Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
TensorNetworks
A TensorNetwork bundles a list of tensors with their hyperedge index lists and defers execution to a contraction path (usually optimized in some ways). The paclet covers explicit and randomized construction of common topologies (MPS, MPO, PEPS, TTN, MERA), Rust-backed greedy and dynamic-programming path optimizers, five interchangeable binary-contraction engines, and chain-specific algorithms for Matrix Product State canonical forms, Schmidt values, entanglement entropy and bond truncation. Two subpackages extend the core: an IndexArray layer adding named indices with explicit covariant and contravariant variance (plus a curated catalog of relativity metrics), and a Symmetry layer providing Young tableaux and the hook-length formula for projecting tensors onto symmetric-group irreducible representations.
— atomic object bundling tensors with hyperedge index lists.
— random network on a given graph or a named topology (MPS, TT, MPO, PEPS, TTN, MERA).
— contracts tensors by Einstein summation, given index lists or an einsum string.
— joins tensors over shared indices, broadcasting along non-shared dimensions.
— yields True for a valid TensorNetwork object.
— returns an Association of vertices, tensors, indices, dimensions, contractions and free indices.
— returns the hyperedges with internal indices replaced by canonical contracted-index labels.
— yields True if every index of the network appears in at most two tensors.
— returns the number of tensors in the network.
— returns the uncontracted (open) indices of the network.
— returns an Association mapping each index to its dimension.
— returns the index specifications for each tensor vertex.
— returns the list of tensors stored in the network.
— converts a hyper-edge network to a pairwise binary one by inserting spider tensors.
— converts the tensors of a network to SparseArray.
— converts a network into an annotated directed graph representation.
— appends a new tensor to the network with specified indices.
— removes the k-th tensor from the network.
— renames indices in the network according to rules.
— inserts cup/cap pairs to make a cyclic graph TN acyclic.
— returns a graph showing the index connectivity of the network.
— dynamic-programming optimum (Method "size", "flops", "max", "write", "combo", "limit").
— fast greedy heuristic with optional temperature, neighbor budget, and seed.
— contracts the network to a single tensor along a given or computed path.
— returns a symbolic Inactive contraction expression for the network and path.
— activates Inactive[TensorProduct], Inactive[TensorContract], Inactive[Transpose] in an expression.
$TensorNetworkContractionMethods
— returns a canonical (normalized) form of a contraction path.
— returns a Tree representing the contraction hierarchy of a network.
— returns the indices contracted at each step of a path.
— yields True for a list of integer pairs encoding a contraction path.
— yields True for a path already in canonical form.
— yields True for a tree-structured contraction path.
— converts a tree-structured contraction path to a linear pairwise path.
— converts a linear pairwise contraction path to a tree-structured path.
— transforms an MPS into left, right, or mixed-canonical form, with optional bond truncation.
— computes the von Neumann entanglement entropy across a bond.
— yields True if an MPS is in the specified canonical form.
— returns an MPS rescaled to unit norm.
— returns the normalized Schmidt coefficients at a specified bond.
— compresses an MPS by truncating bond dimensions to a maximum.
— yields True for a valid tensor-network graph (annotated directed graph).
— returns vertices, tensors, indices, dimensions, contractions of a graph TN.
— converts a tensor network into a Wolfram Neural NetGraph for ML pipelines.
— binds concrete tensors into the boundary vertices of a tensor-network graph.
Named Indices and Metrics
— catalog of metrics (Minkowski, Schwarzschild, Kerr, KerrNewman, FLRW, …) and constructor from a matrix.
— yields True for a valid MetricTensor.
Tensor Symmetries
— Young tableau as a list of rows specifying a tensor-index symmetry class.
— yields True for a valid Young tableau.
— symmetrizes over rows then antisymmetrizes over columns of a tableau.
— yields True for a valid integer partition (non-increasing positive integers).
— returns the conjugate (transpose) of an integer partition.
— returns the shape (row lengths) of a Young tableau.
— returns the total number of boxes in a Young tableau.
— returns the inner row list of a Young tableau (atomic-object accessor).
— returns the column slot lists of a Young tableau (handles ragged shapes).
— hook length at a single cell of a Young tableau.
— all hook lengths for cells of a Young diagram, matching the tableau shape.
— 1/(product of hook lengths) for a partition, via the Frobenius determinant formula.
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