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

Annotations already cover read-only, idempotent and non-destructive behavior, and the description adds substantial context beyond them: zero-polynomial representation as an empty list, modulus reduction semantics, rejection of a zero modulus, and paid access at $0.001 USDC per successful call via x402 on Solana. It stops short of stating the error/response shape for a rejected modulus.

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?

Five compact clauses, front-loaded with the operation and representation rules. The pricing/HTTPS sentence is long but carries real information an agent needs before calling a paid endpoint.

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, and the description never says what multiplication returns (a coefficient list of what length/ordering). Combined with the undisclosed string type of mod and the 12-item cap, an agent must open the schema 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?

With 0% schema description coverage the description must carry the load, and it does explain a/b ordering and what mod does. However, it never reveals that mod is supplied as a decimal *string* matching ^[0-9]{1,200}$ rather than a number, nor the maxItems=12 limit on a and b; the note about coefficients past 15 digits being decimal strings also sits oddly against the schema's integer items capped at 1e8.

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: "Multiply two integer polynomials." It also pins the representation convention (lowest degree first), which separates it cleanly from poly_add, poly_div and poly_eval in the sibling list.

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?

Usage is only implied by the operation itself; there is no statement of when to prefer this over poly_add/poly_eval or of prerequisites. The one alternative it does name is an access channel (the HTTPS endpoint), not a competing tool, so routing guidance is thin.

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