wallCircuits -- distinct codim-2 wall circuits of a triangulation, with sign convention

A codim-2 wall of $T$ is the union of two adjacent maximal simplices, a $(d{+}1)$-element subset $c$ of column indices. The circuit supported on $c$ is the integer kernel relation $\sum_{i \in c} z_i A_i = 0$, restricted to its support (the indices $i$ with $z_i \ne 0$). When the circuit support is strictly smaller than $d{+}1$ -- which happens when one of the wall vertices has $z = 0$ -- the same circuit can appear in several different walls; these duplicates are removed so each entry of the returned list is a distinct circuit.

Each triple $\{inTri, notInTri, z\}$ records:

$\bullet$ inTri: the support indices with $z_i > 0$.

$\bullet$ notInTri: the support indices with $z_i < 0$.

$\bullet$ z: an integer kernel of length $\#(inTri \cup notInTri)$, indexed by position in sort(inTri | notInTri), signed so the facet inequality $$\sum_{i \in inTri \cup notInTri} z_i \, w_i \;\ge\; 0$$ holds for every $w$ that induces $T$.

For a balanced circuit (both signs present), inTri is exactly the half whose simplices $c \setminus \{v\}$ appear in $T$. For a totally cyclic circuit (e.g. when $0$ lies in the interior of $\mathrm{cone}(c)$, as in many complete simplicial fans), $z$ is one-sided: inTri is the full circuit support and notInTri is empty, yet the inequality still holds.