wilson_factorial_mod

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

No annotations are provided, so the description carries the full burden. It mentions 'efficiently,' hinting at performance, but doesn't disclose critical behavioral traits: computational limits (e.g., large k/m), error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding its operation and constraints.

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: one sentence states the core function, followed by a parenthetical domain/category. Every word earns its place with zero waste, making it easy to parse quickly.

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 complexity (mathematical computation with two parameters), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It lacks details on behavior, parameter meanings, return values, and error conditions, leaving the agent under-informed for reliable use.

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 0%, so the schema provides no parameter details. The description adds minimal semantics: 'k' and 'm' are implied as inputs for factorial modulo calculation, but it doesn't explain their roles (e.g., k is the factorial base, m is the modulus), constraints (e.g., non-negative integers), or examples. This insufficiently compensates for the lack of schema documentation.

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: 'Calculate k! mod m efficiently for Wilson's theorem.' It specifies the verb ('calculate'), resource (factorial modulo), and context (Wilson's theorem). However, it doesn't explicitly differentiate from sibling tools like 'wilson_theorem_check' or 'wilson_theorem_test', which appear related to Wilson's theorem but have different functions.

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 guidance: it mentions the domain (arithmetic) and category (primality_tests), implying use in primality testing contexts. However, it lacks explicit when-to-use instructions, alternatives (e.g., vs. other Wilson's theorem tools), or exclusions. The agent must infer usage from the category alone.

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