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IBM

MCP Math Server

by IBM

fibonacci_greedy_egyptian

Convert fractions to Egyptian fractions using the Fibonacci greedy algorithm. Input numerator and denominator to get unit fraction representation.

Instructions

Alternative greedy algorithm for Egyptian fractions (Fibonacci method). (Domain: arithmetic, Category: egyptian_fractions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
numeratorYes
denominatorYes
Behavior1/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries full burden for behavioral disclosure. The description reveals nothing about what the tool does behaviorally - whether it computes, validates, optimizes, or something else. It doesn't mention input constraints (e.g., positive integers), computational characteristics, error conditions, or what the output represents. This is inadequate for a tool with no annotation coverage.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness3/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise (one sentence with parenthetical domain/category), but it's under-specified rather than efficiently informative. The single sentence doesn't waste words, but it also doesn't provide enough information. The domain/category annotation could be considered extraneous repetition since it's already implied by the tool name and context.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness1/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given a mathematical tool with 2 required parameters, 0% schema description coverage, no annotations, and no output schema, the description is completely inadequate. It doesn't explain what the tool computes, what the parameters mean, what the output represents, or when to use it. For a tool in a domain with many alternatives (Egyptian fractions), this leaves critical gaps in understanding.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters1/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, meaning the schema provides no descriptions for the two parameters (numerator, denominator). The description adds absolutely no information about what these parameters represent, their valid ranges, or their relationship. For a mathematical tool with two required integer parameters, this leaves the agent guessing about their meaning and constraints.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose2/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states 'Alternative greedy algorithm for Egyptian fractions (Fibonacci method)' which gives a general domain (Egyptian fractions) and method name (Fibonacci method), but it's vague about what the tool actually does. It doesn't specify the verb (e.g., 'compute', 'generate', 'find') or what output is produced. It distinguishes from siblings by mentioning 'Egyptian fractions' which appears in other tool names, but the purpose remains unclear.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines1/5

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 'Alternative greedy algorithm' but doesn't specify what it's an alternative to, when this method is preferred, or what other Egyptian fraction tools exist (like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' in the sibling list). There's no context for appropriate usage.

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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