![]() Other than the tensor_type data type, the tensor package uses two other kinds of tables to keep track of related sets of quantities. It returns a value of true if its first argument satisfies the properties of a tensor_type object, and false otherwise. The tensor_type type is implemented as a procedure ( `tensor/tensor_type` ) with a Boolean return value. For tensors of rank 0 (that is, scalars, invariants), the index character field is an empty list (), and the components field is an algebraic type. Note that the size of the index character list must match the size of the components array (the rank of the object). Similarly, a negative one (-1) in the ith position in the index character list specifies that the ith index of the object is covariant.įor example, specifies that indices 1 and 4 are contravariant (written as superscripts) and indices 2 and 3 are covariant (written as subscripts). A positive one (1) in the ith position in the index character list specifies that the ith index of the object is contravariant. The index character is stored as a list of positive and negative ones (1 or -1). The components must be stored as an array of size equal to the rank of the object, with all index ranges beginning at one and ending at the dimension of the space (only "square" ranges are allowed). Specifically, a tensor_type is a table with two entries: a compts field, to store the components of the object, and an index_char field, which describes the covariant or contravariant nature of the indices of the object. ![]() ![]() The tensor package uses its own data type, called tensor_type, to represent objects which have possibly both covariant and contravariant indices. Some utilities to help manipulate tensors are also provided. The tensor package ( tensor ) contains commands that deal with tensors, their operations, and their use in General Relativity both in the natural basis and in a moving frame. Use the superseding packages DifferentialGeometry and Physics instead. Important: The tensor package has been deprecated.
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