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IBM

MCP Math Server

by IBM

element_wise_divide

Divide corresponding elements of two vectors to perform element-wise division in linear algebra operations.

Instructions

Divide two vectors element-wise (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
Behavior1/5

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. However, it only states the operation ('Divide two vectors element-wise') without any behavioral details: it doesn't mention error handling (e.g., division by zero, mismatched vector lengths), output format, numerical precision, or side effects. For a mathematical operation tool with no annotation coverage, this is inadequate.

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: a single sentence with domain and category annotations. It's front-loaded with the core operation and wastes no words. Every part ('Divide two vectors element-wise') directly contributes to understanding the tool's purpose, making it efficient and well-structured.

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's mathematical nature, 2 parameters, 0% schema description coverage, no annotations, and no output schema, the description is incomplete. It lacks essential context: behavioral traits (error handling, output), parameter details (vector format, constraints), and usage guidelines. While concise, it doesn't provide enough information for reliable tool invocation in a computational 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?

The input schema has 2 parameters (vector_a, vector_b) with 0% description coverage in the schema. The description adds no parameter semantics beyond naming them implicitly ('two vectors'). It doesn't explain what the vectors represent, expected formats (e.g., arrays of numbers as strings), constraints (e.g., same length), or examples. With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.

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: 'Divide two vectors element-wise' with the domain 'linear_algebra.vectors' and category 'general'. It specifies the verb ('Divide') and resource ('two vectors') with the operation type ('element-wise'), making the purpose unambiguous. However, it doesn't explicitly differentiate from sibling tools like 'divide' (which might be scalar division) or 'element_wise_multiply', though the 'element-wise' qualifier provides some implicit distinction.

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 doesn't specify scenarios, prerequisites, or exclusions. For example, it doesn't clarify if vectors must be same length, handle zero-division cases, or when to choose this over scalar division tools. With many sibling tools (e.g., 'divide', 'element_wise_multiply'), the lack of comparative guidance is a significant gap.

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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