z_transform

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('calculate'), without mentioning computational aspects like performance, error handling, or output format. For a mathematical tool with no annotations, this is a significant gap, as it doesn't address potential limitations or how results are returned.

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 with a single sentence: 'Calculate the Z-transform of a function'. It wastes no words and directly communicates the core purpose without unnecessary elaboration, making it efficient and easy to parse.

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 the complexity of a mathematical transform tool with no annotations and no output schema, the description is incomplete. It doesn't explain what the output looks like (e.g., a symbolic expression, numerical result, or error message), nor does it provide examples or context for usage. This leaves significant gaps for an AI agent to understand how to interpret results or handle edge cases.

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 schema description coverage is 100%, with clear descriptions for all parameters (e.g., 'Function of discrete time' for 'expression'). The description adds no additional parameter semantics beyond what the schema provides. According to the rules, when schema coverage is high (>80%), the baseline score is 3, as the schema adequately documents the parameters without needing extra explanation in the description.

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 clearly states the tool's purpose: 'Calculate the Z-transform of a function'. It specifies the verb 'calculate' and the resource 'Z-transform', which is a well-defined mathematical operation. However, it doesn't explicitly differentiate from sibling tools like 'fourier_transform' or 'laplace_transform', which are related transforms, so it doesn't reach the highest score.

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 provides no guidance on when to use this tool versus alternatives. It doesn't mention sibling tools like 'fourier_transform' or 'laplace_transform', nor does it explain the specific contexts or mathematical problems where the Z-transform is applicable (e.g., discrete-time signal processing vs. continuous-time for Laplace). Without such context, users must infer usage based on domain knowledge.

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