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

With no annotations, the description carries the full load and does well: it discloses determinism/reproducibility, the Krawczyk certification with strict error boxes, exclusion of complex roots, and the honorPaid licensing declaration. It omits failure behavior for malformed or non-polynomial input and does not explain that honorPaid is not present in the declared input schema, which is a notable gap.

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?

Front-loaded with the core purpose and scope, then the coefficient-ordering convention and the licensing note. Four sentences with little waste, though the honorPaid sentence is longer than the information warrants.

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?

No output schema exists, so the description must cover returns; it explains the certificate and error box but not the shape of the result (list of roots? objects with bounds?). It also never reconciles the honorPaid parameter with a schema that lacks it, leaving the agent unsure how to satisfy the licensing requirement.

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% and the schema already documents coefficients ordering and tolerance defaults, so the description's repetition of the [1,-2,-5,6] example adds no new meaning. The only novel parameter information is honorPaid, which is not in the schema at all, creating ambiguity rather than usable semantics.

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?

States a specific verb and resource – returning all real roots of a polynomial – plus the scope qualifier that complex roots are excluded and roots are certified by Krawczyk with a strict error box. It does not explicitly compare itself to siblings like solve or verify, so an agent still has to infer the boundary between this and a general solver.

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?

It advises use 'instead of letting a general language model estimate roots', which implies when to reach for it, but gives no when-not guidance and never names the sibling solve/verify tools it should be preferred over or combined with. Requirements and prerequisites for input are not stated.

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