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math-reasoning-mcp

by TeleEng

laplace_transform_signal

Compute the Laplace transform of a causal signal f(t) to obtain F(s) and its convergence condition.

Instructions

Computes the Laplace transform of a causal signal f(t). Returns F(s) and the convergence condition.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
expressionYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

A3.6/5.0
Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

The description discloses the return value (F(s) and convergence condition) but does not mention any assumptions about the input format, handling of non-causal signals, or potential errors. No annotations are provided to supplement.

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 concise, consisting of two clear sentences that don't waste words. It front-loads the main action and then specifies the output.

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

Completeness3/5

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

The description provides the basic output but lacks details about input format, edge cases, or limitations. Given that there is no output schema, the description could be more informative to fully understand the tool's behavior.

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 sole parameter 'expression' has no schema description, and the tool description does not elaborate on what constitutes a valid expression. It is unclear if it expects a symbolic expression string, a function, or a specific notation.

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

Purpose5/5

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

Clearly states that the tool computes the Laplace transform of a causal signal, with a specific verb 'computes' and resource 'Laplace transform of a causal signal f(t)'. It also mentions the output includes F(s) and convergence condition, which helps distinguish from other transforms.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies the use case (when a Laplace transform is needed), but does not explicitly contrast with alternative tools like inverse Laplace or Fourier transform. It does not provide selection criteria compared to siblings.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.