Graphical representations of tensors

[gh-honglizhaobob]

As outlined in Meta Ticket #31991, a tensor can admit different types of decompositions / tensor networks. We propose to add visualizations to the tensors (depending on decomposition used), possibly by implementing the __repr__ method.

In the diagrams of a tensor network, we may represent a tensor as a node, and the indices in different dimensions as edges. E.g. an order-3 tensor T(j_1,j_2,j_3 ) would look like a node with 3 edges. And connecting two edges from two tensors will denote tensor contractions. In this way, one may visualize the various decompositions of a tensor more intuitively via a tensor network / graph, along with additional information (such as tensor ranks).

• common tensor softwares (​https://tensornetwork.org/software/)
• graphical explanation (​https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams)

[egourgoulhon]

This would be very nice. I'd love to see Penrose graphical notation for tensors in Sage!