elliptic_curve_operation

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

No annotations are provided, so the description must carry the transparency burden. It mentions the mathematical domain (over Q) and input form, but does not disclose operational behavior such as whether a Sage session is required, whether the session parameter affects state, or error behavior. This is a moderate gap for a compute tool.

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 sentences efficiently pack the tool's purpose, scope, and a usage preference. No redundant wording; all information earns its place.

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 is moderately complex but the output schema and parameter descriptions cover much. The description is concise but leaves out session-related behavior and edge cases; however, given the output schema, it's sufficient for most agents to use correctly.

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 coverage is 100%, so the baseline is 3. The description lists the operation names which align with the operation property, and mentions Weierstrass coefficients, but does not add significant detail beyond the schema's own descriptions of coefficients and operation.

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 computes elliptic curve invariants over Q (rank, torsion order, discriminant, j-invariant, conductor, generators) from Weierstrass coefficients. It names specific outputs, distinguishing it from generic math tools like evaluate_sage or number_theory_operation.

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?

Explicitly recommends 'Prefer this over evaluate_sage for curve invariants,' giving direct guidance on when to choose this tool over a sibling. This is exactly what usage guidelines should provide.

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