solve_algebraically

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

With no annotations, the description carries the burden and usefully discloses the prerequisite that expr_key and solve_for_var_name refer to previously introduced objects. It also states that the return value is a LaTeX string for the solution set or an error message string; it does not explicitly discuss side effects or mutation, but the solver nature and return behavior are clear.

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 front-loaded with the core action, then uses clear Args and Returns sections. Every sentence adds necessary information, and there is no redundant restatement of the tool name.

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 three-parameter algebraic solver with an output schema, the description covers the core semantics, parameter meanings, domain options, default, and return type. It is nearly complete, though it could further clarify how this differs from system-solving or inequality-solving siblings.

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 fully, and it does: all three parameters are explained. It clarifies that expr_key and solve_for_var_name refer to previously introduced objects, lists the domain choices, and states the default Domain.COMPLEX.

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: solves an equation, explicitly defined as expression = 0, algebraically for a given variable. This distinguishes it from siblings such as solve_inequality and the system solvers, which handle inequalities or multiple equations rather than a single algebraic 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 implies when the tool is applicable by specifying that it solves expression = 0 for a variable. However, it does not explicitly say when to use this rather than solve_linear_system, solve_nonlinear_system, or other alternatives, nor does it state exclusions.

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