count_solutions_diophantine

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool counts solutions within bounds but does not mention computational complexity, error handling, output format, or any side effects. For a tool with 7 parameters and no annotation coverage, this is a significant gap in transparency.

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, consisting of a single sentence that directly states the tool's purpose, followed by domain and category tags. There is no wasted verbiage, and every word contributes to understanding the tool's function efficiently.

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 (7 parameters, no annotations, no output schema), the description is incomplete. It does not explain the return value format, error conditions, or behavioral nuances. For a mathematical tool with multiple inputs, more context is needed to guide the agent effectively, making this description inadequate for the tool's complexity.

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, and the tool description does not explain any parameters beyond implying 'a', 'b', 'c', and bounds for 'x' and 'y'. It lacks details on parameter constraints, units, or examples, failing to compensate for the schema's lack of descriptions. This leaves the agent guessing about parameter meanings and valid ranges.

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: 'Count integer solutions to ax + by = c within given bounds.' It specifies the verb ('count'), resource ('integer solutions'), and domain context ('diophantine_equations'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'solve_linear_diophantine' or 'diophantine_analysis', 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 no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit instructions on prerequisites, limitations, or comparisons with sibling tools such as 'parametric_solutions_diophantine' or 'solve_linear_diophantine'. This leaves the agent without clear usage context.

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