• SYMMGRP

  • Referenced in 121 articles [sw01066]
  • Macsyma program for the calculation of Lie point symmetries of large systems of differential equations ... works only under Macsyma, the commercial computer algebra system. The 1991 version of symmgrp.max (with...
  • MABSys

  • Referenced in 4 articles [sw13398]
  • systems using scaling type Lie point symmetries with linear algebra We present two new algorithms ... based on Lie symmetries that respectively allow to semi-rectify algebraic systems and reduce...
  • FracSym

  • Referenced in 29 articles [sw16769]
  • algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs ... USATU 9, No. 21, 125–135 (2007); “Symmetry properties of fractional diffusion equations”, Phys ... here to allow for the determination of symmetries for FDEs with n independent variables ... arbitrary functions, which may extend the symmetry algebras, are also determined. For each...
  • DESOLVII

  • Referenced in 23 articles [sw06914]
  • describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade ... allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary...
  • ObservabilityTest

  • Referenced in 20 articles [sw36921]
  • algebraic observability problem which is concerned with the existence of a non trivial Lie subalgebra ... symmetries of the model letting the inputs and the outputs invariant. We present a probabilistic...
  • ODEtools

  • Referenced in 12 articles [sw09257]
  • order ODEs using symmetry methods. A Maple V R.3/4 computer algebra package, ODEtools ... order ordinary differential equations (ODEs) using Lie group symmetry methods is presented...
  • DifferentialGeometry

  • Referenced in 30 articles [sw07593]
  • geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces ... recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development ... Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field...
  • xTensor

  • Referenced in 33 articles [sw04984]
  • xTensor: Fast abstract tensor computer algebra. xTensor extends Mathematica capabilities in abstract tensor calculus, specially ... Relativity. It works with tensors with arbitrary symmetries under permutations of indices, defined on several ... products of them. It computes covariant derivatives, Lie derivatives and parametric derivatives. It allows...
  • cwsLieSymTools

  • Referenced in 1 article [sw39655]
  • automorphisms of lower-dimensional non-Abelian Lie algebras. The first algorithm is a brute-force ... application of this package to symmetry Lie algebras of differential equations, we also provide...
  • cwsAutoClass

  • Referenced in 1 article [sw39656]
  • automorphisms of lower-dimensional non-Abelian Lie algebras. The first algorithm is a brute-force ... application of this package to symmetry Lie algebras of differential equations, we also provide...
  • DETools

  • Referenced in 4 articles [sw00198]
  • fairly general package for Lie symmetry analysis and an algebraic-geometric completion package for overdetermined...
  • MathLie

  • Referenced in 10 articles [sw00555]
  • program for symmetry analysis. We discuss the application of the computer algebra program MathLie ... connection with Lie’s theory of point transformations. The essential points of Lie’s transformation...
  • BIGLIE

  • Referenced in 5 articles [sw09207]
  • group, or rather the Lie algebra, of differential equations, ordinary or partial, single or simultaneous ... have seen the books ”Applications of Lie Groups to Differential Equations” by P. J. Olver ... examples in Chapters 2 and 3 ) or ”Symmetries and Differential Equations” by G. W. Blumen ... article ”Symmetries of Differential Equations: from Sophus Lie to Computer Algebra” by F. Schwarz, SIAM...
  • Exterior

  • Referenced in 3 articles [sw22625]
  • exterior algebras. In particular, it allows the user to compute Lie symmetries of systems...
  • Affine

  • Referenced in 5 articles [sw08572]
  • theory of nite-dimensional and ane Lie algebras and describe implemented algorithms. The algorithms ... properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules ... popular computer algebra system Mathematica and works with nite-dimensional and ane Lie algebras...
  • LieSymm

  • Referenced in 4 articles [sw12188]
  • optics. A Mathematica ® package for finding Lie symmetries of partial differential equations is presented ... package is applied to perform a full Lie group analysis of basic models of nonlinear ... obtained. Comparisons with earlier published computer algebra implementations of the Lie group method are discussed...
  • Affine.m

  • Referenced in 3 articles [sw10836]
  • theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms ... properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules ... popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras...
  • symmetry

  • Referenced in 3 articles [sw14839]
  • Symmetry package for maple. This is a Maple package which can be used ... knowledge of finite groups and compact Lie groups; algebraic groups; Derksen’s algorithm for computation...
  • LIESUPER

  • Referenced in 2 articles [sw15674]
  • package for symbolic computations in (free) Lie (super)algebras. For this purpose we will introduce ... satisfies the bilinearity and the (graded) skew-symmetry of the liebracket. Moreover, we will implement...