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sympy_perfect_power

Check if a given number is a perfect power using SymPy's symbolic mathematics library for number theory computations.

Instructions

Check if n is a perfect power.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes

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 states it 'checks' which implies a read-only operation, but doesn't disclose behavioral traits like what a perfect power means, the return format (though output schema exists), error handling, or performance considerations.

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 a single, efficient sentence with zero waste. It's appropriately sized for a simple checking function and front-loaded with the core purpose.

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 (one parameter, output schema exists), the description is minimally adequate but has gaps. It lacks parameter details and usage context, though the output schema mitigates need to explain return values. Completeness is borderline for a checking tool with no annotations.

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

Parameters2/5

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. It only mentions 'n' without adding meaning beyond the schema, such as expected format (e.g., integer string), constraints, or examples. This leaves the single parameter poorly documented.

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 'Check if n is a perfect power' clearly states the verb ('Check') and resource ('n'), but it's vague about what constitutes a perfect power mathematically. It doesn't distinguish from siblings like 'sympy_isprime' or 'sympy_is_square', which are also checking functions.

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 on when to use this tool versus alternatives. The description doesn't mention prerequisites, context, or compare to sibling tools like 'sympy_is_square' or 'sympy_factorint' that might serve related purposes.

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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