    • 25144462626 scopus 로고    scopus 로고
    • Polyhedral Scene Analysis Combining Parametric Propagation with Calotte Analysis
    • Li, H. et al. (eds.), LNCS 3519, Springer, Berlin, Heidelberg
    • Li, H., Zhao, L., Chen, Y. Polyhedral Scene Analysis Combining Parametric Propagation with Calotte Analysis. In: Li, H. et al. (eds.), Computer Algebra and Geometric Algebra with Applications, LNCS 3519, Springer, Berlin, Heidelberg, pp. 383-402, 2005.
    • (2005) Computer Algebra and Geometric Algebra with Applications , pp. 383-402
    • Li, H.1    Zhao, L.2    Chen, Y.3
  • 123
    • 85032095758 scopus 로고    scopus 로고
    • Geometric Reasoning with Invariant Algebras
    • ATCM Inc., Blacksburg, USA
    • Li, H. Geometric Reasoning with Invariant Algebras. In: Proc. ATCM 2006, ATCM Inc., Blacksburg, USA, pp. 6-19, 2006.
    • (2006) Proc. ATCM 2006 , pp. 6-19
    • Li, H.1
  • 124
    • 36349024704 scopus 로고    scopus 로고
    • A Recipe for Symbolic Geometric Computing: Long Geometric Product, BREEFS and Clifford Factorization
    • Brown, C.W. (ed.), ACM Press, New York
    • Li, H. A Recipe for Symbolic Geometric Computing: Long Geometric Product, BREEFS and Clifford Factorization. In: Brown, C.W. (ed.), Proc. ISSAC 2007, ACM Press, New York, pp. 261-268, 2007.
    • (2007) Proc. ISSAC 2007 , pp. 261-268
    • Li, H.1
  • 126
    • 0011841463 scopus 로고
    • Über Komplexe, inbesondere Linien- und Kugelkomplexe, mit Anwendung auf der Theorie der partieller Differentialgleichungen
    • (Ges. Abh. 2: 1-121)
    • Lie, S. Über Komplexe, inbesondere Linien- und Kugelkomplexe, mit Anwendung auf der Theorie der partieller Differentialgleichungen. Math. Ann. 5: 145-208, 209-256, 1872. (Ges. Abh. 2: 1-121)
    • (1872) Math. Ann , vol.5
    • Lie, S.1
  • 128
  • 129
    • 85032124948 scopus 로고
    • Über eine neue Begründung der regressiven Multiplikation extensiver Grössen in einem Hauptgebeit n-ter Stufe
    • Lotze, A. Über eine neue Begründung der regressiven Multiplikation extensiver Grössen in einem Hauptgebeit n-ter Stufe, Jahresbericht d. Deutschen Mathem. Vereinigung 57: 102-110, 1955.
    • (1955) Jahresbericht d. Deutschen Mathem. Vereinigung , vol.57 , pp. 102-110
    • Lotze, A.1
  • 131
    • 0033145377 scopus 로고    scopus 로고
    • Arguesian Identities in Linear Lattices
    • Mainetti, M. and Yan, C.H. Arguesian Identities in Linear Lattices. Advances in Mathematics 144: 50-93, 1999.
    • (1999) Advances in Mathematics , vol.144 , pp. 50-93
    • Mainetti, M.1    Yan, C.H.2
  • 132
    • 84892266193 scopus 로고
    • Clifford Algebras and Möbius Transformations
    • Micali, A. et al. (eds.), Kluwer, Dordrecht
    • Maks, J. Clifford Algebras and Möbius Transformations. In: Micali, A. et al. (eds.), Clifford Algebras and Their Applications in Mathematical Physics, Kluwer, Dordrecht, pp. 57-63, 1992.
    • (1992) Clifford Algebras and Their Applications in Mathematical Physics , pp. 57-63
    • Maks, J.1
  • 133
    • 0242648857 scopus 로고
    • The Dotted Straightening Algorithm
    • McMillan, T. andWhite, N. The Dotted Straightening Algorithm. J. Symb. Comput. 11: 471-482, 1991.
