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IBM

MCP Math Server

by IBM

unit_fraction_sum

Calculate the sum of unit fractions (1/n) and return the result as a reduced fraction. Use this tool to add fractions with numerator 1 and different denominators.

Instructions

Sum a list of unit fractions and return the result as a reduced fraction. (Domain: arithmetic, Category: egyptian_fractions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
denominatorsYes
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 tool sums unit fractions and returns a reduced fraction, but doesn't disclose behavioral traits such as error handling (e.g., for zero denominators), input constraints (e.g., positive integers), performance characteristics, or what happens with empty lists. This leaves significant gaps for a mutation-like operation.

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—a single sentence that directly states the tool's function and output. It's front-loaded with the core purpose and includes a domain/category hint without unnecessary elaboration, making it 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 lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain input constraints (e.g., valid denominators), error conditions, or the format of the reduced fraction result. For a tool with one parameter and mathematical complexity, more context is needed to ensure correct usage.

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, with one parameter 'denominators' (array of integers) undocumented. The description mentions 'list of unit fractions,' which implies denominators, but doesn't clarify semantics (e.g., that these are the denominators of unit fractions 1/n, or that they must be positive). It adds minimal value beyond the schema's type information.

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: 'Sum a list of unit fractions and return the result as a reduced fraction.' It specifies the verb ('sum'), resource ('list of unit fractions'), and output format ('reduced fraction'), though it doesn't explicitly differentiate from sibling tools like 'egyptian_fraction_decomposition' or 'shortest_egyptian_fraction' beyond the domain/category hint.

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 ('egyptian_fractions'), but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'egyptian_fraction_decomposition' or 'farey_sum', leaving the agent without clear usage direction.

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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