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mcp-parigp

mcp-parigp

by daedalus
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python

polrootsmod

Find all roots of a polynomial modulo a prime p. Useful for number theory and algebraic computations.

Instructions

Compute the roots of a polynomial modulo p.

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": "polrootsmod"
  }
}

Input Schema

NameRequiredDescriptionDefault
pYesPrime modulus.
polYesPolynomial as a string.

Output Schema

NameRequiredDescriptionDefault
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

B3.3/5.0
Behavior2/5

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

No annotations provided, so the description carries the full burden. It does not disclose behavioral traits such as error handling, whether p must be prime (only stated in schema but not repeated), or the format of the results. The description is minimal and lacks behavioral context beyond the basic operation.

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

Conciseness5/5

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

The description is a single sentence with no extraneous words, making it efficient and front-loaded.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given that an output schema exists and the schema descriptions cover parameters, the description is adequate but lacks contextual completeness about the interpretation of 'modulo p' (e.g., over finite field) and potential edge cases. It is acceptable but not thorough.

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 description coverage is 100%, so the baseline is 3. The tool description does not add any additional meaning beyond what the schema descriptions already provide for pol and p. It merely restates the operation in a general way.

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?

Description uses specific verb 'Compute' and resource 'roots of a polynomial modulo p', clearly distinguishing from siblings like polroots (complex roots) and polrootspadic (p-adic roots).

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 on when to use this tool versus alternative root-finding tools such as polroots or polrootspadic. The description only states the function without contextual usage tips.

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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