    • (1991) J. Symb. Comput , vol.11 , pp. 471-482
    • McMillan, T.1    White, N.2
  • 134
    • 0004165092 scopus 로고    scopus 로고
    • Kluwer Academic Publishers, Dordrecht
    • Merlet, J.-P. Parallel Robot. Kluwer Academic Publishers, Dordrecht, 2000.
    • (2000) Parallel Robot
    • Merlet, J.-P.1
  • 135
    • 85032082431 scopus 로고
    • New Aspects of Geometrical Calculus with Invariants
    • Mourrain, B. New Aspects of Geometrical Calculus with Invariants. MEGA’91, 1991.
    • (1991) MEGA’91
    • Mourrain, B.1
  • 137
    • 0342532623 scopus 로고
    • Applications of Clifford Algebras in Robotics
    • Merlet, J.-P. and Ravani, B. (eds, D. Reidel, Dordrecht, Boston
    • Mourrain, B. and Stolfi, N. Applications of Clifford Algebras in Robotics. In: Merlet, J.-P. and Ravani, B. (eds.), Computational Kinematics '95, D. Reidel, Dordrecht, Boston, pp. 141-150, 1995.
    • (1995) Computational Kinematics '95 , pp. 141-150
    • Mourrain, B.1    Stolfi, N.2
  • 141
    • 34250912076 scopus 로고
    • Zur Quantenmechanik des magnetischen Elektrons
    • Pauli, W. Zur Quantenmechanik des magnetischen Elektrons. Z. Phys. 42: 601-623, 1927.
    • (1927) Z. Phys , vol.42 , pp. 601-623
    • Pauli, W.1
  • 144
    • 35248884022 scopus 로고    scopus 로고
    • Spherical Decision Surfaces Using Conformal Modeling
    • Magdeburg, LNCS 2781, Springer, Berlin
    • Perwass, C., Banarer, V. and Sommer, G. Spherical Decision Surfaces Using Conformal Modeling. In: DAGM 2003, Magdeburg, LNCS 2781, Springer, Berlin, pp. 9-16, 2003.
    • (2003) DAGM 2003 , pp. 9-16
    • Perwass, C.1    Banarer, V.2    Sommer, G.3
  • 146
    • 3242693990 scopus 로고    scopus 로고
    • Realizations of the Conformal Group
    • Bayro-Corrochano, E. and Sobczyk, G. (eds.), Birkhäuser, Boston
    • Pozo, J.M. and Sobczyk, G. Realizations of the Conformal Group. In: Bayro-Corrochano, E. and Sobczyk, G. (eds.), Geometric Algebra with Applications in Science and Engineering, Birkhäuser, Boston, pp. 42-60, 2001.
    • (2001) Geometric Algebra with Applications in Science and Engineering , pp. 42-60
    • Pozo, J.M.1    Sobczyk, G.2
  • 150
    • 0009552865 scopus 로고
    • From lecture notes made in 1957-8, edited by Bolinder, E. and Lounesto, P. Kluwer Academic Publisher, Dordrecht
    • Riesz, M. Clifford Numbers and Spinors, 1958. From lecture notes made in 1957-8, edited by Bolinder, E. and Lounesto, P. Kluwer Academic Publisher, Dordrecht, 1993.
    • (1958) Clifford Numbers and Spinors
    • Riesz, M.1
  • 151
    • 84878606150 scopus 로고    scopus 로고
    • Adaptive Pose Estimation for Different Corresponding Entities
    • van Gool, L. (ed.), LNCS 2449, Springer, Berlin, Heidelberg
    • Rosenhahn, B. and Sommer, G. Adaptive Pose Estimation for Different Corresponding Entities, In: van Gool, L. (ed.), Pattern Recognition, 24 Symposium für Mustererkennung, LNCS 2449, Springer, Berlin, Heidelberg, pp. 265-273, 2002.
    • (2002) Pattern Recognition, 24 Symposium für Mustererkennung , pp. 265-273
    • Rosenhahn, B.1    Sommer, G.2
  • 152
    • 3042669256 scopus 로고    scopus 로고
    • Ph.D. Dissertation, CAU zu Kiel
    • Rosenhahn, B. Pose Estimation Revisited. Ph.D. Dissertation, also Technical Report Number 0308, CAU zu Kiel, 2003.
