ComplementaryBasis(S, T)

Initialize a 5-dimensional manifold M with coordinates [x, y, z, u, v].

Example 1.

Example 2.

Note that a basis for S2 is [D_x, D_y] and a basis for T2 is [D_x, D_y, D_x + D_z, D_u].

Example 3.

In most applications the subspace spanned by the first argument S will be a subspace of the span of the second argument T.  However, the procedure works in the more general context described above.

Example 4.

The command ComplementaryBasis works with differential forms.

Example 5.

The command ComplementaryBasis works with tensors.

DifferentialGeometry, Tools, CanonicalBasis, DGbasis, DualBasis