jacobi

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

Without annotations, the description carries the burden. It discloses the basic operation but doesn't mention return value range (-1, 0, 1), error conditions (e.g., what if n is not odd positive), or other behavioral traits. For a standard mathematical function, this is acceptable but not thorough.

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, well-formed sentence with no wasted words. It is appropriately sized for the simple tool.

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?

Given the tool's simplicity (two integer parameters) and the existence of an output schema (expected to describe the return value), the description is mostly adequate. However, it lacks any behavioral notes or usage hints, leaving some gaps for a completely new user.

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 'Integer.' and 'Odd positive integer.' The tool description 'Compute the Jacobi symbol (a/n)' adds minimal extra meaning beyond the schema. It restates the purpose but does not provide additional context like typical ranges or special cases.

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 it computes the Jacobi symbol with parameters a and n, distinguishing it from siblings like legendre (Legendre symbol) though it doesn't explicitly note the generalization. The verb 'Compute' and specific mathematical object make it clear.

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 on when to use this tool vs alternatives like legendre or other number-theoretic functions. No mention of constraints beyond what's in the schema, such as n must be odd and positive, which is already in the schema. No exclusions or context provided.

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