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solve_inequality_system

Solve a system of inequalities to find the intersection of all solutions. Determine valid parameter ranges or feasibility regions by providing multiple constraints and a variable.

Instructions

    Solve a system of inequalities (find the intersection).

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    🆕 NOT AVAILABLE IN SYMPY-MCP!
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    Use cases:
    - Find valid parameter ranges satisfying multiple constraints
    - Optimization feasibility regions
    - Multiple stability conditions

    Args:
        inequalities: List of inequalities
        variable: Variable to solve for

    Returns:
        Solution set (intersection of all solutions)

    Examples:
        # Multiple constraints
        solve_inequality_system(["x > 0", "x < 10", "x**2 < 25"], "x")
        → {"result": "(0, 5)", ...}

        # Therapeutic window
        solve_inequality_system(["C > MIC", "C < toxic_level"], "C")
    

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
variableYes
inequalitiesYes

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 disclosure fully. It adds value by stating the tool returns the intersection of all solutions, provides a caveat about SymPy-MCP availability, and shows example outputs. It does not disclose edge cases like no solution, but the core behavior is transparent.

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 clear sections (use cases, args, returns, examples). The NOT AVAILABLE banner draws attention appropriately. It is longer than minimal but every section contributes; no fluff beyond the banner, which is functional.

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?

Even with an output schema present, the description includes return semantics and complete examples. It covers purpose, usage context, environmental restriction, parameter meaning, and expected results. The only gap is not explicitly connecting to alternative tools, but for a two-parameter solver this is sufficiently complete.

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

Parameters3/5

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

The Args section provides high-level descriptions ('List of inequalities', 'Variable to solve for') that mostly restate the parameter names and schema types (array/string). The examples add meaningful format hints (e.g., 'x > 0'), but coverage is thin for 0% schema description coverage. It does not explain SymPy syntax details or constraints on variable naming.

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 'Solve a system of inequalities (find the intersection)' which is a specific verb-resource pair and clearly distinguishes from its sibling 'solve_inequality' (which handles single inequalities). The use cases and examples reinforce this purpose.

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 'Use cases' section explicitly lists three scenarios (valid parameter ranges, feasibility regions, stability conditions), giving clear context. The prominent 'NOT AVAILABLE IN SYMPY-MCP!' banner is a strong environmental exclusion. However, it does not explicitly contrast with the single-inequality variant or mention when not to use it beyond the environment limitation.

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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