fourier_transform_signal

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

No annotations are present, so the description carries the full burden of behavioral disclosure. It only says the transform is computed and F(w) is returned, but it omits whether the computation is symbolic, what assumptions are made, how invalid expressions are handled, or any other operational behavior beyond the basic operation.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded: the first sentence states the operation and the second states the result. There is no filler or redundant material, making it easy for an agent to parse quickly.

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

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

Given that this is a single-parameter math tool with an output schema, the basic input-to-output contract is communicated: f(t) produces F(w). However, the description leaves gaps around when to choose this tool, how to format the expression argument, and what limitations or assumptions apply, so completeness is only moderate.

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

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

Schema description coverage is 0%, so the description is the only source of meaning for the required 'expression' parameter. It does indicate that the expression represents the signal f(t), which is useful, but it does not specify the expected syntax, the independent variable, or how multi-variable expressions are interpreted.

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

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

The description states a specific verb ('Computes') and resource ('continuous Fourier transform of a signal f(t)'), and clarifies the output as F(w). The qualifier 'continuous' helps distinguish it from discrete transforms like compute_fft and dtft_signal, though no sibling is explicitly named.

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

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

The description gives no explicit guidance about when to use this tool versus alternatives such as laplace_transform_signal, inverse_fourier_transform_signal, or compute_fft. The word 'continuous' is the only implicit hint, but there is no stated decision rule or exclusion context.

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