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IBM

MCP Math Server

by IBM

scalar_projection

Calculate the scalar projection of one vector onto another to determine component length along a direction. Use this linear algebra function to analyze vector relationships in mathematical computations.

Instructions

Calculate scalar projection of one vector onto another (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
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 like input format expectations (e.g., numeric arrays vs. strings), error handling, or output specifics. This is inadequate for a tool with parameters and no output schema.

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 a single, efficient sentence that directly states the tool's purpose with no wasted words. It is appropriately sized and front-loaded, making it easy to parse quickly.

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 tool has 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It fails to explain parameter meanings, behavioral details, or output format, which are essential for correct tool invocation in this context.

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 schema provides no parameter details. The description does not compensate by explaining what 'vector_a' and 'vector_b' represent, their expected formats (e.g., numeric arrays), or any constraints (e.g., same dimension). This leaves parameters largely undocumented.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states the tool calculates scalar projection of one vector onto another, which is a clear purpose. However, it does not differentiate from sibling tools like 'vector_projection' or 'dot_product', which are closely related operations in linear algebra. The domain and category tags add context but do not specify uniqueness.

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 'vector_projection' or 'dot_product'. The description lacks any context about prerequisites, typical use cases, or comparisons to sibling tools, leaving the agent without usage 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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