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AlgebraX

Tensor Einsum

erivlis/algebrax

Tensor Einsum (`algebrax.tensor.einsum`)¶

algebrax.tensor.einsum executes generalized Einstein summation contractions over sparse dictionary tensors and AlgebraicTrie structures under arbitrary semirings.

Syntax & Semantics¶

import algebrax as ax

# Matrix multiplication: C_ik = sum_j A_ij * B_jk
C = ax.tensor.einsum('ij,jk->ik', A, B, semiring=ax.semiring.StandardSemiring())

# Trace: Tr(A) = sum_i A_ii
tr = ax.tensor.einsum('ii->', A)

# Hadamard product: C_ij = A_ij * B_ij
hadamard = ax.tensor.einsum('ij,ij->ij', A, B)

Schwarzschild Black Hole Spacetime — Spacetime metric tensor contraction.
Sparse Tensor Einsum — High-dimensional contractions across semirings.