I.2.4 Transformation of vector and tensor components

The “CoordSys” class defines three methods devoted to the transformation of a vector or tensor components from one coordinate system to another. These methods are similar to the methods used to transform point coordinates in section I.2.3 but with the following differences:

• One modifies the components of a vector or of a tensor.
• A vector is defined as an Array of three real values. A tensor is defined as an Array of three Arrays of three real values.
• If a vector argument is given, the method returns a vector. If a tensor argument is given, the method returns a tensor.
• For each of the methods given here, the coordinates of the point at which the vector or tensor argument is defined, are also given as argument. This means that the methods have one additional argument compared to the corresponding methods of section I.2.3.3. The position of the point matters when curvilinear coordinate systems are involved in the transformation.