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IBM

MCP Math Server

by IBM

palindromic_numbers

Generate palindromic numbers up to a specified limit to identify symmetrical numeric patterns for mathematical analysis and problem-solving.

Instructions

Find all palindromic 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 and category ('Domain: arithmetic, Category: digital_operations'), but this is vague and does not clarify key behaviors like whether the tool returns a list, if it includes the limit itself, performance characteristics, or error handling. For a tool with two parameters and no annotations, this is insufficient.

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 in the first sentence. The additional domain and category information is brief and does not add unnecessary length. However, the lack of detail on parameters and usage slightly undermines its effectiveness, but it remains efficiently structured.

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 has 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It does not explain what the tool returns (e.g., a list of numbers), how 'base' affects the search, or any behavioral nuances. For a tool that generates sequences, more context is needed to guide effective use.

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 the input schema provides no descriptions for the parameters 'limit' and 'base'. The description only mentions 'limit' implicitly ('up to a limit') and does not explain 'base' at all. It fails to compensate for the lack of schema documentation, leaving parameter meanings unclear, especially for 'base' which defaults to 10.

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 palindromic numbers up to a limit.' It specifies the verb ('find'), resource ('palindromic numbers'), and scope ('up to a limit'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'is_palindromic_number' or 'next_palindrome', which test or generate individual palindromic numbers, so it misses full sibling distinction.

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 any mention of prerequisites, exclusions, or comparisons to sibling tools such as 'is_palindromic_number' (for checking a single number) or 'next_palindrome' (for finding the next palindrome). Without this, users must infer usage from the tool name 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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