UT3Tangent.is_gauged

t3toolbox.uniform_manifold.UT3Tangent.is_gauged(atol=1e-09)

def is_gauged(self, atol: float = 1e-9) -> NDArray:  # bool array, shape = variation stack K+C (scalar unstacked)

True (per stack element) if the variations are gauged w.r.t. the frame.

Gauge conditions (needed for the manifold Hilbert-Schmidt inner product / norm to equal the coordinate ones; not enforced at construction): U_i^T dU_i = 0 (all i) and (P_i^L)^T dG_i^L = 0 (i = 0..d-2) – conditions (48)-(49), Appendix A.3 of Alger et al. (2026). Per-stack-element bool array (reduce with .all() for a single verdict).

Parameters:

atol (float)

Return type:

NDArray