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agmonetti

mathmethods-mcp

by agmonetti

root_comparar

Compare bisection, fixed-point, Newton-Raphson, and Aitken methods on a single root-finding problem to evaluate convergence and accuracy.

Instructions

Compare bisection, fixed-point, Newton-Raphson and Aitken on the same problem.

Args: func_str: Math expression for f(x) (used by bisection/Newton). g_str: Math expression for g(x) (used by fixed-point/Aitken). a, b: Bracket for bisection (f(a) and f(b) must differ in sign). x0: Initial guess. tol, max_iter, precision: Shared tolerances.

Returns: Dict with per-method results.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYes
bYes
x0Yes
tolNo
g_strYes
func_strYes
max_iterNo
precisionNo
Install Server

TDQS

A4.1/5.0
Behavior3/5

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

With no annotations, the description must disclose behavioral traits. It provides useful constraints (e.g., 'f(a) and f(b) must differ in sign'), explains shared tolerances, and states the return type. However, it omits failure behavior when methods do not converge and does not describe the structure of the returned dict beyond 'per-method results.'

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a compact docstring with a clear purpose sentence, an Args section listing parameters with roles, and a Returns line. Every sentence earns its place; no filler or redundancy. It is front-loaded and structured for quick scanning.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For an 8-parameter comparison tool with no output schema, the description covers inputs and the general return type, but the return dict's keys and per-method details are unspecified. The tool's behavior under non-convergence or invalid inputs is also unaddressed, leaving gaps that an agent might need to infer.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

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 adds meaning to all parameters: func_str for bisection/Newton, g_str for fixed-point/Aitken, a/b as the bracket, x0 as initial guess, and tol/max_iter/precision as shared tolerances. This is helpful, though exact format examples are not given.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description opens with 'Compare bisection, fixed-point, Newton-Raphson and Aitken on the same problem,' which uses the specific verb 'compare' and a clear resource (four root-finding methods). This distinguishes it from the sibling single-method tools (root_bisection, root_newton_raphson, etc.) and makes the tool's purpose immediate.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The phrase 'on the same problem' clearly indicates when to use this tool: when a comparative evaluation of root-finding methods is desired. It does not explicitly list when not to use it or name alternatives, but the sibling tool context and the opening statement make the use case unambiguous.

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

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