singularis_matrix_exponential

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

With no annotations, the description carries the full burden and does reasonably well: it discloses that input may be inline or a file path, that a vector argument switches the operation to e^{tA}v, that output includes a residual check, and that cost scales as n^3. It omits any statement about matrix assumptions (square, real vs complex) or failure behavior for non-square input.

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?

Front-loaded with the core computation, then use cases, then the selection rule, then input/output facts — a sensible priority order. Dense but each sentence carries information; the domain list is slightly padded but justifiable for discoverability.

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?

An output schema exists, so return values need not be re-explained, and the description still usefully notes the residual check. Given moderate complexity and a 5-parameter schema at 0% coverage, the main gap is the unexplained vector_path parameter and the mutual exclusivity of inline vs path inputs; otherwise the agent has enough to invoke it correctly.

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% for all five parameters, so the description must compensate. It partially does: it names matrix/path as alternative input forms, gives t's role and default, and marks vector as optional. It never mentions vector_path or explains that matrix and path are mutually exclusive mirrors, leaving one parameter completely undisclosed.

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 mathematical verb+resource (compute e^{tA} and its action on a vector) and enumerates concrete application domains: time evolution, Markov chains/rating migration, linear ODEs, graph diffusion. No sibling tool computes a matrix exponential, so the agent can place it instantly against solve_heat, gemm, fft, etc.

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?

Gives an explicit selection rule: 'Use instead of a dense expm whenever n is in the hundreds or more, or when you need a verifiable residual.' That is clear when-to-use guidance tied to problem size and a verification need. It does not state when-not to use it or what the fallback is for small n, leaving that to inference.

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