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sympy_catalan

Compute Catalan numbers for non-negative integers using symbolic mathematics. This tool calculates combinatorial sequences for applications in combinatorics, computer science, and mathematical analysis.

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?

No annotations are provided, so the description must fully disclose behavioral traits. 'Catalan number.' gives no information about what the tool does operationally (e.g., computes, evaluates, returns), its side effects, error handling, or output format. It fails to convey even basic behavior, such as whether it performs a calculation or retrieves a constant, making it inadequate for a tool with no annotation support.

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?

While the description is extremely concise ('Catalan number.'), this brevity results in under-specification rather than effective communication. It lacks a clear structure (e.g., a purpose statement followed by details) and does not front-load essential information. The single phrase fails to earn its place by adding value, making it inefficient despite its short length.

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?

Given the tool's complexity (a mathematical function with one parameter) and the presence of an output schema (which alleviates the need to describe return values), the description is incomplete. It does not state the tool's purpose, behavior, or usage context, leaving significant gaps. With no annotations and minimal description, it fails to provide enough information for effective tool selection and invocation.

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 the parameter 'n' documented as a 'Non-negative integer'. The description adds no meaning beyond this schema, as it does not mention parameters at all. According to the rules, when schema coverage is high (>80%), the baseline score is 3 even with no parameter information in the description, which applies here.

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

Purpose2/5

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

The description 'Catalan number.' is a tautology that merely restates the tool name without specifying what the tool does. It lacks a clear verb (e.g., 'compute', 'calculate', 'generate') and does not distinguish this tool from its many siblings, which appear to be various mathematical functions and operations in SymPy. A minimal viable description would at least indicate this tool computes or returns Catalan numbers.

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

Usage Guidelines1/5

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. With numerous sibling tools (e.g., sympy_factorial, sympy_fibonacci, sympy_binomial) that likely handle other mathematical sequences or functions, there is no indication of context, prerequisites, or comparisons. This leaves the agent without any usage direction.

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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