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amichae2

Math MCP Server

by amichae2

partitions

Count or list all integer partitions of a given number n, optionally restricting to partitions with exactly k parts.

Instructions

Count or list integer partitions.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
operationNocount
kNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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

With no annotations, the description bears full responsibility for behavioral disclosure, but it only mentions counting or listing partitions. There is no information about side effects, performance, valid operation values, or constraints, leaving the agent unaware of important behavior.

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

Conciseness2/5

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

The description is extremely terse (only 5 words), which sacrifices necessary detail. While concise, it fails to be informative enough for an agent to select and invoke the tool correctly.

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 three parameters and an output schema, the description is starkly incomplete. It omits details on return values, operation types, and parameter semantics, making it inadequate for understanding the tool's full functionality.

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?

The input schema has 0% description coverage for its three parameters, and the description provides no additional explanation. The agent must guess that 'n' is the integer to partition, 'operation' controls count vs. list, and 'k' may limit part size, which is a significant gap.

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 states the tool can count or list integer partitions, which clearly indicates its purpose. However, it does not distinguish itself from sibling tools like 'combinatorics' that may also handle partitions, slightly reducing clarity.

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?

No guidance is provided on when to use this tool versus alternatives, nor on the different operations (count vs. list) or the role of the 'k' parameter. The description is too brief to inform usage decisions.

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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