eisenstein

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

With no annotations, the description should disclose behavioral traits. It only says 'Compute the Eisenstein series', omitting details like return type, potential errors, or computational traits (e.g., series expansion nature).

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 sentence that efficiently conveys the core purpose. No extraneous words; it is appropriately concise for a straightforward mathematical function.

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 specialized nature of Eisenstein series and the presence of many sibling modular form tools, the description lacks context (e.g., weight restrictions, series representation, relationship to other modular forms). No output schema exists, increasing the need for description 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 description coverage is 100%, so the schema already documents all parameters. The description adds no extra meaning beyond the schema's field descriptions; 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 'Compute the Eisenstein series E_k(q)', which specifies the verb and resource. However, it does not differentiate from sibling tools like eta or theta, but it is specific enough for an expert.

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., eta, theta, modular_lambda) or what conditions (e.g., k even >=2) are necessary beyond the schema.

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