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solve_inequality

Solve single inequalities to find solution sets, parameter ranges, stability conditions, or domain restrictions. Returns interval notation.

Instructions

    Solve a single inequality.

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    🆕 NOT AVAILABLE IN SYMPY-MCP!
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    Use cases:
    - Find valid parameter ranges
    - Stability conditions
    - Convergence criteria
    - Domain restrictions

    Args:
        inequality: The inequality (use <, >, <=, >=)
        variable: Variable to solve for
        domain: Domain restriction ("real", "positive", "integer")

    Returns:
        Solution set with interval notation

    Examples:
        # Simple inequality
        solve_inequality("x**2 - 4 < 0", "x")
        → {"result": "(-2, 2)", "latex": "-2 < x < 2"}

        # Rational inequality
        solve_inequality("(x-1)/(x+2) >= 0", "x")
        → {"result": "(-oo, -2) ∪ [1, oo)", ...}

        # With domain restriction
        solve_inequality("x**2 < 9", "x", domain="positive")
        → {"result": "(0, 3)", ...}
    

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
domainNoreal
variableYes
inequalityYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior4/5

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

With no annotations, the description carries full responsibility for behavioral disclosure. It includes an availability warning, return format details, and worked examples. It does not mention error handling or side effects, but for a solving tool this is acceptable given the examples.

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 well-structured with sections for use cases, parameters, return format, and examples. The large banner warning adds some visual noise but also provides important availability context. Overall, every section earns its place.

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?

Given the tool's moderate complexity, the presence of an output schema, and the provided examples, the description is complete. It covers purpose, parameters, return format, and usage scenarios, making it self-sufficient for an agent.

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 has 0% description coverage, but the 'Args' section thoroughly explains each parameter (inequality, variable, domain) with formatting details and example usage. This fully compensates for the lack of schema descriptions.

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 explicitly states 'Solve a single inequality' and lists specific use cases (parameter ranges, stability conditions, etc.), making the tool's purpose clear and distinguishing it from the sibling tool solve_inequality_system which handles systems.

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 provides clear use cases and implicitly limits scope to a single inequality. However, it does not explicitly mention alternatives like solve_inequality_system nor give when-not-to-use guidance, though the context is sufficiently clear.

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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