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IBM

MCP Math Server

by IBM

happy_numbers

Identify all happy numbers up to a specified limit by iteratively summing the squares of digits until reaching 1 or entering a cycle.

Instructions

Find all happy 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 happy numbers up to a limit, implying a read-only operation that returns a list, but does not disclose critical behaviors such as performance characteristics (e.g., computational complexity for large limits), error handling (e.g., invalid limits), output format, or any side effects. 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.

Conciseness5/5

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

The description is extremely concise and front-loaded: 'Find all happy numbers up to a limit.' The additional domain and category in parentheses are efficient and relevant. Every word earns its place, with no redundancy or unnecessary elaboration, making it easy for an agent to parse quickly.

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 (iterative sequence generation), lack of annotations, no output schema, and low schema description coverage, the description is incomplete. It does not explain what happy numbers are, the return format (e.g., list of integers), handling of edge cases, or performance considerations. For a tool that likely involves computation and returns structured data, this leaves the agent with insufficient context to use it effectively.

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 0% description coverage, with one required parameter 'limit' of type integer. The description adds minimal semantics by mentioning 'up to a limit,' which clarifies the parameter's role but does not specify constraints (e.g., positive integers, maximum value) or examples. Since schema coverage is low, the description compensates slightly but not fully, meeting the baseline for marginal added value.

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 happy numbers up to a limit.' It specifies the verb ('Find'), resource ('happy numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_happy_number' (which tests a single number), though the domain/category context helps.

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 mentions the domain ('arithmetic') and category ('iterative_sequences'), but does not specify prerequisites, constraints, or when to choose it over similar tools like 'is_happy_number' or 'happy_numbers' vs. other number sequence tools. This leaves the agent without explicit 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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