    • (2003) Pose Estimation Revisited
    • Rosenhahn, B.1
  • 153
    • 21144454563 scopus 로고    scopus 로고
    • Free-form Pose Estimation by Using Twist Representations
    • Rosenhahn, B., Perwass, C. and Sommer, G. Free-form Pose Estimation by Using Twist Representations. Algorithmica 38: 91-113, 2004.
    • (2004) Algorithmica , vol.38 , pp. 91-113
    • Rosenhahn, B.1    Perwass, C.2    Sommer, G.3
  • 154
    • 35048832800 scopus 로고    scopus 로고
    • Pose Estimation of Free-form Objects
    • Prag, LNCS 3021, Springer, Berlin, Heidelberg
    • Rosenhahn, B. and Sommer, G. Pose Estimation of Free-form Objects. In: ECCV 2004, Prag, LNCS 3021, Springer, Berlin, Heidelberg, pp. 414-427, 2004.
    • (2004) ECCV 2004 , pp. 414-427
    • Rosenhahn, B.1    Sommer, G.2
  • 157
    • 85032107498 scopus 로고    scopus 로고
    • Academia Nazionale dei Lincei atti dei Convegni Lincei 17, Colloquio Internazionale sulle Teorie Combinatoire, Tomo 2, Roma
    • Rota, G.-C. and Stein, J. Applications of Cayley Algebras. Academia Nazionale dei Lincei atti dei Convegni Lincei 17, Colloquio Internazionale sulle Teorie Combinatoire, Tomo 2, Roma.
    • Applications of Cayley Algebras
    • Rota, G.-C.1    Stein, J.2
  • 158
    • 0009140223 scopus 로고
    • Symbolic Method in Invariant Theory
    • Rota, G.-C. and Stein, J. Symbolic Method in Invariant Theory, Proc. Nat. Acad. Sci. 83: 844-847, 1986.
    • (1986) Proc. Nat. Acad. Sci , vol.83 , pp. 844-847
    • Rota, G.-C.1    Stein, J.2
  • 159
    • 0009423546 scopus 로고
    • Introduction to Invariant Theory in Superalgebras
    • Staton, D. (ed.), Springer, New York
    • Rota, G.-C. and Sturmfels, B. Introduction to Invariant Theory in Superalgebras. In: Staton, D. (ed.), Invariant Theory and Tableaux, Springer, New York, pp. 1-35, 1990.
    • (1990) Invariant Theory and Tableaux , pp. 1-35
    • Rota, G.-C.1    Sturmfels, B.2
  • 160
    • 5244249302 scopus 로고
    • Conformal Clifford Manifolds Arising in Clifford Analysis
    • Ryan, J. Conformal Clifford Manifolds Arising in Clifford Analysis. Proc. Roy. Irish Acad. Sect. A 85: 1-23, 1985.
    • (1985) Proc. Roy. Irish Acad. Sect. A , vol.85 , pp. 1-23
    • Ryan, J.1
  • 162
    • 25844521197 scopus 로고
    • Distance-Geometric Development of Two-dimensional Euclidean, Hyperbolic and Spherical Geometry I, II
    • Seidel, J.J. Distance-Geometric Development of Two-dimensional Euclidean, Hyperbolic and Spherical Geometry I, II. Simon Stevin 29: 32-50, 65-76, 1952.
    • (1952) Simon Stevin , vol.29
    • Seidel, J.J.1
  • 163
    • 85032073702 scopus 로고
    • Angles and Distances in n-Dimensional Euclidean and Non-Euclidean geometry I-III
    • Seidel, J.J. Angles and Distances in n-Dimensional Euclidean and Non-Euclidean geometry I-III. Indag. Math. 17, № 3 & 4, 1952.
    • (1952) Indag. Math , vol.17 , Issue.3-4
    • Seidel, J.J.1
  • 165
    • 0036573177 scopus 로고    scopus 로고
    • Geometric Algebra in Linear Algebra and Geometry
    • Sobczyk, G. and Pozo, J.M. Geometric Algebra in Linear Algebra and Geometry. Acta Appl. Math. 71: 207-244, 2002.
