Updates to Physics in Maple 16
The Physics package of Maple 16 includes 17 new commands, extended its functionality in Vector and Tensor Analysis, General Relativity and Quantum Fields, and brings with it the largest number of developments since its introduction in Maple 11, underscoring Maple's goal of having a state-of-the-art environment for algebraic computations in Physics.
In addition, a vast number of changes were introduced towards making the computational experience as natural as possible, resembling the paper-and-pencil way of doing computations and with textbook-quality display of results.
Tensors in Special and General Relativity (Examples)
Maple's Physics introduces contravariant indices in a simple way: in your input, prefix contravariant indices with ~; in the output they are displayed as superscripts, without the ~.
In a tensorial expression, you can enter any pair of contracted indices as one covariant, the other contravariant, not being relevant which one is of which kind, so you can also enter both covariant or both contravariant and the system will automatically rewrite them as one covariant and the other contravariant.