waring_representation

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

No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool does mathematically without describing how it behaves: no information about computational complexity, error handling, output format, or limitations (e.g., range constraints for n and k). This is inadequate for a tool with parameters and no output schema.

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—a single sentence plus domain/category tags—with zero wasted words. It's front-loaded with the core purpose and efficiently includes mathematical context. Every element earns its place without redundancy.

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 tool's mathematical complexity, two undocumented parameters, no annotations, and no output schema, the description is incomplete. It identifies the mathematical problem but omits critical details: how results are returned, any constraints on inputs, or what the output represents (e.g., a list of powers or just existence). This leaves significant gaps for an agent to use the tool effectively.

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 parameters n and k are completely undocumented in the schema. The description adds no parameter semantics beyond mentioning 'number' and 'k-th powers'—it doesn't explain what n and k represent, their valid ranges, or examples. With two required parameters and zero coverage, this is insufficient.

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: 'Express a number as sum of k-th powers (Waring's problem).' It specifies both the verb ('express') and the mathematical operation, and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools that might involve power-related computations (like 'power_series' or 'sum_digit_powers'), 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. It mentions the mathematical domain ('additive_number_theory') but gives no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools. Users must infer usage from the mathematical context alone.

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