tensorpow

tensorpow is a small Python library for working with norms and representations of tensor powers. Base matrices can be either 2×2 (using SL(2) representation data) or 3×3 (using SU(3) representation data). The tensor power itself may be any positive integer – the library uses precomputed representation data indexed by that power. A class-based interface computes block decompositions via precomputed SL(2)/SU(3) data and evaluates quantities such as Schatten‑p norms without building the full Kronecker power.

Installation

Requires Python 3.11–3.13.

pip install tensorpow

For development:

pip install -e ".[test]"

Dependencies (numpy, scipy, sympy) are installed automatically.

Data limits

Precomputed SU(3) symmetric representation data is available for degrees 1 through 30. Some large 3×3 tensor powers may require higher degrees; those cases raise a clear error.

Precomputed SL(2) data (sl2reps.txt) supports 2×2 tensor powers n ≤ 79.

Quick start

from tensorpow import TensorPowerCalculator
import numpy as np

# Example 1: 3×3 matrices (SU(3) case)
A = np.eye(3)
B = 2 * np.eye(3)
calc = TensorPowerCalculator()           # no args
# compute Schatten‑2 norm of A⊗A - 1/2 * B⊗B (tensorpower=2) 
norm_3x3 = calc.schatten_p_norm_weighted([A, B], n=2, p=2, coeffs=[1.0, -0.5])
print(f"3×3 result: {norm_3x3}")

# Example 2: 2×2 matrices (SL(2) case)
C = np.eye(2)
D = 2 * np.eye(2)
# compute Schatten‑2 norm of C⊗C - 1/2 * D⊗D (tensorpower=2)
norm_2x2 = calc.schatten_p_norm_weighted([C, D], n=2, p=2, coeffs=[1.0, -0.5])
print(f"2×2 result: {norm_2x2}")

# Example 3: block decomposition of a single 2×2 matrix (tensor power n=5)
M = np.array([[1.0, 0.5], [0.0, 1.0]])
blocks = calc.block_decomposition(M, n=5)
# each entry is (multiplicity, block_matrix)
for mult, block in blocks:
    print(mult, block.shape)

TensorPowerCalculator exposes two public methods:

• block_decomposition — irrep blocks of one matrix's n-th tensor power
• schatten_p_norm_weighted — weighted Schatten-p norm of a linear combination of tensor powers

Both 2×2 and 3×3 matrices are supported; the library dispatches to SL(2) or SU(3) representation data based on matrix dimension.

For 3×3 matrices, block_decomposition may return negative multiplicities (a virtual decomposition). Singular values of the full tensor power are not listed block-by-block; use weighted sums of singular-value powers over blocks (as schatten_p_norm_weighted does internally).

Precomputed data

• 2×2 (SL(2)): downloaded from Zenodo (sl2reps.txt) or generated locally. Supports tensor power n ≤ 79 by default (representations Sym^k for k = 0..79). You can generate larger dimensions:

  python -m tensorpow.sl2_sym_runner --max-k 100
  

• 3×3 (SU(3)): downloaded from Zenodo (piM_sym_<deg>_*.npz) for the degrees required by the Pieri decomposition at your chosen n. If you need dimensions beyond degree 30, you can generate them locally:

  python -m tensorpow.su3_sym_runner --min-k 31 --max-k 35
  

All downloaded and generated files are stored securely in your OS-specific user data directory via platformdirs (e.g. ~/.local/share/tensorpow on Linux), ensuring your custom generated data is never lost during package updates.

Building on the decomposition

block_decomposition exposes the irrep blocks of a single matrix's n-th tensor power. Methods such as schatten_p_norm_weighted combine block singular values without forming the full Kronecker product; you can use the same blocks to define other functionals (other norms, traces, eigenvalue statistics, and so on). Additional calculator methods may be added in future releases; they will build on this decomposition.

Package structure

• tensorpow/core.py – main implementation and TensorPowerCalculator, including SL(2) (2×2) and SU(3) (3×3) block decomposition logic
• tensorpow/*_runner.py – generator tools to calculate arbitrary dimension representations locally
• tensorpow/file_handler.py – loaders for downloaded NPZ tensors (compressed SU(3) representation data; not part of the runtime API)
• tensorpow/sl2_loader.py – loads downloaded sl2reps.txt at runtime

Testing

Run pytest tests to exercise the small test suite.

License

GNU GPLv3 or later (see LICENSE).