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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

dynamic_2d_conservative_solve

Analyze a 2D system to check conservativeness, reconstruct Hamiltonian energy, classify equilibria, and trace closed orbits from differential equations; optionally return a phase portrait.

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. plot: When True, also return a PNG phase portrait.

Returns: Dict with the divergence check, the Hamiltonian reconstruction, the equilibrium classification and the trajectories. With plot=True a list [dict, Image] is returned instead.

Input Schema

NameRequiredDescriptionDefault
hNo
muNo
t0No
x0No
y0No
eq_xNoy
eq_yNox - x**3
plotNo
t_finNo
x_maxNo
x_minNo
y_maxNo
y_minNo
cantidad_trayectoriasNo

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

B3.2/5.0
Behavior3/5

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

No annotations are provided, so the description carries the burden. It does disclose the important behavioral quirk that plot=True changes the return type from a dict to [dict, Image], which is genuinely useful. However it says nothing about the numeric integration approach, failure modes for non-conservative inputs, or cost, so it is only partially transparent for a 14-parameter tool.

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 purpose is front-loaded and the Args/Returns block is a clean, scannable structure. It is appropriately sized for a 14-parameter tool with no wasted filler.

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

Completeness3/5

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

With no output schema the description correctly explains the return payload (divergence check, Hamiltonian, equilibrium classification, trajectories) and the plot=True variant. But given 14 parameters at 0% schema coverage, several inputs remain unexplained, leaving the definition only partially complete.

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 coverage is 0%, so the description must compensate for all 14 parameters. It only meaningfully explains eq_x, eq_y, mu and plot; x0, y0 and the portrait bounds are lumped into a vague 'integration and portrait settings' phrase, and h, t0 and t_fin are never mentioned at all. This leaves several 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?

The description gives a specific verb and resource: 'Analyze a 2D system checking conservativeness (divergence-free), Hamiltonian/energy and closed orbits.' This clearly separates it from the linear/nonlinear/nonhomogeneous 2D solvers among its siblings by naming the conservative-systems focus, though it never names a specific alternative.

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?

Usage is only implied by the framing ('checking conservativeness'), so an agent can infer this tool is for divergence-free/Hamiltonian systems, but there is no explicit when-to-use vs when-not, and no mention of the sibling solvers it competes with.

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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