Foundations of Computational Mathematics (FoCM)
http://www.focm.net

Centre for Experimental and Constructive Mathematics
http://www.cecm.sfu.ca/

Ontario Research Centre for Computational Algebra
http://www.orcca.on.ca/

The Formal Geometry and Mathematical Physics group
http://math.usu.edu/~fg_mp/

OpenXM software project
http://www.openxm.org, http://www.math.kobe-u.ac.jp/OpenXM/index.html

Nonlinear Differential Equations Group
http://www.maths.gla.ac.uk/research/groups/nldes/nldes.html

Software links

rif
The Rif package can be used for the simplification of overdetermined ODE and PDE systems. It is the successor of the Standard Form project, and has the following additional features:
1.Computation with nonlinear systems.
2.Advanced case splitting capablilities for discovery of particular solution branches with desired properties.
3.A visualization tool for examination of the binary tree that results from multiple cases.
4.Algorithms for working with formal power series solutions of the system.
Further information: http://www.cecm.sfu.ca/~wittkopf/rif.html

Indiff
Description: A MAPLE package for overdetermined differential systems with Lie symmetry.
Author: Elizabeth Mansfield
Further information: http://www.ukc.ac.uk/ims/maths/people/E.L.Mansfield.html
Online demo: Coming soon...

diffalg
Description: The diffalg package is a collection of routines to handle systems of polynomial differential equations and inequations. The functionalities include differential elimination, expansion of the solutions into formal power series and analysis of singular solutions. The underlying theory and terminology belongs to differential algebra.
Author: François Boulier , Evelyne Hubert
Further information: http://www-sop.inria.fr/cafe/Evelyne.Hubert/webdiffalg/

diffgrob2
Description: A MAPLE package to simplify overdetermined systems of nonlinear differential equations of polynomial type
Author: Elizabeth Mansfield
Further information: http://www.ukc.ac.uk/ims/maths/people/E.L.Mansfield.html
Online demo: http://centaur.maths.qmw.ac.uk/CATHODE/DiffGrob2_demo.html

Integrability Package
Description: A package for the computation of invariants and symmetries of evolution equations and lattices.
Author: Unal Goktas, Willy Hereman
Further information: http://www.mathsource.com/cgi-bin/msitem?0208-932

LieSym
Description: Lie-point symmetry computations of systems of differential equations
Author: Willy Hereman
Further information: http://www.mines.edu/fs_home/whereman/liesym.html

DimSym
Description: Symmetry Determination and Linear Differential Equation Package
Author: James Sherring
Further information: http://www.latrobe.edu.au/www/mathstats/Maths/Dimsym/

LIE and BIGLIE
Description: Programs to find Lie symmetries of differential equations
Author: Alan Head
Further information: http://www.cmst.csiro.au/LIE/LIE.htm

DESOLV
Description: A Maple program for the determination of Lie Symmetries of differential equations.
Author: J. Carminati, Khai Vu
Further information: http://www.cm.deakin.edu.au/research/jcarm/desolv.htm

LiePDE
Description: Computation of point, contact and higher order symmetries of single and systems of differential equations
Author: Thomas Wolf
Further information: ftp://lie.math.brocku.ca/twolf/crack

ApplySym
Description: For given symmetries it computes symmetry and similarity variables and transforms differential equations to these new variables
Author: Thomas Wolf
Further information: ftp://lie.math.brocku.ca/twolf/crack

CONLAW
Description:The CONLAW package attempts to compute first integrals for single ordinary differential equations (ODEs) or systems of ODEs, and conservation laws for single partial differential equations (PDEs) or systems of PDEs.
Author: Thomas Wolf
Further information: ftp://lie.maths.qmw.ac.uk/pub/compalg/conlaw/
ftp://lie.math.brocku.ca/twolf/crack
Online demo: http://cathode.maths.qmw.ac.uk/CATHODE/ConLaw_demo.html

CRACK
Description: The CRACK package attempts to solve an overdetermined system of algebraic and ordinary or partial differential equations (ODEs/PDEs) with at most polynomial nonlinearities.
Author: Thomas Wolf, Andreas Brand (Jena)
Further information: ftp://lie.maths.qmw.ac.uk/pub/compalg/crack/
ftp://lie.math.brocku.ca/twolf/crack
Online demo: http://cathode.maths.qmw.ac.uk/CATHODE/CRACK_demo.html

VESSIOT
Designed to assist researchers in geometric methods in differential equations.The software package Vessiot contains commands for all the basic operations of calculus on jetspaces.
Further information: http://math.usu.edu/~fg_mp/Pages/SymbolicsPage/Symbolics.html

Vecalc
Description: For doing algebraic and differential calculations with symbolic vector functions (not matrices) in curvilinear coordinates
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm

Grassmann
Description: For symbolic computing with anti-commutative and non-commutative variables
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm

PDEtools
Description: For the analytical solving of Partial Differential Equations
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm

ODEtools
Description: For solving Ordinary Differential Equations using classification, integrating factor and symmetry methods.
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm

partials
Description: For evaluating partial and functional derivatives of (and with respect to) tensor functions
Author: Edgardo Cheb-Terrab
Further information: http://lie.uwaterloo.ca/ecterrab/software.htm