Computes Moebius function values and the Mertens function up to a positive integer bound using a linear sieve, enabling number-theoretic analysis for n up to 10,000,000.
Compute Moebius function values and Mertens function using linear sieve.
| Name | Required | Description | Default |
|---|---|---|---|
| n | Yes | Positive integer upper bound (max 10,000,000) |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full behavioral burden. It mentions the linear sieve algorithm, but it does not state the return format, whether all values up to n are returned, how Mertens is represented, or any time/memory implications beyond the schema's max bound.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
One sentence, front-loaded with the compute action and no filler. It is appropriately sized for the description, though its brevity contributes to other gaps.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
There is no output schema, so the description should explain return values. It does not clarify whether the result is an array of Moebius values up to n, a single Mertens value, or both, leaving an agent uncertain about what to expect.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The single parameter n has 100% schema description coverage, including positive integer and max 10,000,000. The description adds no parameter meaning beyond the schema, so the baseline of 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb and two mathematical resources: Moebius function values and Mertens function, plus the method (linear sieve). It is clear what computation is performed, though it does not distinguish itself from related number-theory siblings or clarify the exact output shape.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is given on when to use this tool instead of alternatives such as sieve_of_eratosthenes, prime_check, or euler_totient. There are no prerequisites, exclusions, or context for choosing this computation.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.