Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

PathIndexContractions

PathIndexContractions [path,indices]
	returns the sequence of index sets contracted at each step of path , given the per-tensor index lists indices .

PathIndexContractions [path,indices,contractions]
	returns the symbolic index sums at each step, mapping the integer positions in indices back to the labels in contractions .

PathIndexContractions [path,data]
	takes an association with keys "Indices" and "Contractions" , such as tn["Data"] .

Details and Options

▪

At each path step

{i,j}

, the function computes the intersection of

indices〚i〛

and

indices〚j〛

— the indices that get contracted away at that step — and replaces the two tensor entries with the union of their remaining indices.

▪

The result is a list of per-step contraction sets. Each entry is the set of indices summed at that step. Outer-product steps (no shared indices) produce an empty contraction and are removed from the output, so the result length is at most

Length

[path]

▪

In the 2-argument form, contractions are tracked by integer position within each tensor's index list. In the 3-argument form, the additional

contractions

argument supplies symbolic labels (e.g. bond names) that the integer positions are mapped back to, which is useful for tracing each contraction to a user-specified index name.

▪

The association form accepts any value with keys

"Indices"

and

"Contractions"

, and returns the catenated symbolic contractions. A