Tensor Operations¶

The pytanga.tensor submodule provides a tensor layer for working with multi-dimensional arrays of multivector components. MVTensor is a plain N‑D tensor where each axis carries a BladeMask (or None for batch axes). MVLabeledTensor wraps an MVTensor with per‑axis label strings, enabling label‑driven arithmetic — multiplication infers Einsum‑style contractions from shared labels, addition broadcasts over non‑matching labels, and arrow syntax ("ij->ji", "->nij") reorders axes. The product_tensor function builds the 3‑D tensor encoding a GA product from blade masks.

from pytanga.tensor import MVTensor, MVLabeledTensor

Reference¶

Topic	Guide
`MVTensor` — slicing, factories, scalar ops, NumPy interop	MVTensor
`MVLabeledTensor` — labels, `*` contraction, `+`/`-` broadcast, `/` division, `->` transpose	Labeled Tensors
`iter_labels` — iterating over a label for per‑element computation	Label Iterator
`product_tensor()` — building the 3‑D product tensor from blade masks	Product Tensor

Quick start¶

from pytanga import Algebra, BladeMask
from pytanga.basis import BasisE3
from pytanga.tensor import MVTensor
from pytanga.tensor.product import product_tensor

alg = BasisE3()
mask = BladeMask.full(alg)       # 8 blades

# A rank-1 tensor holding one multivector
A = MVTensor.zeros([mask])

# A product tensor O_{kij} for the geometric product
O = product_tensor(mask, mask)  # shape 8×8×8

# Label the axes and perform a label‑driven GP
C = (O["kij"] * A["i"] * A["j"])["->k"]