2407.12660
A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks
Marcus S. Aichmayr, Stefan Müller, Georg Regensburger
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states (with citation to prior work) the equivalence sign(ker W) ⊆ sign(ker W̃) ⇔ for all I with det W_I ≠ 0 one has det W_I det W̃_I > 0 (or all < 0), which matches Proposition 2 in the PDF and is standard in this literature. By contrast, the model’s proof of (1) ⇒ (2) is sound, but its (2) ⇒ (1) step incorrectly treats the one-sided minors condition as implying equality of oriented matroids (and thus equality of sign sets), which requires a symmetric condition on zero minors that is not assumed. Hence the model over-claims and does not justify inclusion from (2) as stated.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper correctly states and leverages known oriented-matroid equivalences between sign-vector inclusion and signs of maximal minors, embedding them in a practical computational package with instructive examples. The core statements are accurate and appropriately cited. Minor clarifications would improve accessibility and self-containment.