inverse_fourier_transform_expression

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

With no annotations provided, the description carries the full behavioral burden. It discloses the return type ('Spatial/time-domain function f(x)') and provides worked examples with expected outputs, but it does not discuss assumptions, convergence conditions, or failure modes when the inverse transform does not exist.

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 well-organized into Use cases, Args, Returns, and Examples sections, with the core definition front-loaded. Some decorative content like the 'PHASE 2' banner and 'PK' note is non-essential, but the structure makes the longer length acceptable.

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?

For a symbolic transform tool with an output schema, the description covers input semantics, defaults, use cases, return type, and gives concrete expected outputs. It lacks explicit normalization-convention details and limitations, but is sufficiently complete for an agent to select and invoke the tool correctly.

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 Args block is essential and fully compensates. It explains that expression is the frequency-domain expression F(k), freq_var is the frequency variable (default 'k'), and space_var is the space/time variable (default 'x'), adding semantic meaning not available in the schema.

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 opens with a precise mathematical definition: 'Inverse Fourier transform: F(k) → f(x).' and states it 'Transforms frequency domain back to spatial/time domain.' This uses a specific verb and resource, clearly distinguishing it from forward Fourier and Laplace transform siblings.

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 lists four concrete use cases (reconstruct signal from spectrum, inverse filter design, synthesize periodic patterns, diffusion problem solutions) that signal when to use the tool. It does not explicitly name alternatives or exclusions, but the forward/inverse distinction and sibling tool names provide adequate context.

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