is_fermat_pseudoprime

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 performs a 'Check', implying a read-only operation, but does not elaborate on computational complexity, error handling, or output format. For a mathematical verification tool with zero annotation coverage, this is insufficient to inform the agent adequately.

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, consisting of a single sentence that directly states the tool's purpose, followed by domain/category tags. There is no wasted verbiage, and the information is front-loaded, making it efficient for quick understanding.

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 lack of annotations and output schema, the description is incomplete. It does not explain what a Fermat pseudoprime is, the mathematical condition being checked, or the return value (e.g., boolean or detailed result). For a specialized mathematical tool with no structured support, more explanatory context is needed.

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 parameters 'n' and 'a' documented only by type. The description adds minimal context by naming the parameters in the phrase 'n is a Fermat pseudoprime to base a', which clarifies their roles but does not provide constraints, typical values, or examples. This partial compensation justifies a baseline score.

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: 'Check if n is a Fermat pseudoprime to base a.' It specifies the verb ('Check') and the mathematical concept, and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'fermat_primality_check' or 'fermat_primality_test', which might have overlapping functionality, so it misses the highest 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 lacks information on prerequisites, typical use cases, or comparisons to sibling tools such as 'fermat_primality_check' or 'strong_pseudoprime_test'. This leaves the agent without clear direction on tool selection.

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