Equation solver

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

Going well beyond readOnlyHint/idempotentHint, it discloses output behavior the agent could not otherwise predict: exact rational or surd roots, complex roots, 10-significant-digit fallback for cubics, Gauss–Jordan for systems, and detection plus parametrisation of no-solution/infinite-solution cases. Worked steps are also promised, which matters for how the result should be presented.

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?

A single dense sentence front-loads the verb and the equation types, with progressively finer detail after it. It is information-rich rather than padded, though the website link and the "like the website" phrasing consume space without helping tool selection.

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 no output schema, the description carries the return-value burden and does so at a high level (exact roots, worked steps, precision, parametrised infinite solutions). It stops short of describing the actual response shape, so an agent knows what to expect conceptually but not structurally.

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 coverage is 100%, so the baseline is 3, but the description adds real semantics: it maps each `type` value to the coefficient layout and spells out the accepted string encodings ("3/4", "-1 1/2", e-notation) that the schema only hints at with number|string. It does not explicitly restate the `system` augmented-matrix row shape, leaving that to the schema.

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?

States a specific verb ("solve") and resource ("equations") and then enumerates exactly which equation families are in scope: linear a·x + b = c, quadratic, cubic, and 2x2/3x3 linear systems. That enumeration cleanly separates it from siblings such as calc_expression (arithmetic evaluation) or calc_fraction, so an agent can route without opening the schema.

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 supported-type list implicitly defines when to use it and the coefficient formats accepted ("integers, decimals, fractions, mixed numbers, e-notation") tell the agent what input is legal. It never names an alternative tool or states an explicit when-not condition (e.g. use calc_expression for plain arithmetic), so it stops short of a 5.

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