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sympy_conjugate

Compute the complex conjugate of a symbolic mathematical expression. Simplifies expressions involving complex numbers.

Instructions

Complex conjugate.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • The function that implements the sympy_conjugate tool. It takes a string expression, converts it to a SymPy object via _sympify(), computes the complex conjugate using sympy.conjugate(), and returns the result as a string.
    @mcp.tool()
    def sympy_conjugate(expr: str) -> str:
        """Complex conjugate."""
        return str(sympy.conjugate(_sympify(expr)))
  • The _sympify helper function that converts string expressions to SymPy objects, used by sympy_conjugate.
    def _sympify(expr: str) -> sympy.Basic:
        """Convert string expression to SymPy object."""
        return sympy.sympify(expr)
  • Uses the @mcp.tool() decorator (defined via fastmcp.FastMCP on line 119) which registers the tool; the function signature (expr: str -> str) defines the input/output schema.
    @mcp.tool()
    def sympy_rational(num: str, den: str) -> str:
        """Create Rational."""
        return str(Rational(num, den))
Behavior2/5

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

With no annotations, the description bears full burden for behavioral disclosure. It only states the basic operation, omitting details like whether it conjugates all imaginary units, handles complex numbers, or any side effects. Agents have insufficient info to anticipate behavior.

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?

Extremely terse (two words) but under-specification, not conciseness. The description fails to provide necessary information in an efficient manner; it's too brief to be useful.

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?

Despite the presence of an output schema (which may document return format), the description lacks crucial context about the input string format, complex conjugate behavior, and relationship to sibling tools. It is incomplete for effective use.

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

Parameters2/5

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

The sole parameter 'expr' is a string, but the description offers no semantics about what it should contain (e.g., a sympy expression string). With 0% schema description coverage, the description must compensate, but it does not, leaving agents unsure of valid input.

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

Purpose3/5

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

The description 'Complex conjugate.' and the tool name clearly indicate the function computes the complex conjugate. However, it doesn't specify the input format (e.g., symbolic expression string) or the output. For a mathematical tool, this is minimally adequate but lacks specificity to distinguish from siblings like sympy_re or sympy_im.

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. For example, could use sympy_conjugate for full conjugation, but sympy_re and sympy_im for real/imaginary parts. No prerequisites or context given.

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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