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mcp-parigp

mcp-parigp

by daedalus
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python

hess

Compute the Hessenberg form of a square matrix, reducing it to upper Hessenberg form through orthogonal similarity transformations.

Instructions

Compute the Hessenberg form 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": "hess"
  }
}

Input Schema

NameRequiredDescriptionDefault
mYesSquare matrix.

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

C2.9/5.0
Behavior2/5

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

No annotations provided. Description does not disclose behavioral traits such as whether the input matrix is modified, the output format (e.g., matrix type), or any numerical properties. It simply states computation, leaving the agent uncertain about side effects or return values.

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?

Extremely concise. Single sentence clearly states purpose. No unnecessary words. Front-loaded with verb and resource.

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 description is minimal. It does not explain the output format or any preconditions beyond square matrix (already in schema). No mention of complex numbers or field. For a mathematical computation, users would benefit from knowing the return type and any limitations. With no output schema, the description carries extra burden which it fails to meet.

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?

Parameter 'm' is described in schema as 'Square matrix.' with 100% coverage, so baseline is 3. The description does not add further parameter semantics, but that is acceptable when schema is sufficient.

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?

Description clearly states the tool computes the Hessenberg form of a matrix, using a specific verb and resource. It is unambiguous and distinct from sibling tools which include other matrix operations like matdet, mateigen, etc. However, it could be slightly more descriptive (e.g., specifying it produces an upper Hessenberg matrix).

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 alternatives. The description does not mention any context in which Hessenberg form is preferable (e.g., for eigenvalue algorithms). The parameter description specifies square matrix, but that is minimal and from the schema.

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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