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

With no annotations, the description bears the full behavioral burden. It discloses that the operation performs an exact equality check, explicitly does not invert the matrix, and refuses float inputs. This is meaningful behavioral context. It stops short of describing return values or error handling for refused inputs.

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?

Five short fragments, each adding distinct information: identity, constraints, operation, non-inversion, and input policy. There is no filler, and the most important scope-limiting facts are front-loaded.

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?

Given no output schema and no annotations, the description omits the return behavior of the check, the required string format for matrix and rationals, and the outcome when invalid inputs are passed. It conveys overall intent well but is not fully actionable for an agent making an automated call.

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?

The input schema provides only parameter names and types with zero descriptions. The description compensates by mapping matrix to integer A and b/x to rational values, and by adding the n<=2 restriction. Yet it leaves the string encoding of rationals and the matrix representation unspecified, so parameters remain only partially explained.

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 specifies a precise verb ('Checks'), a clear resource ('HHL'), and an exact mathematical condition (A x = b). It also distinguishes itself from solvers by stating 'Does not invert', which separates it from siblings that might perform inversion or transformation.

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 clear applicability constraints: n<=2, integer A, rational b and x, and 'Floats refused'. This gives an agent concrete guidance about when inputs are acceptable. However, it does not explicitly name alternative tools or state fallback options when these constraints are violated.

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