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mcp-parigp

mcp-parigp

by daedalus
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python

matcharpoly

Computes the characteristic polynomial of a square matrix, with an option to specify the variable name.

Instructions

Compute the characteristic polynomial of a matrix.

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": {
      "m": "<m>"
    },
    "name": "matcharpoly"
  }
}

Input Schema

NameRequiredDescriptionDefault
mYesSquare matrix.
vNoVariable name.x

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

B3.2/5.0
Behavior2/5

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

No annotations are provided, so the description must disclose behavioral traits. It does not mention the output format (a polynomial), the role of the variable parameter 'v', or any constraints beyond the input parameter descriptions. This is insufficient.

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 a single, concise sentence. It earns its place by stating the primary purpose, but could benefit from slightly more detail without sacrificing brevity.

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 the complexity of computing a characteristic polynomial, the description is adequate for an expert user. However, the lack of output schema or mention of return type makes it incomplete for an AI agent. The parameter descriptions help, but the description could elaborate on the variable parameter.

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 baseline is 3. The description adds no extra meaning beyond the parameter descriptions; it merely restates the concept.

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 tool's action: 'Compute the characteristic polynomial of a matrix.' This is a specific verb-resource combination that distinguishes it from sibling tools like matdet or mateigen.

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 is given on when to use this tool versus alternatives such as mateigen or matdet. There is no mention of prerequisites or context for usage.

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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