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sympy_Circle

Define a circle symbolically by specifying its center point and radius.

Instructions

Create a circle.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
centerYesCenter point
radiusYesRadius

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • The main handler function for the sympy_Circle tool. It takes a center point string and radius string, converts them to SymPy objects via _sympify, constructs a Circle object, and returns its string representation.
    @mcp.tool()
    def sympy_Circle(center: str, radius: str) -> str:
        """Create a circle.
    
        Args:
            center: Center point
            radius: Radius
    
        Returns:
            Circle as string
    
        Example:
            >>> sympy_Circle("(0, 0)", "1")
            "Circle(Point2D(0, 0), 1)"
        """
        return str(Circle(_sympify(center), _sympify(radius)))
  • The @mcp.tool() decorator registers sympy_Circle as a tool in the MCP server (mcp = fastmcp.FastMCP('mcp-sympy')).
    @mcp.tool()
  • The _sympify helper function used to convert the string inputs (center and radius) into SymPy objects before constructing the Circle.
    def _sympify(expr: str) -> sympy.Basic:
        """Convert string expression to SymPy object."""
        return sympy.sympify(expr)
  • Type annotations define the input schema: center (str) and radius (str), returning a string representation.
    def sympy_Circle(center: str, radius: str) -> str:
Behavior2/5

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

No annotations are provided, and the description offers no insight into behavioral traits such as side effects (e.g., symbol creation), validation, or return format. The presence of an output schema is not discussed.

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 extremely concise, consisting of a single sentence. It is front-loaded but lacks any substantive detail that would warrant a higher score.

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

Completeness2/5

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

Given the two-parameter geometry tool and the existence of an output schema, the description is too sparse. It does not explain what the tool returns or how the inputs relate to the geometry.

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 input schema already describes both parameters ('Center point', 'Radius') with 100% coverage. The description adds no additional semantic meaning, so baseline score applies.

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

Purpose4/5

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

The description 'Create a circle.' clearly states the action and resource. However, it does not distinguish this tool from other geometry siblings like sympy_Point or sympy_Line.

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

Usage Guidelines2/5

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

No guidance on when to use this tool versus alternatives. The description lacks any contextual hints about prerequisites or appropriate use cases.

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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