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agmonetti

mathmethods-mcp

by agmonetti

dynamic_1d_solve

Analyze 1D autonomous dynamical systems by computing equilibria, stability, phase portraits, and time series for custom or standard models.

Instructions

Analyze the 1D autonomous system x' = f(x): equilibria, stability, phase portrait and time series.

Args: func_str: f(x) used when model is 'custom'. model: 'custom' | 'malthus' (rx) | 'verhulst' (mux*(1-x/K)) | 'newton' (-k*(x-Ta)). params: parameter values, e.g. {'r': 1.5} or {'mu': 1.0, 'K': 2.0}. x_min, x_max: state window. t_max: final time of the time series. n_phase: resolution of the phase analysis. n_time: number of time steps. initial_conditions: starting states, e.g. [0.1, 1.0]. control_enabled: add a constant control term -h (verhulst/custom only).

Returns: Dict with equilibria, their stability, the phase portrait data and time solutions.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
modelNocustom
t_maxNo
x_maxNo
x_minNo
n_timeNo
paramsNo
n_phaseNo
func_strNox
control_enabledNo
initial_conditionsNo
Install Server

TDQS

A4.2/5.0
Behavior4/5

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 enumerates model choices with formulas, explains the custom func_str parameter, and notes that control_enabled adds -h only for verhulst/custom. This adds meaningful behavioral context beyond the schema, though it does not describe the numerical method or exact return format.

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 purpose and uses a compact Args/Returns structure. Each parameter line conveys necessary information without filler or redundant restatement of the tool name.

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 tool with 10 parameters, no annotations, and no output schema, the description covers all arguments, model formulas, and high-level return categories. It falls slightly short of excellent because it lacks a precise output dict structure and does not address edge cases or numerical behavior.

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?

With 0% schema description coverage, the description compensates well by listing every parameter with a concise meaning, including model-specific formulas and examples like {'r': 1.5}. It clarifies func_str's role and control_enabled restrictions, providing semantic value well beyond the raw schema.

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 a specific verb and resource: 'Analyze the 1D autonomous system x' = f(x): equilibria, stability, phase portrait and time series.' This clearly distinguishes it from sibling tools like dynamic_1d_equilibria (equilibria-only) and 2D solvers.

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

Usage Guidelines3/5

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

The context is clear: it is for 1D autonomous systems. However, it does not explicitly state when to prefer this tool over dynamic_1d_equilibria, dynamic_1d_bifurcation, or numeric ODE solvers like ode_euler. Usage guidance is implied rather than explicitly contrasted with alternatives.

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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