    • (2002) Acta Appl. Math , vol.71 , pp. 207-244
    • Sobczyk, G.1    Pozo, J.M.2
  • 167
    • 33749076380 scopus 로고    scopus 로고
    • A Geometric Algebra Approach to Some Problems of Robot Vision
    • Byrnes, J. (ed.), Kluwer Acad., NATO Science Series 136
    • Sommer, G. A Geometric Algebra Approach to Some Problems of Robot Vision. In: Byrnes, J. (ed.), Computational Noncommunicative Algebra and Applications, Kluwer Acad., NATO Science Series 136, pp. 309-338, 2004.
    • (2004) Computational Noncommunicative Algebra and Applications , pp. 309-338
    • Sommer, G.1
  • 168
    • 25144492746 scopus 로고    scopus 로고
    • Application of Geometric Algebra in Robot Vision
    • Li, H. et al. (eds.), LNCS 3519, Springer, Berlin, Heidelberg
    • Sommer, G. Application of Geometric Algebra in Robot Vision. In: Li, H. et al. (eds.), Computer Algebra and Geometric Algebra with Applications, LNCS 3519, Springer, Berlin, Heidelberg, pp. 258-277, 2005.
    • (2005) Computer Algebra and Geometric Algebra with Applications , pp. 258-277
    • Sommer, G.1
  • 169
    • 25144455022 scopus 로고    scopus 로고
    • Twists - An Operational Representation of Shape
    • Li, H. et al. (eds.), LNCS 3519, Springer, Berlin, Heidelberg
    • Sommer, G., Rosenhahn, B. and Perwass, C. Twists - An Operational Representation of Shape. In: Li, H. et al. (eds.), Computer Algebra and Geometric Algebra with Applications, LNCS 3519, Springer, Berlin, Heidelberg, pp. 278-297, 2005.
    • (2005) Computer Algebra and Geometric Algebra with Applications , pp. 278-297
    • Sommer, G.1    Rosenhahn, B.2    Perwass, C.3
  • 171
  • 173
    • 0242397116 scopus 로고
    • Computing Final Polynomials and Final Syzygies Using Buchberger’s Gröbner Basis Method
    • Sturmfels, B. Computing Final Polynomials and Final Syzygies Using Buchberger’s Gröbner Basis Method. Result in Math. 15: 551-360, 1989.
    • (1989) Result in Math , vol.15 , pp. 551-1360
    • Sturmfels, B.1
  • 174
    • 38249025110 scopus 로고
    • Gröbner Bases and Invariant Theory
    • Sturmfels, B. and White, N. Gröbner Bases and Invariant Theory. Advances in Mathematics 76: 245-259, 1989.
    • (1989) Advances in Mathematics , vol.76 , pp. 245-259
    • Sturmfels, B.1    White, N.2
  • 175
    • 0038749021 scopus 로고
    • Computational Algebraic Geometry of Projective Configurations
    • Sturmfels, B. Computational Algebraic Geometry of Projective Configurations. J. Symbolic Computation 11: 595-618, 1991.
    • (1991) J. Symbolic Computation , vol.11 , pp. 595-618
    • Sturmfels, B.1
  • 176
    • 84967686160 scopus 로고
    • On the Synthetic Factorization of Homogeneous Invariants
    • Sturmfels, B. and Whiteley, W. On the Synthetic Factorization of Homogeneous Invariants. J. Symbolic Computation 11: 439-454, 1991.
    • (1991) J. Symbolic Computation , vol.11 , pp. 439-454
    • Sturmfels, B.1    Whiteley, W.2
  • 181
    • 27244442941 scopus 로고    scopus 로고
    • Projective Model for Central Catadioptric Cameras Using Clifford Algebra
    • LNCS 3663, Springer, Berlin, Heidelberg
    • Tolvanen, A., Perwass, C. and Sommer, G. Projective Model for Central Catadioptric Cameras Using Clifford Algebra. In: DAGM 2005, LNCS 3663, Springer, Berlin, Heidelberg, pp. 192-199, 2005.
    • (2005) DAGM 2005 , pp. 192-199
    • Tolvanen, A.1    Perwass, C.2    Sommer, G.3
  • 183
    • 0142067384 scopus 로고
    • Linear Invariants of Ten Quaternary Quadrics
    • Turnbull, H.W. and Young, A. Linear Invariants of Ten Quaternary Quadrics. Trans. Camb. Phil. Soc. 23: 265-301, 1926.
