order_modulo

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

No annotations are provided, so the description carries the full burden. It mentions the mathematical concept but doesn't disclose behavioral traits such as error handling (e.g., what happens if a and n aren't coprime), computational complexity, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.

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—just one sentence plus domain/category tags. It's front-loaded with the core purpose and wastes no words. Every part earns its place by defining the tool's function and context 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?

Given the complexity of modular arithmetic, no annotations, no output schema, and low schema description coverage, the description is incomplete. It doesn't explain what the multiplicative order is, how it's computed, what the output looks like, or edge cases. For a mathematical tool with no structured support, more explanatory context is needed.

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?

The input schema has 0% description coverage, so the description must compensate. It names the parameters ('a' and 'n') implicitly in the phrase 'a modulo n' and clarifies they are integers, but doesn't explain their mathematical roles (e.g., that 'a' is the base and 'n' is the modulus) or constraints (e.g., n > 1, a and n coprime). This adds some meaning but falls short of fully documenting the parameters.

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 the multiplicative order of a modulo n.' It specifies the verb ('Find') and the mathematical operation ('multiplicative order'), and provides domain/category context. However, it doesn't differentiate from sibling tools like 'primitive_root' or 'discrete_log_naive' that also involve modular arithmetic concepts.

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?

No guidance is provided about when to use this tool versus alternatives. The description only states what it does, with no mention of prerequisites, constraints (e.g., that a and n must be coprime), or related tools for similar tasks like computing primitive roots or solving discrete logarithms.

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