tensorpow 0.1.0

Norms and block decompositions for 2x2 and 3x3 tensor powers.

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, pulp, scipy, sympy) are installed automatically.

Data limits

Precomputed SU(3) symmetric representation data is bundled for degrees 1 through 26. 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}")

Only the schatten_p_norm_weighted method is currently implemented. Both 2×2 and 3×3 matrices are fully supported; the library automatically dispatches to the appropriate representation system (SL(2) or SU(3)) based on matrix dimension.

Precomputed data

• 2×2 (SL(2)): requires data/sl2reps.txt (bundled in the public tensorpow package). Supports tensor power n ≤ 79 (representations Sym^k for k = 0..79). Regenerate with:

  python -m tensorprod.sl2_sym_runner --max-k 79
  

• 3×3 (SU(3)): requires data/piM_sym_<deg>_*.npz files for the degrees used by the Pieri decomposition at your chosen n. Additional routines (e.g. other norms or eigenvalue statistics) can be added to TensorPowerCalculator and will automatically reuse the underlying block decomposition.

Package structure

• tensorpow/core.py – main implementation and TensorPowerCalculator, includes both SL(2) (2×2) and SU(3) (3×3) block decomposition logic
• tensorpow/file_handler.py – loaders for bundled _data/ NPZ tensors compressed SU(3) representation data data (not part of the runtime API)
• tensorpow/sl2_loader.py – loads data/sl2reps.txt at runtime
• tensorpow/sl2_sym_runner.py – generator for data/sl2reps.txt (dev only)

Testing

Run pytest tests to exercise the small test suite.

License

GNU GPLv3 or later (see LICENSE).