Example 1.
First initialize a 4-dimensional manifold M with coordinates [x, y, z, w].
>
|
|
Show that the vector subspaces spanned by the lists of vectors S1 and S2 are the same.
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
Show that the subspaces of differential forms spanned by the lists of 2-forms S3 and S4 are not the same.
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
| (6) |
Example 2.
First initialize manifolds M and N with coordinates [x, y] and [u, v].
>
|
|
Show that the transformations Phi1 and Phi2 are the same.
>
|
|
| (7) |
>
|
|
| (8) |
>
|
|
| (9) |
Show that the transformations Phi3 and Phi4 are not the same without assuming that x > 0.
>
|
|
| (10) |
>
|
|
| (11) |
>
|
|
| (12) |
>
|
|
| (13) |
Example 3.
Define two Lie algebras data structures. Check that they are equal.
>
|
|
| (14) |
>
|
|
| (15) |
>
|
|
| (16) |
>
|
|
| (17) |
Example 4.
Define two representations of a Lie algebra and test for equality. First define the Lie algebra.
>
|
|
| (18) |
>
|
|
| (19) |
Define the representation space V.
>
|
|
| (20) |
>
|
|
| (21) |
>
|
|
| (22) |
Make a change of basis in the representation space.
>
|
|
| (23) |
The representations rho1 and rho2 are equivalent but they are not equal.
>
|
|
| (24) |
A1 >
|
|