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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive). The description adds real behavioral context beyond them: trailing-zero normalization, empty-list-zero convention, modulus zero rejection, per-call pricing, and an alternate HTTPS endpoint. Only missing detail is error behavior on oversized inputs.

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?

Dense and front-loaded, with core purpose and canonical output behavior first. The pricing and endpoint sentences are necessary context for this paid x402 tool, though insertion mid-paragraph slightly interrupts flow.

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, yet the description explains return shape (trailing zeros dropped, empty list for zero polynomial), which is exactly the missing output info. With annotations covering safety, an agent has enough to call this correctly.

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 description coverage is 0%, so the description carries the burden and does so well: it explains a/b are coefficient lists ordered lowest-degree-first with normalization rules, and that mod reduces each coefficient while rejecting zero. Direct mapping to parameter names is left implicit.

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 ('Add two integer polynomials') plus the representation convention (lowest degree first). Clear on its own, but does not differentiate from polynomial siblings like poly_mul, poly_eval, or poly_deriv.

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?

Implicitly tells the agent this is the addition tool, and 'zero is rejected' constrains the modulus. But there is no explicit when/when-not guidance or reference to the closely related poly_mul/poly_div siblings, leaving selection to inference.

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