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sympy_divisors

Calculate all divisors of a positive integer using symbolic mathematics for number theory and algebraic computations.

Instructions

Return divisors of n.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYesPositive integer

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior2/5

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

No annotations are provided, so the description carries full burden. It doesn't disclose behavioral traits such as performance characteristics, error handling for invalid inputs (e.g., non-positive integers), or whether the output is sorted. 'Return divisors' implies a read-only operation but lacks details on output format or any side effects.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise with a single sentence ('Return divisors of n.'), which is front-loaded and wastes no words. It directly states the purpose without unnecessary elaboration, making it efficient for an AI agent to parse.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's low complexity (single parameter, mathematical function) and the presence of an output schema (which handles return values), the description is minimally adequate. However, it lacks context on usage, behavioral details, and sibling differentiation, leaving gaps in overall completeness for effective tool selection.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 100% description coverage, with 'n' documented as a 'Positive integer'. The description adds no additional parameter semantics beyond this, as it only repeats 'n' without elaboration. With high schema coverage, the baseline is 3, and the description doesn't compensate with extra insights.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description 'Return divisors of n' clearly states the verb ('return') and resource ('divisors'), but it's somewhat vague about the mathematical context. It doesn't distinguish this tool from similar mathematical computation tools in the sibling list, like 'sympy_divisor_sigma' which might return divisor sums rather than the divisors themselves.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites, limitations, or when other tools (like 'sympy_factorint' for factorization) might be more appropriate. It's a standalone statement with no context.

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

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