sum_of_two_squares_all

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 (representation as sum of two squares) but doesn't describe how it behaves: whether it returns all representations or just one, what happens with non-representable integers, whether there are computational limits, or what the output format looks like. This leaves significant gaps for a tool that solves a mathematical problem.

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 extremely concise and front-loaded: the core purpose is stated in the first phrase, followed by domain/category tags. There is zero wasted verbiage, and every element (mathematical operation, input type, categorization) serves a clear purpose. This is a model of efficiency for a simple mathematical 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 mathematical complexity (solving a diophantine equation) and the absence of both annotations and an output schema, the description is inadequate. It doesn't explain what the tool returns (e.g., pairs of integers, existence boolean, error handling), behavioral constraints, or usage examples. For a tool that could have multiple behavioral interpretations, this leaves too much ambiguity.

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, with a single parameter 'n' of type integer. The description adds some semantic context by specifying this represents 'integer as sum of two squares,' clarifying that 'n' is the integer to be represented. However, it doesn't provide details about valid ranges, constraints (e.g., non-negative integers), or examples, which would be needed for full compensation of the schema gap.

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: 'Represent integer as sum of two squares x² + y².' It specifies the mathematical operation (representation as sum of two squares) and the resource (integer input). However, it doesn't explicitly distinguish this from sibling tools like 'sum_of_two_squares' or other diophantine equation tools, which prevents 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 through the domain/category tags ('Domain: arithmetic, Category: diophantine_equations'), which implies when this mathematical tool might be applicable. However, it offers no explicit guidance on when to use this tool versus alternatives like 'sum_of_two_squares' or other representation tools, nor does it mention any prerequisites or constraints.

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