legendre

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

With no annotations, the description carries full burden but only states basic operation. It does not disclose error behavior for non-prime p, output values, or other edge cases.

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 a single concise sentence with no wasted words, effectively communicating the core purpose.

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 simple mathematical function with param schema and output schema covered, the description is adequate but could mention output interpretation or error cases for completeness.

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 100% with descriptions for 'a' and 'p'. The description adds no extra semantic value beyond what is already in the schema, so baseline 3 is appropriate.

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 clearly states the function: 'Compute the Legendre symbol (a/p)'. It uses a specific verb and resource, distinguishing it from sibling tools like 'jacobi' or 'hilbert'.

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?

No guidance is provided on when to use this tool versus alternatives (e.g., Jacobi symbol). The description only explains what it does, not the context or prerequisites.

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