quadratic_residues

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 'Find[s] all quadratic residues modulo n,' which implies a read-only operation that returns a list, but it does not specify output format (e.g., list of integers), handling of edge cases (e.g., negative n, n=0, or n=1), performance characteristics, or error conditions. This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.

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: it states the core purpose in the first phrase, followed by domain and category metadata. There is no wasted verbiage or redundancy, making it efficient for quick understanding. Every sentence (or phrase) earns its place by providing essential information.

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 function with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not cover parameter semantics, output format, error handling, or usage context relative to siblings. While concise, it lacks the depth needed for an agent to use the tool effectively without additional assumptions.

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 one parameter 'n' with 0% description coverage, and the description does not add any semantic details about it. It does not explain what 'n' represents (e.g., a positive integer modulus), valid ranges, or constraints (e.g., n > 1 for meaningful residues). With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.

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: 'Find all quadratic residues modulo n.' It specifies the verb ('Find'), resource ('quadratic residues'), and domain context ('modulo n'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'is_quadratic_residue' or 'jacobi_symbol', which are related modular arithmetic tools, 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 mentions the domain ('arithmetic') and category ('modular_arithmetic'), but this is too general and does not help an agent choose between this and similar tools like 'is_quadratic_residue' (which checks a single residue) or 'jacobi_symbol' (which computes a related symbol). No explicit when-to-use or when-not-to-use instructions are given.

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