math_quadratic_solver

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

Annotations already declare readOnlyHint=true, destructiveHint=false, and idempotentHint=true. The description adds valuable behavioral context: 'Runs locally on the numbers you provide: read-only, non-destructive, contacts no external service, and is rate-limited (60 requests/minute).' It also details the output for the solve operation, which is not in annotations.

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 at 8 sentences, front-loaded with purpose, structured by operation, and every sentence adds value. It covers purpose, operations, outputs, usage guidance, and behavioral traits without redundancy.

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?

The tool has three operations and 7 parameters. The description explains all operations, required parameters per operation, degenerate cases (a=0), output details, and behavioral traits. It is completely adequate given the schema and annotations.

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 baseline is 3. The description adds high-level context about which operation uses which parameters but does not deepen the meaning of individual parameters beyond what the schema already provides.

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 it solves quadratic equations, evaluates f(x), and builds monic quadratics from roots. It explicitly distinguishes from sibling tools math_scientific_calculator and math_matrix_calculator, which prevents confusion.

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 explicit when-to-use instructions: 'Use this for second-degree polynomial algebra; use math_scientific_calculator for general expression evaluation and math_matrix_calculator for linear algebra.' It also explains the three operations and their required parameters.

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