check_time_invariance

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

No annotations are provided, but the description itself fully discloses the algorithm: it computes y(t-t0) vs T{x(t-t0)} for memoryless systems and y[n-n0] vs T{x[n-n0]} for difference systems. It also states the return value includes a symbolic proof, giving the agent a clear behavioral model.

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 a one-line summary followed by clear sections for each system_type. The repeated computation phrasing could be slightly more compact, but every sentence contributes useful information and the structure aids scanning.

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 two-parameter tool with no annotations, the description supplies enough context to call it correctly: supported system types, expected expression variables, the equality check performed, and the symbolic-proof return. The existence of an output schema means return details are not required in the description.

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 must compensate for both parameters. It explains system_type values ('memoryless' and 'difference') and specifies what variables the system_expression should contain in each mode. This adds meaning far beyond the bare schema property names.

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 specific verb and resource: 'Checks if a system is time-invariant.' It clearly identifies the tool's purpose and distinguishes it from siblings like check_linearity because time invariance is a distinct property. The detailed per-system_type behavior further clarifies what the tool operates on.

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 clear context on how to use the tool for each supported system_type, including expected variable conventions. It does not explicitly mention alternative tools or exclusion criteria, so it stops short of full when-to-use-versus-alternatives guidance.

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