jacobi_symbol

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

No annotations are provided, so the description carries full behavioral disclosure burden. It states the computation and the odd-n constraint, but doesn't describe error handling (e.g., what happens if n is even), input validation, performance characteristics, or output format. For a mathematical function with no annotation coverage, this leaves significant behavioral gaps.

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 extremely concise—one sentence plus domain/category tags—with zero wasted words. It front-loads the core purpose and constraint efficiently. Every element (computation, symbol notation, constraint, tags) earns its place 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?

Given the tool's mathematical nature, 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain the Jacobi symbol's definition, return values (-1, 0, 1), or edge cases. The domain/category tags help but don't substitute for functional 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 description coverage is 0%, so the description must compensate. It names the parameters implicitly via '(a/n)' and adds the constraint 'for odd n', giving some semantic meaning to n. However, it doesn't explain what a and n represent mathematically (integer arguments to the Jacobi symbol), their valid ranges beyond the odd requirement, or the relationship between them.

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 tool's purpose: 'Compute Jacobi symbol (a/n) for odd n.' It specifies the mathematical operation (compute), the resource (Jacobi symbol), and includes a domain constraint (odd n). However, it doesn't explicitly differentiate from sibling tools like 'legendre_symbol' or 'is_quadratic_residue', which are related modular arithmetic functions.

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 minimal usage guidance through the constraint 'for odd n', but offers no explicit when-to-use advice, no comparison with alternatives (like legendre_symbol for prime modulus), and no prerequisites. The domain/category tags ('arithmetic, modular_arithmetic') give some context but aren't actionable guidelines.

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