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IBM

MCP Math Server

by IBM

vector_norm

Calculate vector magnitude (norm) for linear algebra applications. Supports customizable p-norm calculations to determine vector length from components.

Instructions

Calculate the norm (magnitude) of a vector (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vectorYes
pNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks details on behavior: it doesn't mention error handling (e.g., for invalid inputs), performance characteristics, or output format (since there's no output schema). The domain/category hint at context but don't add actionable behavioral traits.

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 concise and front-loaded with the core purpose in the first phrase. The domain/category information is additional but not redundant. It avoids unnecessary words, though it could be slightly more informative without losing conciseness.

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 complexity (a mathematical operation with two parameters, one with a default), lack of annotations, and no output schema, the description is incomplete. It doesn't explain the 'p' parameter's role, potential constraints (e.g., p >= 1), or what the tool returns. For a tool with 0% schema coverage, more context is needed to be fully helpful.

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 for undocumented parameters. It mentions 'norm (magnitude)' and 'vector', which partially explains the 'vector' parameter, but does not clarify the 'p' parameter (e.g., that it's the p-norm order, with default 2 for Euclidean norm). The description adds minimal semantic value beyond the bare schema.

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 the tool's purpose: 'Calculate the norm (magnitude) of a vector'. It specifies the verb ('calculate') and resource ('norm of a vector'), and includes domain/category context ('Domain: linear_algebra.vectors, Category: general'). However, it does not explicitly differentiate from sibling tools like 'euclidean_norm' or 'manhattan_norm', which are likely related but not directly named as alternatives.

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. It mentions the domain and category but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if this is for general p-norms or specific cases, or when to choose it over sibling tools like 'euclidean_norm' (which might be a specific case with p=2).

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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