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agmonetti

mathmethods-mcp

by agmonetti

ode_euler

Solve first-order ODEs y'(x)=f(x,y) with initial condition using the explicit Euler method, returning numerical solution, exact solution when available, and error estimates.

Instructions

Solve y'(x) = f(x, y), y(x0) = y0 with the explicit Euler method (1st order).

Args: ecuacion_str: Right-hand side f(x, y). x0, y0: Initial condition. xf: Final x (must be > x0). h: Step size (must be positive). tol: Optional tolerance flag for the final error. precision: Rounding digits.

Returns: Dict with the numerical solution, exact solution (when available) and errors.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
hYes
x0Yes
xfYes
y0Yes
tolNo
precisionNo
ecuacion_strYes
Install Server

TDQS

A3.8/5.0
Behavior3/5

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

With no annotations, the description carries the full burden for behavioral disclosure. It does mention the first-order nature, constraints (xf > x0, h > 0), and the return contents. However, it omits potential limitations such as instability, accuracy trade-offs, or what happens when the exact solution is unavailable.

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 highly concise: a one-line math definition, an organized argument list, and a returns line. Every sentence earns its place without redundancy.

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?

Given the tool's complexity (7 params, no output schema, no annotations), the description is largely complete: it covers the method, all parameters, constraints, and return type. Gaps remain around the exact equation syntax and the precise structure of the returned dictionary, but the essential invocation context is present.

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 schema description coverage is 0%, so the description must compensate, and it does by explaining each parameter's mathematical meaning and constraints (e.g., xf must be > x0, h positive). Minor issues: 'tol' is described as a 'flag' but the schema shows it is a numeric tolerance, and the format of 'ecuacion_str' is not specified.

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 clearly states it solves a first-order ODE using the explicit Euler method, with the mathematical notation y'(x)=f(x,y), y(x0)=y0. This specific verb+resource+method distinguishes it from sibling tools like ode_heun and ode_rk4.

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?

The description provides no guidance on when to choose the explicit Euler method over alternatives, nor any exclusions or prerequisites. It defines the method but does not help an agent select among the many ODE solver siblings, leaving use-case decisions entirely implicit.

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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