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3 years ago Description changed:
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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).
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+- common tensor softwares (https://tensornetwork.org/software/)
+- graphical explanation (https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams)
egourgoulhon
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).
CC: @mkoeppe @egourgoulhon @dimpase
Component: graphics
Issue created by migration from https://trac.sagemath.org/ticket/32034