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IBM

MCP Math Server

by IBM

triple_scalar_product

Calculate the triple scalar product of three 3D vectors to determine volume and orientation in linear algebra applications.

Instructions

Calculate the triple scalar product of three 3D vectors (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
vector_cYes
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. It mentions the calculation but does not disclose behavioral traits such as input validation (e.g., vector length must be 3), error handling, numerical precision, or output format. For a mathematical tool with no annotations, this is a significant gap in transparency.

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 in a single sentence, with no wasted words. It efficiently states the core purpose and includes domain/category information. However, it could be slightly more structured by separating usage notes or parameter details, but it's appropriately sized for its content.

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 (mathematical operation with 3 parameters), no annotations, 0% schema coverage, and no output schema, the description is incomplete. It lacks details on input validation, output format, error conditions, and practical usage examples. For a tool with no structured support, the description should provide more context 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?

The schema description coverage is 0%, and the description does not add any parameter semantics. It names the parameters ('three 3D vectors') but does not explain their format (e.g., arrays of numbers as strings), constraints (e.g., must have 3 elements), or examples. With 3 undocumented parameters, the description fails to compensate for the lack of schema documentation.

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 triple scalar product of three 3D vectors.' It specifies the verb ('calculate'), resource ('triple scalar product'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'dot_product' or 'cross_product' beyond the domain/category hint, which is why it's not a 5.

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 ('linear_algebra.vectors') and category ('general'), but does not specify scenarios, prerequisites, or comparisons to sibling tools (e.g., 'dot_product', 'cross_product', 'triple_vector_product'). This lack of explicit usage context limits its helpfulness.

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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