frontiermath_algebraic_geometry

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It merely says 'perform computations' without stating whether the operation is read-only, what output to expect, or that the only supported operation is count_points. This leaves significant ambiguity for an agent deciding whether to call it.

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 sentence, front-loaded with the action and resource. It contains no filler or redundancy, earning a high conciseness score despite the 'etc.' being slightly lazy.

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?

With no output schema and no annotations, the description should clarify return values and limitations. It only gives a vague 'etc.' and doesn't explain what the result of 'curve point counting' looks like. The tool appears simple, but the missing return/behavior details leave the description incomplete.

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%—all three parameters (curve, field, operation) have clear descriptions. The tool description adds no parameter-specific meaning, so the baseline score of 3 applies per the rubric.

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 states the tool performs algebraic geometry computations, with a concrete example (curve point counting). This clearly identifies the resource domain and distinguishes it from sibling math tools (number theory, finite fields, representation theory). However, the verb 'perform' is generic and 'etc.' introduces vagueness.

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?

Usage is implied by the domain name and description—this tool is for algebraic geometry problems—but there is no explicit guidance about when to use it versus siblings, nor any exclusions or prerequisites. The description relies on the user to infer fit from the tool name and example.

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