math-reasoning-mcp

Overview Schema Source Related Servers Discussions Admin

check_linearity

Determine whether a given system is linear by applying the superposition principle, returning a symbolic proof. Supports both memoryless expressions and difference equations.

Instructions

Checks if a system is linear using the superposition principle.

For system_type='memoryless': expression is in terms of 'x' and optionally 't'. Example: 'x**2', '3x', 'tx + 5'

For system_type='difference': expression is a difference equation in terms of 'x_n', 'x_n1' (x[n-1]), 'x_n2' (x[n-2]), 'y_n1' (y[n-1]), etc. Example: 'x_n + x_n1' (y[n] = x[n] + x[n-1])

Returns whether the system is linear with a symbolic proof.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`system_type`	No		memoryless
`system_expression`	Yes

Output Schema

TableJSON Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.1.0Sep 8, 2026

TDQS

A4.6/5.0

Behavior4/5

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

No annotations are provided, so the description carries the behavioral disclosure burden. It states that the tool returns a boolean result with a symbolic proof and explains the accepted expression formats for both system types. It does not cover error behavior or limitations, but the core behavior is well disclosed.

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 efficient and scannable: a one-sentence purpose, then a clearly separated breakdown by system_type with concrete examples. Every sentence earns its place, and the examples are highly relevant to correct invocation.

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

Completeness5/5

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

For a tool with no annotations, 0% schema parameter coverage, and a somewhat nuanced mathematical input, the description is remarkably complete. It defines the valid expression grammar for both supported system types, explains what the tool returns, and provides enough examples. The output schema can supply the formal return structure.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, and the description fully compensates. It explains system_type values and gives detailed syntax rules and examples for system_expression in both memoryless and difference cases. An agent could construct valid inputs from this description alone.

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 a specific verb and resource: 'Checks if a system is linear' and names the method (superposition principle). It is clearly distinct from sibling tools like transformation tools or check_time_invariance, so an agent can identify what this tool is for.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives clear usage context by explaining exactly how to express memoryless systems and difference equations, with examples for each system_type. It does not explicitly state when not to use the tool or mention alternatives such as check_time_invariance, so it stops short of a 5.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.