polynomial_ops

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

With no annotations, the description carries the full burden, and it discloses only the coefficient-ordering convention. It says nothing about what is returned (coefficients vs. expression string), how mismatched-length polynomials are handled in add, whether results are normalized, or error behavior for invalid operations.

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 tight sentences: the operation list is front-loaded and the coefficient-ordering constraint follows immediately. Nothing is padded and nothing extraneous is included.

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 4-parameter math tool with full schema coverage but no output schema, the description is minimally adequate. The most significant gap is the return contract — an agent cannot tell whether evaluate returns a scalar and derivative returns coefficients — which the missing output schema would otherwise have covered.

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 100%, so the schema already documents x, coefficients, coefficients2 and the operation enum. The description restates the 'highest degree first' convention already present in the coefficients schema field and adds no new parameter meaning, so the baseline 3 applies.

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 names a specific resource (polynomials) and enumerates the concrete operations performed (evaluate, derivative, integral, add, multiply), so an agent knows exactly what capability is exposed. It does not differentiate from any near-sibling, but no sibling tool in the list overlaps meaningfully with polynomial algebra.

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?

Listing the operations implies when each is applicable, but there is no explicit guidance on selecting among them, no prerequisites, and no mention that add/multiply require a second polynomial argument. Usage is inferable rather than stated.

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