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IBM

MCP Math Server

by IBM

narcissistic_numbers

Identify narcissistic numbers (Armstrong numbers) up to a specified limit by checking if each number equals the sum of its digits raised to the power of the digit count.

Instructions

Find all narcissistic numbers up to a limit. (Domain: arithmetic, Category: iterative_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
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 states the tool finds numbers 'up to a limit' but does not describe output format (e.g., list, array), performance characteristics (e.g., computational complexity for large limits), or error handling. For a tool with no annotations, this is a significant gap in transparency.

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, consisting of a single sentence that directly states the tool's purpose. The additional domain and category tags ('Domain: arithmetic, Category: iterative_sequences') are brief and relevant, adding context without unnecessary verbosity. However, the structure could be improved by integrating usage hints more seamlessly.

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 (involves mathematical computation), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It fails to explain the return values, error conditions, or behavioral nuances, leaving the agent with insufficient information for reliable 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 1 parameter ('limit') with 0% description coverage, so the schema provides no semantic information. The description adds meaning by indicating 'limit' defines the upper bound for searching narcissistic numbers, but it does not specify constraints (e.g., positive integer, range) or units. This partial compensation aligns with the baseline for low schema coverage.

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: 'Find all narcissistic numbers up to a limit.' It specifies the verb ('Find'), resource ('narcissistic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_narcissistic_number' or 'armstrong_numbers' (which may be related), so it falls short of a perfect score.

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 on prerequisites, exclusions, or comparisons to sibling tools such as 'is_narcissistic_number' (which checks a single number) or 'armstrong_numbers' (which might be similar). This omission leaves the agent without clear 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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