check_exercise

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

Beyond the annotations the description discloses genuinely useful behavior: no-solution, multiple-solution, non-linear, or variable-denominator cases return "待复核" (pending review), and expressions must use explicit '*'. It does not address the side effects implied by readOnlyHint=false / idempotentHint=false, so the non-read-only nature of the tool remains unexplained.

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?

It is a single dense paragraph with the core purpose front-loaded and no filler; each clause (modes, examples, edge cases, scope) carries information. The density makes it slightly harder to scan, but nothing is wasted.

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 an output schema present, return values need not be explained, and the description covers modes, format requirements, edge-case behavior, and scope limits. The main remaining gap is the absence of any mention of side effects, despite readOnlyHint=false.

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 the params, and it does: it explains both values of `kind` and the default, the `expression` format (explicit '*', with examples), and `proposed_answer` (supplied without 'x=', e.g. 2). This meaningfully compensates for the empty schema documentation.

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 gives a specific verb+resource ("精确有理数验算") and then pins down the two exact verification modes it performs: polynomial identity in variable x and the unique solution of a simplified one-variable linear equation, each with concrete examples. It is clearly understandable in isolation, though it does not explicitly distinguish itself from related sibling tools such as review_practice_attempt or record_practice.

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?

It states when each mode applies (polynomial_identity is the default; linear_equation handles simplified linear equations) and gives worked examples for both. It also adds a scope exclusion – it only verifies the given expression and does not guarantee intent/answer matching or teaching effect – but it does not point to any alternative tool for those other needs.

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