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agmonetti

mathmethods-mcp

by agmonetti

dynamic_2d_lanchester_solve

Solve Lanchester combat models analytically to determine winner and survivors, and numerically simulate force trajectories over time.

Instructions

Simulate a Lanchester combat model x' = f(x,y), y' = g(x,y) with analytic time-to-annihilation.

Args: eq_x, eq_y: Math expressions (classic default is x'=-αy, y'=-βx). alpha, beta, gamma, epsilon, mu, delta: Greek parameter values. x0, y0: initial force sizes. t0, t_fin, h: simulation grid.

Returns: Dict with the analytic winner/survivors, state equation and the numerical trajectories.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
hNo
muNo
t0No
x0No
y0No
betaNo
eq_xNo-α * y
eq_yNo-β * x
alphaNo
deltaNo
gammaNo
t_finNo
epsilonNo
Install Server

TDQS

B3.3/5.0
Behavior3/5

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

The description discloses the analytic winner/survivors and state equation plus numerical trajectories in the Returns section, providing some behavioral context. However, with no annotations, it fails to mention any error conditions, edge cases, or limits (e.g., parameter constraints for analytic solution).

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 with a clear intro, bulleted args, and returns. No unnecessary words.

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?

Given 13 parameters and no schema descriptions or output schema, the description provides a helpful overview but omits details like the exact roles of subsidiary Greek parameters and any constraints on equations. It is adequate for basic use but not fully complete for complex configuration.

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?

The description groups parameters and explains each category (Math expressions, Greek parameters, initial forces, simulation grid), adding meaning beyond the bare schema properties. Yet it does not individually define gamma/epsilon/mu/delta roles, leaving some ambiguity.

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 clearly states 'Simulate a Lanchester combat model' with equations, making the tool's purpose obvious. It distinguishes itself from integral/root/ODE siblings by specifying the Lanchester model, though it doesn't explicitly contrast with other dynamic_2d tools.

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 guidance is given on when to choose this over sibling tools like dynamic_2d_linear_solve or ode_rk4. The description only explains what it does, not when it is preferred.

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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