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sympy_catalan

Calculate the Catalan number for a non-negative integer using symbolic computation.

Instructions

Catalan number.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYesNon-negative integer

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior1/5

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

With no annotations, the description should disclose return types, side effects, or edge cases. It only states the concept, omitting what the tool actually does (e.g., returns a number). No behavioral detail is added.

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

Conciseness2/5

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

The description is extremely brief but lacks essential elements such as a verb or return value. It is underspecified rather than concise.

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

Completeness2/5

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

Although an output schema exists, the description does not explain the tool's output (e.g., 'returns the nth Catalan number'). The context is incomplete for a mathematical function.

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 already describes the single parameter 'n' as a non-negative integer. The description adds no extra meaning; baseline 3 is appropriate given 100% schema coverage.

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 'Catalan number.' identifies the mathematical concept but lacks a verb or action. It does not specify that the tool computes the nth Catalan number, nor does it differentiate from siblings like sympy_fibonacci or sympy_factorial beyond the name.

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 does not mention context, prerequisites, or limitations.

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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