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 lists operation categories but does not mention return format, error behavior, side effects, or whether results are exact/deterministic. This is a significant gap for a compute tool.

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 a single concise, front-loaded sentence with a comma-separated operation list; every word adds information. However, the list format lacks any structural guidance on parameters or usage, keeping it from a higher score.

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 (9 parameters, 0% schema coverage, no annotations, and an unseen output schema), the description is woefully incomplete. An agent cannot determine valid operation strings, parameter roles, or invocation patterns from this text alone.

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 description must compensate for 9 cryptic parameters (a, b, c, k, m, n, moduli, remainders, operation). It names plausible operation values (primality, factoring, etc.) but does not map them to parameters or explain required inputs per operation, leaving most parameters unexplained.

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 identifies the tool as performing number theory computations, listing specific operations like primality, factoring, extended GCD, and CRT. This distinguishes it from sibling math tools such as solve_arithmetic or matrix_algebra, though the verb 'compute' is only implied by the tool name.

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?

There is no guidance on when to use this tool versus alternative cognitive math tools, nor any exclusions or prerequisites. The operation list implies usage for number theory problems, but the description does not state conditions or mention alternatives, leaving the agent to infer.

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