solve_linear_system

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

With no annotations, the description carries full behavioral burden. It discloses the key domain constraint (A square and non-singular), which tells the agent the tool is invalid for singular or non-square matrices. It does not describe error behavior, numerical method, or precision, leaving some behavioral gaps.

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 description is a single, front-loaded sentence with no wasted words. It states the operation and the key precondition immediately, making it easy to parse.

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?

An output schema exists, so return values need not be explained. For a two-parameter mathematical solver, the description covers the core operation and its main validity constraint. It could be more complete by noting behavior on singular matrices or parameter shape expectations, but is largely sufficient.

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 compensate. The equation 'A x = b' implicitly defines the roles of both parameters: A as the coefficient matrix and b as the right-hand side vector. However, it does not specify expected shapes (e.g., n×n for A, length n for b) or ordering, beyond the square constraint on A.

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 mathematical operation (solving A x = b for x) and adds a validity constraint (A square and non-singular). This clearly distinguishes it from sibling matrix operations like matrix_multiply or matrix_inverse. However, it does not explicitly name or contrast with the closest alternative, solve_symbolic_equation.

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 gives a prerequisite (A must be square and non-singular), which implies when the tool is applicable. It does not explain when to choose this over using matrix_inverse and multiplication, nor when to prefer a symbolic solver. Guidance is implied rather than explicit.

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