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mathmethods-mcp

mathmethods-mcp

mc_estadistico_1d

Run replicated Monte Carlo integration with statistical analysis on a math expression over [a,b], returning estimate distributions, confidence intervals, and an optional histogram.

Instructions

Replicated Monte Carlo experiment (M repetitions of N samples) with statistical analysis.

Args: func_str: Math expression in x. a, b: Integration limits (b > a). N: Samples per replication. M: Number of replications. nivel_confianza: Confidence level in (0, 1). seed: Optional RNG seed. precision: Rounding digits. plot: When True, also return a PNG histogram of the estimates.

Returns: Dict with the distribution of estimates and confidence intervals. With plot=True a list [dict, Image] is returned instead.

Input Schema

NameRequiredDescriptionDefault
MNo
NNo
aYes
bYes
plotNo
seedNo
func_strYes
precisionNo
nivel_confianzaNo

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

A3.5/5.0
Behavior3/5

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

With no annotations, the description must carry the behavioral burden, and it does disclose key traits: the return is a dict of estimates and confidence intervals, plot=True returns a list containing a dict and an image, and a/b require b > a. However, it does not explain error conditions, the exact statistical analysis performed, RNG behavior when seed is omitted, or computational cost.

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 front-loaded with the core purpose and then uses clean Args and Returns sections. The parameter documentation is necessary for a nine-parameter tool with no schema descriptions, and there is no wasted 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 nine-parameter tool with no annotations and no output schema, the definition is fairly complete: it describes all parameters and the return shape, including the plot variant. It still lacks sibling differentiation and deeper statistical or failure-mode context, which keeps it from being fully complete.

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 documents all nine parameters with meaning beyond their names. It clarifies a/b as integration limits with b > a, N and M as sample and replication counts, nivel_confianza as a value in (0, 1), seed as optional RNG input, precision as rounding digits, and plot as triggering a PNG histogram return. The main gap is that func_str is only described as a math expression in x, without syntax examples.

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?

The description states a specific computational resource and method: a replicated Monte Carlo experiment with M replications of N samples and statistical analysis. It is clearly more than a tautology and the integration limits show it performs Monte Carlo integration, but it does not explicitly distinguish itself from sibling tools such as mc_convergencia_1d or mc_valor_promedio_1d.

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?

The description implies that this tool is for repeated Monte Carlo sampling with confidence intervals, but it gives no explicit guidance on when to choose it over the many sibling Monte Carlo and numerical integration tools. There are no stated prerequisites, exclusions, or alternatives.

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