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IBM

MCP Math Server

by IBM

scalar_multiply

Multiply a vector by a scalar value to scale its magnitude in linear algebra operations. This tool performs scalar-vector multiplication for mathematical computations.

Instructions

Multiply a vector by a scalar value (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vectorYes
scalarYes
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 mentions the domain ('linear_algebra.vectors') and category ('general'), but fails to describe key behavioral traits such as input validation (e.g., handling of non-numeric strings in the vector array), error conditions, or the format of the output (since there is no output schema). This leaves significant gaps in understanding how the tool behaves.

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?

The description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted language, and the domain/category information is efficiently appended. This makes it easy to parse and understand quickly, earning a high score for 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 of a mathematical operation with two parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It fails to provide necessary context such as parameter details, behavioral expectations, or output format. While the domain/category hint is helpful, it does not compensate for the lack of essential information needed for correct tool invocation.

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%, meaning the input schema provides no descriptions for the 'vector' and 'scalar' parameters. The description adds minimal semantic value by naming the parameters ('vector' and 'scalar') but does not explain their expected formats, constraints, or usage. For example, it does not clarify that 'vector' is an array of strings (likely representing numbers) or how the scalar multiplication is applied. This insufficient compensation for the low schema coverage results in a low score.

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: 'Multiply a vector by a scalar value.' It specifies the verb ('Multiply') and the resources ('vector' and 'scalar'), and the domain/category context ('linear_algebra.vectors, Category: general') provides additional clarity. However, it does not explicitly differentiate from sibling tools like 'element_wise_multiply' or 'matrix_scalar_multiply', which could cause confusion in selection.

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 lacks context about when this operation is appropriate, such as for linear algebra computations, and does not mention sibling tools like 'element_wise_multiply' or 'matrix_scalar_multiply' that might be relevant for similar tasks. This absence of usage instructions leaves the agent without clear direction.

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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