min_waring_number

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. While it states what the tool computes, it doesn't describe important behavioral aspects: computational complexity, input constraints (e.g., valid ranges for n and k), error handling, or output format. For a mathematical computation tool with zero annotation coverage, this is a significant gap in transparency.

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 extremely concise and front-loaded: the core purpose is stated in the first sentence, with domain context efficiently added in parentheses. There is zero wasted verbiage, and every word earns its place. This is a model of conciseness for a mathematical tool.

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?

Given the complexity of the Waring's problem computation, the lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the output represents (e.g., an integer count, or possibly a representation), error conditions, or performance characteristics. For a non-trivial number theory tool, more context is needed for effective agent use.

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%, meaning neither parameter (n, k) has descriptions in the schema. The tool description mentions 'n' and 'k' but provides no semantic clarification beyond what's implied by the problem statement. It doesn't explain what n represents (the target number) or k (the exponent), nor any constraints (e.g., n must be positive, k typically ≥ 2). With low schema coverage, the description fails to compensate adequately.

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 clearly states the tool's purpose: 'Find minimum number of k-th powers needed to represent n.' It specifies both the verb ('Find minimum number') and the resource ('k-th powers needed to represent n'), and provides domain context ('Domain: arithmetic, Category: additive_number_theory'). However, it doesn't explicitly differentiate from sibling tools like 'waring_representation' or 'sum_of_four_squares', which prevents a perfect score.

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 provides no guidance on when to use this tool versus alternatives. There are no explicit when/when-not statements, no mention of prerequisites, and no named alternatives. The domain/category tags offer some context but don't constitute actionable usage guidelines for an AI agent.

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