calculate_quadratic_equation

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

With no annotations, description carries full burden. Mentions output fields (roots, discriminant, vertex) and handles complex numbers, but does not address edge cases like a=0 (not a quadratic) or error behavior.

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?

Three concise sentences, front-loaded with purpose and output. No redundant information.

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?

Output schema exists, so return values are covered. Description includes discriminant analysis and vertex, but misses edge case handling (e.g., a=0) for full completeness.

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 has 100% coverage with descriptions for each coefficient. Description merely repeats 'Inputs: coefficients a, b, c' without adding constraints (e.g., a ≠ 0) or further semantics beyond 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?

Clearly states 'Solve quadratic equation ax²+bx+c=0 with discriminant analysis', specifying verb and resource. However, it does not explicitly distinguish from sibling tools like 'calculate_equation' for general 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?

Indicates use for 'math homework or physics problems' but lacks when-not-to-use or explicit alternatives. Points to list_bundles for related calculators, but that is indirect.

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