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sympy_groebner

Simplify and solve systems of polynomial equations by computing their Groebner basis. Accepts a set of polynomial expressions as input.

Instructions

Groebner basis.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprsYes
variableNox

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • The handler function for the sympy_groebner tool. Takes a comma-separated string of expressions and a variable, computes the Groebner basis using sympy.groebner(), and returns the result as a string.
    @mcp.tool()
    def sympy_groebner(exprs: str, variable: str = "x") -> str:
        """Groebner basis."""
        expr_list = [_sympify(e) for e in exprs.split(",")]
        return str(sympy.groebner(expr_list, _sympify(variable)))
  • The tool is registered with the MCP server via the @mcp.tool() decorator on line 2456. The 'mcp' instance is created earlier in the file (line 119: mcp = fastmcp.FastMCP("mcp-sympy")).
    @mcp.tool()
  • Helper function _sympify is used within sympy_groebner to convert input strings into SymPy objects before computing the Groebner basis.
    def _sympify(expr: str) -> sympy.Basic:
        """Convert string expression to SymPy object."""
        return sympy.sympify(expr)
Behavior1/5

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

No annotations exist, and the description provides zero behavioral details. The agent cannot infer side effects, computational cost, or required assumptions from the description alone.

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?

While extremely short, it is under-specified to the point of being unhelpful. Valuable real estate is wasted on a single terse phrase that could have been expanded with key 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 mathematical complexity of Groebner basis, the lack of annotations, and an existing output schema, the description fails to convey what the tool returns or any constraints on inputs.

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?

Schema description coverage is 0% and the description adds no explanation for the 'exprs' or 'variable' parameters. The agent has no clue what format 'exprs' should take or how 'variable' is used.

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

Purpose2/5

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

Description is a noun phrase 'Groebner basis' rather than an actionable verb phrase. It restates the tool name without clarifying the specific function or distinguishing it from sibling tools like solving or factoring.

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 is provided on when to use this tool versus alternatives. The description does not mention prerequisites, typical use cases, or exclusions.

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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