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

Annotations already carry the safety profile (readOnly, idempotent, openWorld, non-destructive), so the description focuses on things annotations cannot express: the result is a reduced fraction, and the call is paid at $0.001 USDC per successful call via x402 on Solana, with an equivalent HTTPS POST endpoint. The pricing and payment model are material operational context not derivable from structured fields.

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?

Purpose is front-loaded, followed immediately by concrete examples, then domain limits, then pricing and endpoint. Every sentence carries distinct information with no filler.

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?

With no output schema, the description correctly fills that gap by specifying the reduced-fraction return type and illustrating it. It omits error behavior for out-of-range inputs and what payment failure looks like, which are minor gaps for an idempotent pure-math call.

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 must compensate; it identifies n as the polynomial index (0-32) and x as the integer evaluation point (-1000 to 1000), effectively restating the schema bounds while conveying the parameter roles through P(n, x) notation. It adds modest meaning but nothing about integer-only behavior beyond the schema types.

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/resource pairing: computes the Legendre polynomial P(n, x) and returns it as a reduced fraction, with two worked examples (P(n,1)=1, P(2,2)=11/2) that pin down the exact output form. It does not explicitly distance itself from the nearby legendre_symbol sibling, leaving the distinction to domain knowledge.

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?

The valid domain (n 0-32, x -1000 to 1000) implies when the call is appropriate, and the worked examples show expected usage. There is no explicit when-to-use/when-not-to-use guidance or reference to an alternative for related Legendre computations.

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