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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

dynamic_1d_equilibria

Find and classify equilibria of x' = f(x) to analyze one-dimensional dynamic systems; optionally generate phase and time-series plots.

Instructions

Find the equilibria of x' = f(x) and classify their stability.

With plot=True a PNG of f(x) with the equilibria and the time series is returned as [dict, Image] alongside the numeric result.

Input Schema

NameRequiredDescriptionDefault
plotNo
modelNocustom
x_maxNo
x_minNo
paramsNo
n_phaseNo
func_strNox
control_enabledNo

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

B3/5.0
Behavior3/5

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

No annotations are provided, so the description carries the full burden. It usefully discloses the plot=True return shape as [dict, Image] alongside the numeric result, but omits other behavioral details such as the output dict structure, stability classification method, and any parameter side effects.

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?

Two sentences, front-loaded with the core purpose and then the plot-specific return behavior. No filler or repetition.

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

Completeness2/5

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

Given 8 parameters with zero schema descriptions, no annotations, and no output schema, the description is not complete enough. It partially documents return behavior but leaves parameter semantics and usage context absent.

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

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0% and there are 8 parameters. The description explains only plot's effect and gives no meaning for model, func_str, params, x_min, x_max, n_phase, or control_enabled, leaving most parameters undocumented in both schema and description.

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 and resource: find equilibria of x' = f(x) and classify their stability. Clear what the tool does, but it does not differentiate itself from siblings like dynamic_1d_solve, dynamic_1d_bifurcation, or root_bisection.

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 explicit when-to-use, when-not-to-use, or alternative guidance. The description implies equilibrium analysis but gives no conditions for choosing this tool over other dynamic or root-finding siblings.

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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