The MapToBasis(V, c) calling sequence converts the Vector or vector field V to the coordinate system c.

If V is a Vector-valued procedure, it is interpreted as a vector field.

If c is not specified, the current default coordinate system is used as the new coordinate system.

If c is specified and V represents a vector field, the new coordinate system must be indexed with the names of the new coordinates.  Otherwise, an error is raised.  If V represents a Vector, no coordinate names are required.

If a coordinate system attribute is specified on V, V is interpreted in this coordinate system.

If a coordinate system attribute is not specified on V, V is interpreted as a Vector or vector field in the current default coordinate system.  If the default coordinate system is not compatible with the new coordinate system, an error is raised.