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mcp-parigp

mcp-parigp

by daedalus
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python

factorpadic

Factor a polynomial over p-adic numbers. Provide the polynomial as a string, a prime p, and optionally set the p-adic precision.

Instructions

Factor a polynomial over the p-adic numbers.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "pol": "<pol>",
      "p": "<p>"
    },
    "name": "factorpadic"
  }
}

Input Schema

NameRequiredDescriptionDefault
nNop-adic precision.
pYesPrime p.
polYesPolynomial as a string.

Output Schema

NameRequiredDescriptionDefault
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

C2.8/5.0
Behavior1/5

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

With no annotations, the description carries the full burden of behavioral disclosure. It fails to mention what the tool returns (e.g., list of factors), whether it modifies state, or any side effects. This is insufficient for a specialized mathematical operation.

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 a single sentence that is front-loaded and concise, but it is arguably under-specified for a specialized tool. It meets the minimum standard but could include more detail without becoming verbose.

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?

Despite having an output schema, the description provides insufficient context for an agent to correctly invoke the tool. It omits the expected polynomial string format, the meaning of precision, and the structure of the return value.

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?

Schema coverage is 100%, and each parameter has a description. The tool description adds no additional meaning beyond the schema's parameter definitions, achieving the baseline for this dimension.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the action (Factor), the resource (a polynomial), and the specific context (over p-adic numbers). It effectively distinguishes from siblings like 'factor' and 'polrootspadic' by using precise mathematical language.

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 such as 'factor' or 'polrootsmod'. It does not explain prerequisites, typical use cases, or exclusion conditions.

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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