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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

dynamic_1d_bifurcation

Performs bifurcation analysis for 1D dynamical systems by computing equilibria across parameter sweeps. Returns tables, symbolic analysis, phase slices, and optionally a bifurcation diagram.

Instructions

Bifurcation analysis of x' = f(x; bif_param): equilibria vs parameter sweep.

Args: func_str: f(x) used when model is 'custom'. model: 'custom' | 'malthus' | 'verhulst' | 'newton'. params: values of the other model parameters, e.g. {'K': 2.0}. bif_param: name of the bifurcation parameter swept between bif_min and bif_max. bif_min, bif_max, bif_steps: parameter sweep range/resolution. x_min, x_max, n_phase: state window for finding equilibria. phase_params: optional explicit parameter values for phase slices. control_enabled: add a constant control term -h (verhulst/custom only). plot: When True, also return a PNG of the bifurcation diagram.

Returns: Dict with the equilibria-vs-parameter table, exact symbolic analysis and phase slices. With plot=True a list [dict, Image] is returned.

Input Schema

NameRequiredDescriptionDefault
plotNo
modelNocustom
x_maxNo
x_minNo
paramsNo
bif_maxNo
bif_minNo
n_phaseNo
func_strNox
bif_paramNor
bif_stepsNo
phase_paramsNo
control_enabledNo

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

A3.9/5.0
Behavior3/5

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

With no annotations, the description carries the full burden. It does disclose a valuable behavioral trait: plot=True changes the return shape to [dict, Image]. However it says nothing about runtime cost, numeric failure modes, or permission requirements for this heavy sweep 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?

It is a compact docstring: a one-line summary followed by tightly grouped Args and a Returns block. Size is proportionate to a 13-parameter tool with no wasted prose, though the Args grouping (bif_min, bif_max, bif_steps) is slightly terse.

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 13 parameters, no annotations and no output schema, the description supplies both the argument semantics and the return contract (table + symbolic analysis + phase slices, or [dict, Image]). Missing only operational caveats, which for a complex analysis tool would be a nice-to-have.

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?

Schema description coverage is 0%, so the description must compensate, and it largely does: nearly all 13 parameters are annotated with meaning and constraints (model enum values, the role of bif_param, sweep range/resolution, control term scope). Only phase_params ('explicit parameter values for phase slices') remains somewhat vague.

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 opening line gives a precise verb (bifurcation analysis), the exact system class (x' = f(x; bif_param)), and the deliverable (equilibria vs parameter sweep). This clearly separates it from dynamic_1d_solve and dynamic_1d_equilibria, which lack the sweep dimension.

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 implied by the purpose rather than stated. The only conditional guidance is embedded notes such as 'func_str used when model is custom' and 'control_enabled ... verhulst/custom only', but there is no explicit when-to-use-this-vs-alternatives framing.

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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