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IBM

MCP Math Server

by IBM

automorphic_numbers

Calculate automorphic numbers up to a specified limit to identify numbers whose square ends with the same digits as the number itself.

Instructions

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

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
Behavior1/5

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. The description only states what the tool does without any information on performance, limitations, error handling, or output format. For a tool with no annotations, this lack of behavioral context is a significant gap, leaving the agent unaware of how the tool behaves beyond its basic function.

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, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information is brief and does not detract from clarity. There is no wasted verbiage, making it efficient for quick comprehension.

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 complexity of finding automorphic numbers (which involves mathematical computation), the description is insufficient. There are no annotations, no output schema, and minimal parameter semantics. The description does not explain what automorphic numbers are, how they are returned, or any computational limits, making it incomplete for effective tool use by an agent.

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 one parameter 'limit' with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'up to a limit' but does not clarify what 'limit' represents (e.g., maximum value, count), its valid range, or units. This adds minimal value beyond the schema, failing to compensate for the low coverage and leaving the parameter poorly understood.

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 automorphic numbers up to a limit.' It specifies the verb ('find'), resource ('automorphic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly distinguish this tool from its sibling 'is_automorphic_number', which tests individual numbers, leaving room for ambiguity in sibling differentiation.

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 ('digital_operations'), but this is generic and does not help an agent decide between this tool and its sibling 'is_automorphic_number' or other related tools. There are no explicit instructions on prerequisites, constraints, or typical use cases.

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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