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IBM

MCP Math Server

by IBM

generate_partitions

Generate all integer partitions of a given number to analyze its additive combinations for mathematical computations.

Instructions

Generate all integer partitions of n. (Domain: arithmetic, Category: partitions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
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. It states what the tool does but doesn't describe how it behaves: no information on performance characteristics (e.g., computational complexity for large n), output format (e.g., list of lists, sorted order), error handling (e.g., for negative n), or any side effects. The description is minimal and lacks behavioral context.

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 very concise—a single sentence plus domain/category tags. It's front-loaded with the core purpose. However, the domain/category note might be redundant if the tool name is clear, and the brevity comes at the cost of completeness, but it's efficiently structured.

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 (generating all partitions is computationally intensive), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address output format, performance limits, or error conditions. For a tool with potential high computational cost, 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.

Parameters3/5

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

The input schema has 1 parameter with 0% description coverage, so the schema provides no semantic information. The description adds minimal context by naming the parameter 'n' and implying it's an integer for partition generation, but doesn't explain its meaning (e.g., 'n is the integer to partition, must be non-negative') or constraints. This partially compensates but leaves gaps.

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: 'Generate all integer partitions of n.' It specifies the verb ('generate'), resource ('integer partitions'), and domain context ('arithmetic, Category: partitions'). However, it doesn't explicitly differentiate from sibling tools like 'distinct_partitions' or 'restricted_partitions', which are related but distinct partition functions.

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 and category but doesn't explain when to choose this over similar partition tools (e.g., 'distinct_partitions' for partitions without repetition, 'restricted_partitions' for constraints). There's no mention of prerequisites, limitations, or typical use cases.

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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