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IBM

MCP Math Server

by IBM

improper_to_egyptian

Convert improper fractions to mixed numbers with Egyptian fraction representation for the fractional part using arithmetic operations.

Instructions

Convert improper fraction to mixed number and Egyptian fraction for fractional part. (Domain: arithmetic, Category: egyptian_fractions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
numeratorYes
denominatorYes
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. It states the conversion action but does not disclose behavioral traits such as error handling (e.g., for invalid inputs like zero denominator), computational constraints, or output format details. The description is basic and lacks critical operational context 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 in a single sentence, with no wasted words. It efficiently conveys the core purpose and domain/category. However, the brevity comes at the cost of completeness, as noted in other dimensions.

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 (a conversion tool with 2 parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain parameter meanings, output format, or error conditions, making it inadequate for reliable tool invocation by an AI 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 2 parameters (numerator, denominator) with 0% description coverage, meaning no schema documentation. The description does not add any parameter semantics—it does not explain what these parameters represent, their constraints (e.g., integers, non-zero denominator), or how they relate to the conversion. This fails to compensate for the low schema coverage.

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: 'Convert improper fraction to mixed number and Egyptian fraction for fractional part.' It specifies the verb (convert) and the resource (improper fraction), and distinguishes the output types (mixed number and Egyptian fraction). However, it does not explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'binary_remainder_egyptian', which might handle similar conversions, so it's not a perfect 5.

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 mentions the domain (arithmetic) and category (egyptian_fractions), which implies context but does not specify when to use this tool versus alternatives like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction'. There is no explicit when/when-not or named alternatives, leaving usage vague.

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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