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amichae2

Math MCP Server

by amichae2

factor_int

Decompose an integer into prime factors. Specify the integer and optionally choose a factorization method.

Instructions

Factor an integer into prime factors.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
methodNoauto

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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

No annotations are provided, so the description must carry the full burden of behavioral disclosure. It does not mention whether the tool is safe (read-only) or destructive, what errors may occur, the format of the output, or any edge cases. The brief statement only covers the high-level purpose, leaving significant behavioral details undisclosed.

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 extremely concise (one sentence with seven words). While brevity is generally good, this level of conciseness omits necessary details (e.g., parameter meanings, output format). It is efficient but incomplete, balancing conciseness and utility only moderately.

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?

The tool has an output schema (not shown), but the description does not indicate what the output represents (e.g., list of factors, sorted?). With no annotations and 0% parameter coverage, the description leaves significant gaps for an AI agent to understand how to correctly invoke and interpret results. It is not complete enough for reliable use.

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 neither schema nor description explain the parameters. The description does not clarify that 'n' expects a string representation of an integer, nor does it explain the 'method' parameter's options or default behavior ('auto'). The description adds zero semantic value beyond what the schema already sparsely provides.

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 'Factor an integer into prime factors' clearly states the action and resource. The verb 'factor' and resource 'integer' are specific, and the task (prime factorization) is distinct from general factorization or primality checking. However, it does not explicitly differentiate from the sibling 'factor' tool, which could perform similar or broader factorization, 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?

The description provides no guidance on when to use this tool versus alternatives like 'factor' or 'is_prime'. There is no mention of prerequisites, limitations, or when not to use it. The context signals show many math-related siblings, but the description gives no comparative information.

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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