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IBM

MCP Math Server

by IBM

taxi_numbers

Calculate taxi numbers by finding integers that can be expressed as sums of two cubes in multiple ways up to a specified limit.

Instructions

Find all taxi numbers (sums of two cubes in multiple ways) up to limit. (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
limitYes
min_waysNo
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. The description states what the tool does but does not cover important behavioral aspects such as performance characteristics (e.g., computational complexity for large limits), error handling, or output format. It mentions 'up to limit' but does not clarify if the limit is inclusive or how results are returned (e.g., list, count). This leaves gaps for an AI agent to understand operational details.

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. There is no wasted verbiage or redundancy. The additional domain and category information in parentheses is brief and relevant, making the description efficient and easy to parse.

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 a mathematical computation tool with 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is insufficient. It does not explain parameter details, behavioral traits, or what the output will look like (e.g., list of numbers, their cube representations). For a tool that performs a non-trivial arithmetic search, 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?

The input schema has 0% description coverage, so the description must compensate. It mentions 'up to limit' which partially explains the 'limit' parameter, but does not define what 'limit' represents (e.g., maximum number value, count of results). It does not mention the 'min_ways' parameter at all, leaving its purpose undocumented. Thus, the description adds minimal semantic 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 taxi numbers (sums of two cubes in multiple ways) up to limit.' It specifies the verb ('Find'), resource ('taxi numbers'), and domain context ('sums of two cubes in multiple ways'), which is specific and informative. However, it does not explicitly differentiate from sibling tools, as the sibling list contains many arithmetic/number theory tools but none specifically for taxi numbers, so the distinction is implicit rather than explicit.

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 ('special_numbers'), but does not specify prerequisites, exclusions, or recommend other tools for related tasks. For example, it does not indicate if this is for mathematical exploration, verification, or if other tools might handle similar number sequences.

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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