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

The annotations already cover safety properties such as readOnlyHint, idempotentHint, and destructiveHint=false. The description adds useful behavioral context beyond the annotations: exact-division requirements, rejection of zero divisors and non-integral quotients, payment cost, and an HTTPS alternative endpoint.

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 purpose and core constraints are front-loaded, and every sentence adds useful information: mathematical requirements, rejection behavior, payment details, and an alternate HTTPS endpoint. There is no obvious filler.

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 two-parameter polynomial arithmetic tool with annotations covering read-only and idempotent behavior, the description is mostly complete. It covers preconditions, cost, and access details; the main remaining gap is the lack of explicit parameter mapping and output format detail, though the operation is mathematically standard.

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 carry parameter meaning. It explains that the inputs represent integer polynomials and that one is a divisor subject to non-zero and integral-division constraints, but it does not explicitly map the parameters a and b to dividend and divisor or clarify coefficient ordering.

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 a specific operation and resource: the exact quotient of two integer polynomials. It is clear enough to distinguish division from related sibling tools like poly_add, poly_mul, and poly_deriv, though it does not explicitly name or route against those alternatives.

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 important applicability conditions: the divisor must be non-zero and the division must be integral at each leading step. However, it does not explicitly say when to choose this tool over sibling polynomial operations or what alternatives to use when exact integer division is impossible.

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