For Maple 17, the DifferentialGeometry package contains over 40 new commands or commands with enhanced functionality or improved efficiency.
Updates to the DifferentialGeometry package:
DGsetup has a new keyword argument for declaring certain coordinates to be complex.
The new command DGconjugate calculates the complex conjugate of a vector, tensor or differential form, quaternion or octonion.
The new commands DGRe and DGIm calculate the real and imaginary parts of a vector, tensor, differential form, quaternion or octonion.
The new commands DGsolve, DGNullSpace and DGImageSpace provide useful utilities for solving equations whose unknowns are tensors or differential forms.
The new command `&algmult` computes non-commutative multiplication in general algebras.
A new geometric type, "multivector", has been created. This significantly improves computational efficiency when working with contravariant skew-symmetric tensors. The commands convert, Hook, RaiseLowerIndices, and LieDerivative have been extended to accept multi-vector arguments.
This is a new package for the study of differential systems.
The first release of this package contains 5 commands. These commands calculate the Cauchy characteristics, derived flags, first integrals, integral manifolds, and infinitesimal symmetries of Pfaffian differential systems.