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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

root_aitken

Accelerate fixed-point iteration to find a root using Aitken's delta-squared method, an iteration function g(x), and an initial guess.

Instructions

Accelerate fixed-point iteration with Aitken's delta-squared method.

Args: g_str: Math expression for the iteration function g(x). x0: Initial guess. tol: Convergence tolerance. max_iter: Maximum iterations. precision: Rounding digits. plot: When True, also return a PNG plot of g(x) and y = x.

Returns: Dict with the accelerated root, iteration table and convergence flag. With plot=True a list [dict, Image] is returned instead.

Input Schema

NameRequiredDescriptionDefault
x0Yes
tolNo
plotNo
g_strYes
max_iterNo
precisionNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changedv0.2.1
    • addedInput schema / properties / plot
      Added value: +{
+  "default": false,
+  "title": "Plot",
+  "type": "boolean"
+}
  2. First observedv0.1.0

TDQS

B3.4/5.0
Behavior3/5

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

No annotations exist, so the description carries full burden. It usefully discloses the return shape (dict with root, iteration table and convergence flag; [dict, Image] when plot=True) but says nothing about convergence failure behavior, iteration limits, or computational constraints.

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

Conciseness4/5

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

Front-loads the purpose, then lists args and returns in a compact docstring form. Slightly formulaic but every line carries information with no filler.

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

Completeness4/5

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

For a 6-parameter numerical tool with no output schema, no annotations, and 0% schema coverage, the description covers purpose, all parameters, and both possible return shapes. Remaining gaps (failure/convergence edge cases) are minor for a well-specified math routine.

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, and it does: all six parameters (g_str, x0, tol, max_iter, precision, plot) are given one-line meanings. It does not restate defaults, but the semantic intent of each argument is clear.

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

Purpose4/5

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

States a specific verb ('Accelerate') plus resource (fixed-point iteration) and names the exact numerical technique (Aitken's delta-squared method). This implicitly distinguishes it from plain root_punto_fijo and the other root siblings, though it does not name an alternative directly.

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

Usage Guidelines2/5

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

No guidance on when to prefer this over root_punto_fijo, root_newton_raphson, or root_bisection. The agent must infer that it applies to fixed-point problems that need speedup, and there are no stated prerequisites or exclusions.

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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