solve_linear_recurrence

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

No annotations are provided, so the description carries full burden. It states what the tool does but lacks behavioral details: it doesn't specify what algorithm is used, computational complexity, precision/accuracy considerations, error handling for invalid inputs, or output format. For a mathematical solver with no annotation coverage, this is a significant gap.

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 (one sentence plus domain/category) with zero wasted words. It's front-loaded with the core purpose, and the parenthetical adds useful context without redundancy. Every element earns its place.

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 no annotations, no output schema, and 0% schema description coverage for a mathematical solver with 3 parameters, the description is incomplete. It doesn't explain what the tool returns (e.g., nth term, closed form, sequence up to n), error conditions, or mathematical assumptions. For this complexity level, more 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?

Schema description coverage is 0%, so the description must compensate. It mentions 'coefficients and initial values' and 'n', which maps to the three parameters (coeffs, initial, n), providing basic semantic meaning. However, it doesn't explain parameter constraints (e.g., length relationships between coeffs and initial arrays, n's role as term index), leaving gaps that the schema alone doesn't address.

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: 'Solve general linear recurrence relation with given coefficients and initial values.' It specifies the verb ('solve') and the resource ('linear recurrence relation'), and includes domain/category context. However, it doesn't differentiate from potential siblings like 'fibonacci_sequence' or 'lucas_sequence' that might solve specific recurrences.

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. While it mentions the domain ('arithmetic') and category ('recursive_sequences'), it doesn't specify when this general solver is preferable over specialized tools for specific recurrence types (like Fibonacci or Lucas) that exist among the sibling tools.

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