cartan

ext_diff (form) — Function

The exterior derivative operator. It takes one argument, which should be a differential form.

init_cartan ([x_1, …, x_m]) — Function

Initializes some global variables for the package. The argument, a Maxima list, is an ordered list of coordinates. The coordinate list is stored as the value of the variable cartan_coords. The value of the variable cartan_basis is a list of the basis 1-forms. The dimension is stored as the value of the variable cartan_dim.

lie_diff (vector1, [vector2, form]) — Function

The Lie derivative operator. The first argument is a vector field. The second argument may be either a vector field or a differential form.

Function: |

The bar “|” is an infix operator which defines the contraction of a vector on a form. The vector should be given on the left.

Function: ~

The tilde “~” is an infix operator which denotes the exterior (wedge) product. The canonical ordering of the products is determined by the order in which the coordinates were specified. For example, if the coordinate list is specified as [x,y,z], then the two-form dy~dx simplifies to -dx~dy.