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sympy_image_set

Plots the set of points satisfying a mathematical expression for a given variable, visualizing symbolic solutions.

Instructions

Image set.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYes
variableYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • The actual tool handler function for 'sympy_image_set'. It converts the expression string to a SymPy expression, creates a Symbol from the variable string, and returns the string representation of an ImageSet (the set of values obtained by substituting an integer variable into the expression).
    @mcp.tool()
    def sympy_image_set(expr: str, variable: str) -> str:
        """Image set."""
        var = sympy.Symbol(variable)
        return str(sympy.ImageSet(_sympify(expr), var))
  • The @mcp.tool() decorator registers 'sympy_image_set' as an MCP tool on the FastMCP server instance.
    @mcp.tool()
  • The type hints define the input schema: 'expr' (string expression) and 'variable' (string symbol name), returning a string.
    def sympy_image_set(expr: str, variable: str) -> str:
  • The _sympify helper utility used to convert the input string expression into a SymPy object before passing it to ImageSet.
    def _sympify(expr: str) -> sympy.Basic:
        """Convert string expression to SymPy object."""
        return sympy.sympify(expr)
  • The FastMCP server instance that the @mcp.tool() decorator registers tools on.
    mcp = fastmcp.FastMCP("mcp-sympy")
Behavior1/5

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

With no annotations provided, the description bears full responsibility for disclosing behavioral traits. It offers none—no mention of return type, side effects, permissions, or constraints. The agent has no idea what 'image set' entails.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness2/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is short but fails to convey essential information, making it under-specified rather than concise. It does not front-load functional details.

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

Completeness1/5

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

Given the tool's complexity (symbolic computation) and the presence of an output schema, the description is utterly incomplete. An agent cannot reliably select or invoke this tool based solely on the provided text.

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

Parameters1/5

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

The input schema has zero description coverage for its two parameters (expr and variable), and the description does not clarify their meaning or expected format. The agent cannot determine how to fill these parameters correctly.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose1/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description 'Image set.' is essentially a repetition of the tool name without a verb, failing to state what the tool does or what action it performs. It provides no actionable information for an agent.

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

Usage Guidelines1/5

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

No guidance is given on when to use this tool versus its many siblings (e.g., solve, solveset, simplify). There are no contexts, prerequisites, or alternatives mentioned.

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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