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 12 articles )

Showing results 1 to 12 of 12.
Sorted by year (citations)

  1. de DonĂ¡, J.; Tehseen, N.; Vassiliou, P. J.: Symmetry reduction, contact geometry, and partial feedback linearization (2018)
  2. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for spherical layer flows of viscid fluids (2018)
  3. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for plane flows of inviscid fluids (2018)
  4. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for spherical flows of a viscid fluid (2018)
  5. Duyunova, A.; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for plane flows of viscid fluids (2017)
  6. Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey: Differential invariants for flows of viscid fluids (2017)
  7. Lisle, Ian G.; Huang, S.-L. Tracy: Algorithmic calculus for Lie determining systems (2017)
  8. Galaev, Anton: How to find the holonomy algebra of a Lorentzian manifold (2015)
  9. Anderson, I. M.; Torre, C. G.: New symbolic tools for differential geometry, gravitation, and field theory (2012)
  10. Poole, Douglas; Hereman, Willy: Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions (2011)
  11. Hereman, Willy; Adams, Paul J.; Eklund, Holly L.; Hickman, Mark S.; Herbst, Barend M.: Direct methods and symbolic software for conservation laws of nonlinear equations (2009)
  12. Hubert, Evelyne: Differential algebra for derivations with nontrivial commutation rules (2005)