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IBM

MCP Math Server

by IBM

wave_amplitude_analysis

Analyze amplitude and phase of sinusoidal waves to understand wave characteristics and behavior in trigonometric applications.

Instructions

Analyze amplitude and phase of a general sinusoidal wave. (Domain: trigonometry, Category: wave_analysis)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
amplitudeYes
frequencyYes
phaseNo
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 states the tool analyzes amplitude and phase, implying a read-only computation, but does not detail output format, error conditions, or computational limits. For a tool with no annotations, this leaves significant behavioral gaps, such as whether it returns a single value, a report, or has any side effects.

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, consisting of a single sentence that directly states the purpose, followed by domain and category in parentheses. There is no wasted verbiage, and the structure is efficient. However, it could be more informative without sacrificing brevity.

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 complexity (wave analysis with 3 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain what the analysis entails, the output format, or any behavioral nuances. For a computational tool with undocumented parameters and no structured output, this description is insufficient to guide effective use.

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 3 parameters with 0% description coverage, meaning no parameter details are provided in the schema. The description does not add any parameter semantics—it does not explain what 'amplitude', 'frequency', or 'phase' represent, their units, or valid ranges. This fails to compensate for the low schema coverage, leaving 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 'Analyze amplitude and phase of a general sinusoidal wave', which provides a clear verb ('Analyze') and resource ('amplitude and phase of a general sinusoidal wave'). However, it does not differentiate from sibling tools like 'amplitude_from_coefficients' or 'phase_shift_analysis', making it somewhat vague in comparison. The domain and category annotations add context but do not enhance specificity.

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. Without explicit when-to-use instructions or named alternatives, the agent lacks clear 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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