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 goes beyond them by disclosing the output domain (-1, 0, or 1), input validation behavior for invalid n, and the pricing model ($0.001 USDC per successful call via x402 on Solana), plus an alternative HTTPS endpoint. That is meaningful extra context an agent needs before paying for a call.

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 definition, then constraints, then the return domain, then cost and alternate endpoint. Every sentence carries operational information and nothing is padded.

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?

For a 2-parameter, no-output-schema tool with full annotation coverage, the description supplies the return values, validity rules, and payment model. The only gap is the semantics/format of parameter a, which an agent must infer from the regex pattern.

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 0%, so the description must carry the burden. It documents the constraint on n (odd, positive) but says nothing about a's domain (any integer, supplied as a string up to 200 digits per the pattern), leaving the schema pattern as the only signal for both parameters.

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 names the exact mathematical object, the Jacobi symbol (a/n), so an agent knows precisely what is computed. It does not explicitly differentiate from close siblings like legendre_symbol or kronecker, but the resource identity is unambiguous.

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 states a hard precondition (n must be odd and positive, even or non-positive n is rejected), which implicitly tells the agent when the tool is callable. However, there is no guidance on when to prefer this over legendre_symbol or kronecker, so sibling selection is left to inference.

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