solve

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full behavioral burden and delivers: determinism/reproducibility, fixed 6-decimal output (not switchable), hard limits (≤6 variables, 1–64 equations, ≥ variable count, ≤100KB), default domain ±1e6, honest truncated=true semantics (not proven exhaustive, may miss solutions in pathological cases), certification tiers (proven/likely/candidate), and error.type values. This is exemplary disclosure with no contradiction.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Every clause earns its place—there is no filler—and the text is front-loaded with the core purpose and determinism guarantee before moving to inputs and outputs. The only weakness is that it is one dense unbroken paragraph; section breaks or bullets would materially improve scannability for an agent.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

There is no output schema, so the description correctly carries the full return contract: resultType enum with meanings, solutions[] structure (values/tier/certified/text/internals), certified, recommended, truncated semantics, and error types. Minor gaps remain: fastMode's trade-offs and the semantics of budget/maxDepth in options are only hinted at via the schema example.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3; the description adds value beyond the schema by stating hard limits (variable/equation counts, equation-text size), the default domain of ±1e6, the constraint that equation count must be ≥ variable count, and the link between domain choice and truncation. The schema already documents formats and examples, and the description complements rather than repeats it.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description opens with a specific verb and resource — '求解实数方程组的确定性数值引擎' (deterministic numerical engine for solving real equation systems) — and explicitly contrasts itself with LLMs ('非大模型，无随机'), positioning it as a hallucination-free math backend for AI agents. It also names give_feedback as the sibling for feedback, so an agent can tell them apart without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Provides explicit '适用' (suitable for) and '不适用' (not suitable for) lists: verifiable real solutions with common transcendental functions vs. symbolic derivation, ODE initial value problems, and integer/hard constraints. It further routes feedback to give_feedback, advises narrowing domain or raising budget on truncation, and endorses safe caching.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.