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Differential Geometry

 

For Maple 17, the DifferentialGeometry package contains over 40 new commands or commands with enhanced functionality or improved efficiency.

 

Updates to the DifferentialGeometry package:

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DGsetup has a new keyword argument for declaring certain coordinates to be complex.

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The new command DGconjugate calculates the complex conjugate of a vector, tensor or differential form, quaternion or octonion.

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The new commands DGRe and DGIm calculate the real and imaginary parts of a vector, tensor, differential form, quaternion or octonion.

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The new commands DGsolve, DGNullSpace and DGImageSpace provide useful utilities for solving equations whose unknowns are tensors or differential forms.

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The new command `&algmult` computes non-commutative multiplication in general algebras.

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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.

 

ExteriorDifferentialSystems

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This is a new package for the study of differential systems.

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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.

 

Library

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Over 100 new metrics have been added to the database of solutions to the Einstein equations.

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A command line version of the MetricSearch maplet is now available.

 

LieAlgebras

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