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amichae2

Math MCP Server

by amichae2

eigen_decomp

Compute eigenvalues and optionally eigenvectors of a matrix input. Returns eigenvalues and eigenvectors if requested.

Instructions

Compute eigenvalues and optionally eigenvectors.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
matrixYes
compute_vectorsNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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

No annotations are provided, so the description must disclose behavior. It only mentions computation of eigenvalues and eigenvectors, but does not state what happens for non-square matrices, the order of eigenvalues, numerical precision, or whether the operation is destructive. The output schema exists but is not referenced.

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 sentence that is front-loaded with the verb 'Compute'. It is concise with no redundant words. However, it may be too terse, lacking necessary details for a non-trivial tool.

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?

Given the presence of an output schema, return values need not be explained, but the description omits input constraints (e.g., square matrix required) and does not mention potential errors or edge cases. With no annotations, the description is incomplete for a tool with two parameters.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It adds minimal information beyond parameter names: 'compute_vectors' is hinted as controlling optional eigenvector computation. No details on matrix shape or constraints, and the boolean parameter's effect is only implied.

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?

The description clearly states it computes eigenvalues and optionally eigenvectors, which is a specific verb+resource. However, it does not differentiate from sibling tools like gpu_eigen_batch or matrix_decompose, which may perform similar decompositions.

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 provided on when to use this tool versus alternatives such as gpu_eigen_batch or matrix_decompose. There is also no indication of prerequisites (e.g., matrix must be square) or when to set compute_vectors to true/false.

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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