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

Annotations already declare readOnly, non-destructive, and closed-world, so the safety profile is covered. The description adds that results are classified as unique, none, or infinite solutions, which is genuinely useful behavioral context, but it says nothing about equation syntax expectations or failure modes.

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 short sentences, scope first and result behavior second, with no filler. Every clause contributes information an agent can act on.

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 annotations covering safety, an output schema covering return values, and only one parameter, the description supplies the remaining essentials: supported system size and solution classification. Minor gap is that equation-string formatting constraints are left entirely to the schema example.

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?

There is a single required parameter at 100% schema description coverage with an inline example, so the schema carries the burden. The description adds no detail on how equations must be formatted (variable names, ordering of terms), so it does not go beyond the structured data.

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 verb and resource ('solve ... linear systems') and pins the supported size to 2×2 or 3×3, which cleanly separates it from single-equation siblings like calculator_linear_equation. It never names an alternative sibling, so differentiation is implicit rather than explicit.

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 '2×2 or 3×3' clause implies when this tool applies and implicitly excludes larger systems, but there is no explicit when-to-use/when-not guidance or pointer to substitutes such as calculator_numerical_solve for nonlinear cases. Usage is inferable from scope alone.

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