DifferentialGeometry

New symbolic tools for differential geometry, gravitation, and field theory. DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.


References in zbMATH (referenced in 26 articles )

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  1. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Symmetry classification of viscid flows on space curves (2021)
  2. Anderson, Ian; Torre, Charles: Spacetime groups (2020)
  3. Doubrov, Boris; Medvedev, Alexandr; The, Dennis: Homogeneous integrable Legendrian contact structures in dimension five (2020)
  4. Duyunova, A.; Lychagin, V.; Tychkov, S.: Symmetries and differential invariants for inviscid flows on a curve (2020)
  5. Hrdina, Jaroslav; Zalabová, Lenka: Local geometric control of a certain mechanism with the growth vector ((4,7)) (2020)
  6. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for spherical layer flows of inviscid fluids (2019)
  7. Mohammadi, Zahra; Reid, Gregory J.; Huang, Tracy Shih-lung: Introduction of the MapDE algorithm for determination of mappings relating differential equations (2019)
  8. Shpiz, G.; Kryukov, A.: Canonical representation of polynomial expressions with indices (2019)
  9. Tychkov, Sergey N.: Introduction to symbolic computations in differential geometry with Maple (2019)
  10. de Doná, J.; Tehseen, N.; Vassiliou, P. J.: Symmetry reduction, contact geometry, and partial feedback linearization (2018)
  11. Duyunova, A. A.; Lychagin, V. V.; Tychkov, S. N.: Differential invariants for spherical flows of inviscid fluid (2018)
  12. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for spherical layer flows of viscid fluids (2018)
  13. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for spherical flows of a viscid fluid (2018)
  14. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for plane flows of inviscid fluids (2018)
  15. Furutani, Kenro; Molina, Mauricio Godoy; Markina, Irina; Morimoto, Tohru; Vasil’ev, Alexander: Lie algebras attached to Clifford modules and simple graded Lie algebras (2018)
  16. Vassiliou, Peter J.: Cascade linearization of invariant control systems (2018)
  17. Duyunova, A.; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for plane flows of viscid fluids (2017)
  18. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for flows of viscid fluids (2017)
  19. Lisle, Ian G.; Huang, S.-L. Tracy: Algorithmic calculus for Lie determining systems (2017)
  20. Sagerschnig, Katja; Willse, Travis: The almost Einstein operator for ((2,3,5)) distributions. (2017)

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