Module diffgeom::tensors

Module containing definitions of tensors and operations on them.

Structs

ContravariantIndex	Type representing a contravariant (upper) tensor index.
CovariantIndex	Type representing a covariant (lower) tensor index.
Tensor	Struct representing a tensor.

Enums

IndexType

This enum serves to represent the type of a tensor. A tensor can have any number of indices, and each one can be either covariant (a lower index), or contravariant (an upper index). For example, a vector is a tensor with only one contravariant index.

Traits

Concat	Operator trait used for concatenating two variances.
Contract	An operator trait representing tensor contraction
InnerProduct	Trait representing the inner product of two tensors.
OtherIndex	Trait representing the other index type
TensorIndex	Trait identifying a type as representing a tensor index. It is implemented for CovariantIndex and ContravariantIndex.
Variance	Trait identifying a type as representing a tensor variance. It is implemented for CovariantIndex, ContravariantIndex and tuples (Index, Variance).

Type Definitions

Contracted	Helper type for contraction
Covector	A covector type (rank 1 covariant tensor)
InvTwoForm	A rank 2 doubly contravariant tensor
Joined	Helper type for variance concatenation.
Matrix	A matrix type (rank 2 contravariant-covariant tensor)
TwoForm	A bilinear form type (rank 2 doubly covariant tensor)
Vector	A vector type (rank 1 contravariant tensor)