matrix_chain_order

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

No annotations are provided, so the description carries the full behavioral burden. It states the computation but omits whether the tool is deterministic, whether it has side effects, what it returns (order only, cost only, or both), and how invalid dimensions are handled.

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 repetition. It communicates the core operation efficiently.

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?

There is no output schema, and the description does not explain what the tool returns. For an algorithmic tool, the agent needs to know whether to expect a parenthesization, a scalar multiplication count, or both.

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%, and the schema fully explains the single 'dimensions' parameter including the N+1 convention. The description adds no parameter semantics beyond the schema, so the baseline 3 is appropriate.

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 ('Find optimal parenthesization'), resource ('matrix chain multiplication'), and optimization goal ('minimize scalar multiplications'). This distinguishes it from generic matrix-operation siblings without needing to name them.

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?

Provides no explicit when-to-use, when-not-to-use, prerequisites, or alternatives. An agent must infer that this is the right tool only from the mathematical term in the description.

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