Abstract
In this survey paper we give the basic properties of Grassmann algebras, present a generalised theory of area from a Grassmann algebra perspective, present a version for Grassmann algebras of the Buchberger algorithm, and give examples of computation and deduction in Grassmann geometry.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Apel, J., A relationship between Gröbner bases of ideals and vector modules of G-algebras, Contemporary Mathematics 131 (1992), 195–204.
Buchberger, B., Gröbner bases: An algorithmic method in polynomial ideal theory, in Multidimensional Systems Theory, ed. Bose, N. K., Reidel, 1985, 184–232.
Chou, S., Proving elementary geometry theorems using Wu's algorithm, in Automated Theorem Proving: After 25 Years, ed. Bledsoe, W. W., and Loveland, D. W., Am. Math. Soc., 1984, 243–286.
Chou, S., Mechanical Geometry Theorem Proving, Reidel, 1988.
Chou, S., Gao, X., and Zhang, J., Automated geometry theorem proving using vector calculation, in Proc. ISSAC (Kiev, 1993), 284–291.
Chou, S., Gao, X., and Zhang, J., Automated production of traditional proofs for constructive geometry theorems, in Proc. 8th IEEE Symbolic Logic in Computer Science (1993), 48–56.
Chou, S., Gao, X., and Zhang, J., Automated production of traditional proofs in solid geometry, J. Ant. Reas. 14, 257–291.
Coxeter, H. S. M., and Greitzer, G., Geometry Revisited, Math. Ass. Am., 1967.
Doubilet, P., Rota, G., and Stein, J., On the foundations of combinatorial theory IX: Combinatorial methods in invariant theory, Studies in Applied Math. 57 (1974), 185–216.
Fearnley-Sander, D., Hermann Grassmann and the creation of linear algebra, Am. Math. Monthly 86 (1979), 809–817.
Fearnley-Sander, D., Affine geometry and exterior algebra, Houston J. Math. 6 (1980), 53–58.
Fearnley-Sander, D., Hermann Grassmann and the prehistory of universal algebra, Am. Math. Monthly 89 (1982), 161–166.
Fearnley-Sander, D., The Idea of a Diagram, in Resolution of Equations in Algebraic Structures, ed. Ait-Kaçi, H., and Nivat, M., Academic Press 1989, 127–150.
Feynman, R. P., Leighton, R. B., and Sands, M., Lectures on Physics, Addison-Wesley, 1963.
Grassmann, H. G., Gesammelte Mathematische and Physikalische Werke, ed. Engel, F., 3 vols. in 6 parts, Leipzig, 1894–1911.
Hestenes, D., New Foundations for Classical Mechanics, Kluwer, 1986.
Hestenes, D., and Ziegler, R., Projective geometry with Clifford algebra, Acta. Appl. Math. 23 (1991).
Hong, H., Wang, D., and Winkler, F. (eds.), Algebraic approaches to geometric reasoning, Ann. Math. and AI 13 (1, 2) (1995).
Hungerford, T. W., Algebra, Holt, Rinehart and Winston, 1974.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fearnley-Sander, D., Stokes, T. (1998). Area in Grassmann geometry. In: Wang, D. (eds) Automated Deduction in Geometry. ADG 1996. Lecture Notes in Computer Science, vol 1360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022724
Download citation
DOI: https://doi.org/10.1007/BFb0022724
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64297-8
Online ISBN: 978-3-540-69717-6
eBook Packages: Springer Book Archive