    • (1926) Trans. Camb. Phil. Soc , vol.23 , pp. 265-301
    • Turnbull, H.W.1    Young, A.2
  • 184
    • 0039881441 scopus 로고
    • Úber Bewegungen und komplexe Zahlen
    • Vahlen, K. Úber Bewegungen und komplexe Zahlen. Math. Ann. 55: 585-593, 1902.
    • (1902) Math. Ann , vol.55 , pp. 585-593
    • Vahlen, K.1
  • 186
    • 0040936024 scopus 로고    scopus 로고
    • Clifford Algebraic Calculus for Geometric Reasoning, with Application to Computer Vision
    • Wang, D. (ed.), LNAI 1360, Springer, Berlin, Heidelberg
    • Wang, D. Clifford Algebraic Calculus for Geometric Reasoning, with Application to Computer Vision. In: Wang, D. (ed.), Automated Deduction in Geometry, LNAI 1360, Springer, Berlin, Heidelberg, pp. 115-140, 1996.
    • (1996) Automated Deduction in Geometry , pp. 115-140
    • Wang, D.1
  • 187
    • 36349033247 scopus 로고    scopus 로고
    • Geometric Reasoning with Geometric Algebra
    • Bayro-Corrochano, E. and Sobczyk, G. (eds.), Birkhäuser, Boston
    • Wang, D. Geometric Reasoning with Geometric Algebra. In: Bayro-Corrochano, E. and Sobczyk, G. (eds.) Geometric Algebra with Applications in Science and Engineering, Birkhäuser, Boston, pp. 89-109, 2001.
    • (2001) Geometric Algebra with Applications in Science and Engineering , pp. 89-109
    • Wang, D.1
  • 189
    • 0004109271 scopus 로고
    • Princeton Mathematics Series, Princeton University Press, Princeton, New Jersey
    • Weyl, H. The Classical Groups. Princeton Mathematics Series, Princeton University Press, Princeton, New Jersey, 1939.
    • (1939) The Classical Groups
    • Weyl, H.1
  • 190
    • 84968518142 scopus 로고
    • The Bracket Ring of Combinatorial Geometry I
    • White, N. The Bracket Ring of Combinatorial Geometry I. Trans. Amer. Math. Soc. 202: 79-103, 1975.
    • (1975) Trans. Amer. Math. Soc , vol.202 , pp. 79-103
    • White, N.1
  • 191
    • 84919956109 scopus 로고
    • Implementation of the Straightening Algorithm of Classical Invariant Theory
    • Staton, D. (ed.), Springer, New York
    • White, N. Implementation of the Straightening Algorithm of Classical Invariant Theory. In: Staton, D. (ed.), Invariant Theory and Tableaux, Springer, New York, pp. 36-45, 1990.
    • (1990) Invariant Theory and Tableaux , pp. 36-45
    • White, N.1
  • 192
    • 0141974028 scopus 로고
    • Multilinear Cayley Factorization
    • White, N. Multilinear Cayley Factorization. J. Symb. Comput. 11: 421-438, 1991.
    • (1991) J. Symb. Comput , vol.11 , pp. 421-438
    • White, N.1
  • 194
    • 0005036749 scopus 로고    scopus 로고
    • Geometric Applications of the Grassmann-Cayley Algebra
    • Goodman, J. E. and O’Rourke, J. (eds.), CRC Press, Florida
    • White, N. Geometric Applications of the Grassmann-Cayley Algebra. In: Goodman, J. E. and O’Rourke, J. (eds.), Handbook of Discrete and Computational Geometry, CRC Press, Florida, 1997.
    • (1997) Handbook of Discrete and Computational Geometry
    • White, N.1
  • 195
    • 58249113209 scopus 로고    scopus 로고
    • Grassmann-Cayley Algebra and Robotics Applications
    • Bayro-Corrochano, E. (ed.), Springer, Heidelberg
    • White, N. Grassmann-Cayley Algebra and Robotics Applications. In: Bayro-Corrochano, E. (ed.), Handbook of Geometric Computing, Springer, Heidelberg, pp. 629-656, 2005.
