SageManifolds deals with " tensor fields " and not tensor components in a given vector frame or coordinate chart.
42.
Vector or tensor fields simply have more components, and independent creation and destruction operators must be introduced for each independent component.
43.
An extension of the tensor field idea incorporates an extra line bundle " L " on " M ".
44.
These constraints, along with the equilibrium equation ( or equation of motion for elastodynamics ) allow the calculation of the stress tensor field.
45.
While much of the notation may be applied with any tensors, operations relating to a differential structure are only applicable to tensor fields.
46.
Note that J's treatment also allows the representation of some tensor fields, as a and b may be functions instead of constants.
47.
This allows one to define the concept of "'tensor density "', a'twisted'type of tensor field.
48.
The notion of " G "-structures includes many other structures on manifolds, some of them being defined by tensor fields.
49.
Thus one obtains a system of partial differential equations involving the stress tensor field and the strain tensor field, as unknown functions to be determined.
50.
Thus one obtains a system of partial differential equations involving the stress tensor field and the strain tensor field, as unknown functions to be determined.
