fourier_series_approximation

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

No annotations are provided, so the description carries the full burden. It mentions the tool computes an approximation, which implies it is a read-only operation, but does not disclose any behavioral traits such as computational complexity, accuracy limitations, or output format. For a tool with 5 parameters and no annotations, this is a significant gap in transparency.

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 concise and front-loaded with the core purpose. The domain/category tags are somewhat redundant but do not significantly detract. It is appropriately sized for a tool with this complexity, with no wasted sentences.

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 tool's complexity (5 parameters, no annotations, no output schema), the description is incomplete. It does not explain what the tool returns, how the approximation is computed, or any constraints on inputs. The lack of parameter semantics and behavioral transparency makes it inadequate for effective use.

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%, meaning none of the 5 parameters are documented in the schema. The description does not add any meaning to parameters like 'f', 'period', 'n_terms', 'x', or 'n_samples'. It fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.

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 the tool 'Compute Fourier series approximation of periodic function', which provides a clear verb ('Compute') and resource ('Fourier series approximation'). However, it does not distinguish from sibling tools like 'fourier_coefficients_basic' or 'harmonic_analysis', and the domain/category tags add minimal value. The purpose is clear but lacks sibling differentiation.

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 mentions a domain and category, but this does not help an agent choose between this and related tools (e.g., 'fourier_coefficients_basic', 'harmonic_analysis', or 'maclaurin_series'). There is no explicit or implied context for usage.

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