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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It discloses nothing about side effects, return values, error behavior, or required inputs. Given that a Legendre symbol computation logically requires two integer arguments, the empty schema and silent description leave the agent completely in the dark.

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?

The description is short, but this is under-specification, not conciseness. It repeats the name with a colon and provides zero informational value. No part of the description earns its place because there is nothing informative to earn a place.

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 mathematical tool that requires parameters and has no annotations, no output schema, and no sibling differentiation, the description is completely inadequate. An agent cannot determine how to call it, what to pass, or what to expect back. This is one of the most incomplete possible definitions.

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?

The schema has zero parameters, so the normal 0-param baseline would be 4, but this is a case where the tool's name implies it needs two inputs (a and p). The description adds no explanation of how to supply those inputs via prompt or any other mechanism. The empty schema plus tautological description is misleading, not helpful.

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 is 'Legendre Symbol: Legendre Symbol' — a pure tautology that restates the tool name. It does not state what the tool computes, what inputs it takes, or what output it produces, and it does nothing to distinguish this tool from sibling tools like x402-is-quadratic-residue.

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?

There is no guidance on when to use this tool versus any alternative. The description does not mention a use case, prerequisites, or context. It is entirely unhelpful for an agent deciding whether to invoke it.

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