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IBM

MCP Math Server

by IBM

phase_shift_analysis

Analyze phase relationships between waves to determine synchronization, interference patterns, or signal alignment in trigonometric wave analysis.

Instructions

Analyze phase relationships between waves. (Domain: trigonometry, Category: wave_analysis)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
phase_diffYes
frequencyNo
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. The description only states what the tool does ('Analyze phase relationships') without any information on how it behaves—such as whether it performs calculations, returns data, requires specific inputs beyond parameters, or has side effects. 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 extremely concise—a single sentence with domain and category annotations. It is front-loaded with the core purpose and wastes no words. Every part of the description earns its place by providing essential context without redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness1/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of wave analysis, the lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not explain what the tool returns, how to interpret results, or provide any behavioral context. For a tool with parameters and mathematical operations, this leaves critical gaps in understanding its functionality.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters1/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, and the description does not mention parameters at all. With two parameters ('phase_diff' and 'frequency'), one required, the description fails to add any meaning beyond the schema. It does not explain what these parameters represent, their units, or how they relate to the analysis, leaving them completely 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: 'Analyze phase relationships between waves' with domain and category context. It specifies the verb ('Analyze') and resource ('phase relationships between waves'), making the intent unambiguous. However, it does not differentiate from sibling tools like 'wave_amplitude_analysis' or 'wave_interference', which are related but not explicitly contrasted.

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 ('trigonometry') and category ('wave_analysis'), which implies context, but does not specify scenarios, prerequisites, or exclusions. With many sibling tools in wave analysis and trigonometry, the lack of explicit usage guidelines leaves the agent to infer applicability.

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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