quadratic_forms

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

No annotations are provided, so the description must fully disclose behavior. It omits that reduced forms are typically for negative discriminants D < 0, and does not state what happens with positive D. The schema only notes D ≡ 0,1 mod 4 and D ≠ 0, missing the sign constraint.

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 a single concise sentence that efficiently communicates the tool's core function without any unnecessary words. However, it is slightly under-specified for the complexity of the operation.

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 availability of an output schema and a single parameter, the description is minimally adequate. However, it lacks clarity on the mathematical context (e.g., D must be negative) and does not help the agent distinguish from closely related siblings.

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?

With 100% schema description coverage for the single parameter D, the baseline is 3. The tool description adds no further parameter guidance beyond 'compute reduced binary quadratic forms of discriminant D', which is already implied by the schema.

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 verb 'Compute' and the resource 'reduced binary quadratic forms of discriminant D', which is specific and distinct from sibling tools like qfbclassno (class number) and qfbsolve (solve equations).

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?

No guidance on when to use this tool versus alternatives such as qfbclassno, qfbsolve, or quadregulator. The description does not mention prerequisites or typical use cases, leaving the agent without selection context.

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