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agmonetti

mathmethods-mcp

by agmonetti

dynamic_2d_conservative_solve

Check 2D systems for conservativeness (divergence-free), Hamiltonian/energy, and closed orbits, while classifying equilibria and computing trajectories.

Instructions

Analyze a 2D system checking conservativeness (divergence-free), Hamiltonian/energy and closed orbits.

Args: eq_x, eq_y: Math expressions for x' and y'. mu: parameter value. x0..y_max, cantidad_trayectorias: integration and portrait settings.

Returns: Dict with the divergence check, the Hamiltonian reconstruction, the equilibrium classification and the trajectories.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
hNo
muNo
t0No
x0No
y0No
eq_xNoy
eq_yNox - x**3
t_finNo
x_maxNo
x_minNo
y_maxNo
y_minNo
cantidad_trayectoriasNo
Install Server

TDQS

B3.4/5.0
Behavior3/5

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

With no annotations, the description carries the full burden of behavioral disclosure. It lists the return dict contents (divergence check, Hamiltonian reconstruction, equilibrium classification, trajectories) and mentions integration/portrait settings, but it does not disclose the numerical method, limitations, or how the analysis is performed beyond the high-level outputs.

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?

The description is compact and well-structured with clear 'Args' and 'Returns' sections, and front-loads the purpose. However, the shorthand 'x0..y_max' is ambiguous, slightly reducing clarity.

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?

The tool has 13 parameters, no annotations, and no output schema, so the description must compensate. It provides a high-level purpose and return dict contents, but omits per-parameter semantics for most parameters and lacks usage guidance relative to siblings, leaving significant gaps for an agent to use the tool correctly.

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?

The description explains eq_x, eq_y, and mu, but lumps all remaining parameters as 'x0..y_max, cantidad_trayectorias: integration and portrait settings' without individual meaning. With 0% schema parameter descriptions, the agent cannot learn the roles of h, t0, t_fin, x_min, x_max, y_min, y_max from this description.

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 'Analyze a 2D system checking conservativeness (divergence-free), Hamiltonian/energy and closed orbits', which clearly identifies the tool's specific purpose and distinguishes it from sibling tools like dynamic_2d_nonlinear_solve or dynamic_2d_linear_solve.

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 description implies that the tool is for conservative 2D systems but never explicitly states when to use it over alternatives. No sibling tools are named, and no exclusions or conditions are given, so the agent must infer the appropriate context.

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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