    • (2005) Handbook of Geometric Computing , pp. 629-656
    • White, N.1
  • 196
    • 0242480576 scopus 로고
    • Invariant Computations for Analytic Projective Geometry
    • Whiteley, W. Invariant Computations for Analytic Projective Geometry. J. Symb. Comput. 11: 549-578, 1991.
    • (1991) J. Symb. Comput , vol.11 , pp. 549-578
    • Whiteley, W.1
  • 199
    • 0002972607 scopus 로고
    • Theorie der quadratischen Formen in beliebigen Körpern
    • Witt, E. Theorie der quadratischen Formen in beliebigen Körpern. J. Reine Angew. Math. 176: 31-44, 1937.
    • (1937) J. Reine Angew. Math , vol.176 , pp. 31-44
    • Witt, E.1
  • 200
    • 8344262968 scopus 로고    scopus 로고
    • Lightlike Infinity in CGA Models of Spacetime
    • Witte, F.M.C. Lightlike Infinity in CGA Models of Spacetime. J. of Physics A -Mathematics and General 37(42): 9965-9973, 2004.
    • (2004) J. of Physics A -Mathematics and General , vol.37 , Issue.42 , pp. 9965-9973
    • Witte, F.M.C.1
  • 201
    • 0347232227 scopus 로고
    • On the Mechanization of Theorem-Proving in Elementary Differential Geometry
    • Math
    • Wu, W.-T. On the Mechanization of Theorem-Proving in Elementary Differential Geometry. Scientia Sinica (Math Suppl. I): 94-102, 1979.
    • (1979) Scientia Sinica , pp. 94-102
    • Wu, W.-T.1
  • 203
    • 0242480577 scopus 로고    scopus 로고
    • Science Press and Kluwer Academic, Beijing
    • Wu, W.-T. Mathematics Mechanization. Science Press and Kluwer Academic, Beijing, 2000.
    • (2000) Mathematics Mechanization
    • Wu, W.-T.1
  • 204
    • 33750036953 scopus 로고    scopus 로고
    • Automated Reasoning and Equation Solving with the Characteristic Set Method
    • Wu, W.-T. and Gao, X.S. Automated Reasoning and Equation Solving with the Characteristic Set Method. J. Computer Science and Technology 22(2): 756-764, 2007.
    • (2007) J. Computer Science and Technology , vol.22 , Issue.2 , pp. 756-764
    • Wu, W.-T.1    Gao, X.S.2
  • 206
    • 85032076781 scopus 로고    scopus 로고
    • Ph.D. Dissertation, Acad. Math. and Sys. Sci., Chinese Academy of Sciences, Beijing
    • Xu, R. Clifford Coalgebra and Geometric Theorem Completion. Ph.D. Dissertation, Acad. Math. and Sys. Sci., Chinese Academy of Sciences, Beijing, 2006.
    • (2006) Clifford Coalgebra and Geometric Theorem Completion
    • Xu, R.1
  • 207
    • 0042647231 scopus 로고
    • Birkhäuser, Boston, Basel, Translated by Sosdsinsky, S
    • Yaglom, I.M. Felix Klein and Sophus Lie. Birkhäuser, Boston, Basel, 1988. Translated by Sosdsinsky, S.
    • (1988) Felix Klein and Sophus Lie
    • Yaglom, I.M.1
  • 208
    • 85013917341 scopus 로고
    • Application of Dual Number Quaternion Algebra to the Analysis of Spatial Mechanisms
    • Yang, A.T. and Freudenstein, F. Application of Dual Number Quaternion Algebra to the Analysis of Spatial Mechanisms. J. Appl. Mech. 31: 300-308, 1964.
    • (1964) J. Appl. Mech , vol.31 , pp. 300-308
    • Yang, A.T.1    Freudenstein, F.2
  • 210
    • 3242694180 scopus 로고    scopus 로고
    • Modeling and Visualization of 3D Polygonal Mesh Surfaces using Geometric Algebra
    • Zaharia, M.D. and Dorst, L. Modeling and Visualization of 3D Polygonal Mesh Surfaces using Geometric Algebra. Computers and Graphics 28(4): 519-526, 2004.
    • (2004) Computers and Graphics , vol.28 , Issue.4 , pp. 519-526
    • Zaharia, M.D.1    Dorst, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.