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IBM

MCP Math Server

by IBM

narayana_triangle_row

Calculate row n of the Narayana triangle to obtain combinatorial numbers for mathematical analysis and problem-solving.

Instructions

Generate row n of Narayana triangle - FIXED. (Domain: arithmetic, Category: combinatorial_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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 mentions 'FIXED' but does not clarify what this means (e.g., fixed output format, immutable algorithm). It fails to describe critical behaviors like error handling for invalid inputs, performance characteristics, or the format of the returned row. This leaves significant gaps for a tool with a single parameter.

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

Conciseness4/5

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

The description is concise and front-loaded with the core purpose. It consists of a single sentence that directly states the tool's function, with no unnecessary words. The domain and category annotations are efficiently appended, though they could be integrated more smoothly.

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 lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not compensate for these gaps by explaining the parameter, return format, or behavioral details. For a combinatorial tool that likely returns a sequence or array, this omission makes it difficult for an agent to use effectively.

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?

The input schema has 0% description coverage, and the tool description does not explain the parameter 'n'. It does not specify what 'n' represents (e.g., row index starting from 0 or 1), valid ranges, or constraints. For a single-parameter tool with no schema documentation, this is a major deficiency that hinders correct usage.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Generate row n of Narayana triangle - FIXED.' It specifies the verb ('Generate'), resource ('row n of Narayana triangle'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'narayana_number' or 'narayana_cow_number', which are related but distinct combinatorial tools.

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?

The description provides no guidance on when to use this tool versus alternatives. It lacks context about the Narayana triangle's applications, prerequisites, or comparisons to other combinatorial number tools (e.g., 'catalan_number', 'bell_triangle'). Without such information, users must infer usage from the tool name and category alone.

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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