sum_of_four_squares

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does (expresses a number as sum of four squares) but doesn't describe important behavioral aspects: what format the output takes (e.g., list of integers, string representation), whether there are multiple valid decompositions and how one is chosen, input constraints (e.g., non-negative integers only), or error handling. For a tool with no annotation coverage, this is insufficient.

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 appropriately concise - a single sentence that states the core purpose with mathematical context. It's front-loaded with the main functionality. The parenthetical domain/category information is potentially useful but could be considered slightly extraneous. Overall, it's efficient with minimal waste.

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 complexity (mathematical decomposition algorithm), no annotations, no output schema, and poor parameter documentation, the description is incomplete. It doesn't explain what the tool returns, how results are formatted, input constraints, or algorithmic behavior. For a tool implementing Lagrange's theorem with one parameter, users need more context about the output and any limitations.

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 input schema has 0% description coverage, providing only that parameter 'n' is an integer. The description adds no parameter semantics whatsoever - it doesn't explain what 'n' represents (presumably the number to decompose), its valid range, or any constraints. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.

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 tool's purpose: 'Express a number as sum of four squares (Lagrange's theorem).' It specifies both the action ('Express') and the mathematical resource ('sum of four squares'), and references Lagrange's theorem for context. However, it doesn't explicitly differentiate from sibling tools like 'sum_of_two_squares' or 'sum_of_two_squares_all', which would be needed for a perfect score.

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?

The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('additive_number_theory'), which gives some context about when this mathematical tool might be relevant, but offers no explicit guidance on when to use this versus alternatives like 'sum_of_two_squares' or other decomposition tools. There are no when/when-not instructions or named alternatives.

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