Lingshu Solver

The four math tools (solve, poly_roots, geometry, verify) have largely distinct roles, but poly_roots is essentially a special case of solve, and verify overlaps with solve's built-in trust/certification block, creating some boundary confusion. give_feedback and pay are clearly separate utility tools. Descriptions help disambiguate but a couple of overlaps remain.

There is a mixed convention: verbs like solve, verify, pay, and give_feedback sit alongside nouns like geometry and poly_roots. All are snake_case/lowercase so nothing is chaotic, but there is no predictable verb_noun pattern across the set.

Six tools is well-scoped for a deterministic math solver: four core computational tools (solve, poly_roots, geometry, verify) plus two auxiliary tools (give_feedback, pay). No tool feels redundant or gratuitous at the count level.

Coverage of the deterministic-math domain is strong: equation systems, certified polynomial roots, extensive geometry ops, and an answer verifier form a coherent workflow. Some gaps remain (complex roots, symbolic derivation, ODEs, integer constraints are explicitly excluded), but these are stated limitations rather than dead ends.