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IBM

MCP Math Server

by IBM

harshad_numbers

Find all Harshad numbers up to a specified limit. A Harshad number is divisible by the sum of its digits in a given base, useful for number theory and digital arithmetic calculations.

Instructions

Find all Harshad numbers up to a limit. (Domain: arithmetic, Category: digital_operations)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
baseNo
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 the domain ('arithmetic') and category ('digital_operations'), but fails to describe key behaviors: whether the tool is read-only or mutative, what the output format is (e.g., list of integers), performance considerations, or error handling. This leaves significant gaps for a tool with parameters.

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 a single sentence stating the core functionality followed by domain/category tags. There is no wasted text, and it efficiently communicates the essential purpose without unnecessary elaboration.

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 (2 parameters, no annotations, no output schema), the description is inadequate. It lacks details on parameter meanings, output format, behavioral traits, and usage context. For a tool that generates a list of numbers, more completeness is needed to guide the agent 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?

Schema description coverage is 0%, meaning parameters 'limit' and 'base' are undocumented in the schema. The description only mentions 'limit' indirectly ('up to a limit') and omits 'base' entirely, failing to explain their purposes (e.g., 'limit' as the upper bound, 'base' as the numeral system defaulting to 10). It adds minimal value beyond the bare schema.

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 Harshad numbers up to a limit.' It specifies the verb ('find'), resource ('Harshad numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_harshad_number' or 'harshad_numbers' (if duplicates exist), keeping it from 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 minimal guidance: it implies usage for finding Harshad numbers within a limit, but offers no explicit advice on when to use this tool versus alternatives (e.g., 'is_harshad_number' for checking individual numbers) or any prerequisites. Without such context, the agent lacks clear direction for tool selection.

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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