continuous_convolution

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

With no annotations, the description carries the full transparency burden. It discloses two important behavioral traits: Heaviside terms are handled automatically, and signals without Heaviside terms are assumed zero for t < 0. It does not mention output formatting or edge cases, but the output schema covers return structure.

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?

Two short sentences front-load the operation and then add the two necessary caveats: Heaviside handling and causality. There is no filler, redundancy, or irrelevant detail.

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 convolution tool, the description provides the core mathematical meaning, causality assumption, and Heaviside handling, and an output schema exists so return values need not be described. The main missing piece is explicit parameter format, which leaves the agent to infer how the f_t and g_t strings should be written.

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?

The input schema contains only two untyped string fields with 0% description coverage, so the description must compensate. It establishes that f_t and g_t are continuous-time causal signal expressions and that Heaviside terms may be embedded, but it gives no concrete syntax, variable conventions, or examples for these strings.

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 uses a specific verb ('computes') and identifies the exact operation by name and formula: continuous-time convolution (f * g)(t). It also sets the scope to causal signals, which clearly distinguishes it from the transform and discrete-analysis siblings such as laplace_transform_signal, dtft_signal, and compute_fft.

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 states the tool is for causal continuous-time signals and explains the Heaviside/causality assumption, giving the agent a clear context for when to invoke it. However, it does not name alternative tools or explicitly say when not to use it, so some usage routing is left implicit.

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