chinese_remainder

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

With no annotations, the description carries the full behavioral burden, but it discloses almost nothing: not whether the system may be inconsistent (no solution), whether moduli must be pairwise coprime, what happens on failure, or what the output looks like. 'Generalised' is the only behavioral hint, and it is left undefined.

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 front-loaded sentence with no filler or redundancy. It is efficient, though the brevity contributes to the disclosure gaps noted elsewhere.

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 two-parameter math utility with fully documented parameters and no output schema, the definition is minimally sufficient to invoke the tool. It is nonetheless thin on edge-case behavior (inconsistent systems, non-coprime moduli) that matters for a generalised CRT solver.

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 100% — both moduli and remainders are documented in the schema as positive integers and remainders respectively. The description adds no additional parameter meaning, so the baseline of 3 applies.

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 concrete verb and resource: 'Solve simultaneous congruences,' with the added qualifier 'generalised' hinting at non-coprime modulus support. However, it never names or distinguishes itself from the sibling tool chinese_remainder_theorem, which sits in the same namespace with a nearly identical name.

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?

There is no when-to-use guidance, no prerequisites, and no routing away from the near-identical sibling chinese_remainder_theorem. An agent choosing between the two must infer the difference from the word 'generalised' alone.

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