sigma

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

With no annotations, the description must disclose behavioral traits. It only states the computation but does not mention domain restrictions (e.g., n must be positive integer, mentioned in schema but not description), side effects, or edge cases.

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?

Single sentence with no wasted words. Front-loaded with purpose.

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?

For a simple computation, the description is minimal but adequate. However, it lacks any explanation of return values or behavior, despite the context indicating an output schema exists (not shown).

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 covers both parameters with 100% description coverage. The description adds no semantic value beyond what the schema already provides, so baseline score of 3 applies.

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 mathematical operation: computing the sum of k-th powers of divisors of n. It uses specific verb 'compute' and resource 'sum of k-th powers of divisors', which distinguishes it from arithmetic siblings like 'factor' or 'isprime'.

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?

No guidance on when to use sigma vs other tools. Siblings include many math functions, but there is no comparison or context for selection.

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