Symbolic Algebra MCP Server

matrix_determinant

Computes a matrix determinant from its stored matrix key, returning a key for the symbolic determinant expression.

Instructions

Calculates the determinant of a matrix using SymPy's det method.

Args:
    matrix_key: The key of the matrix to calculate the determinant for.

Example:
    # Create a matrix
    matrix_key = create_matrix([[1, 2], [3, 4]])

    # Calculate its determinant
    det_key = matrix_determinant(matrix_key)
    # Results in -2

Returns:
    A key for the determinant expression.

Input Schema

Name	Required	Description	Default
`matrix_key`	Yes

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.1.0Oct 29, 2026

TDQS

B3.1/5.0

Behavior2/5

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

No annotations are provided, so the description bears full behavioral burden. It discloses that it uses SymPy's det and returns a key, but omits critical behavior: whether the matrix must be square, what happens on error, and whether the operation is pure/side-effect free.

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?

Well-structured with Args, Example, and Returns sections; the purpose is front-loaded. The example earns its place by demonstrating the create-then-determinant workflow, though it adds length.

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

Completeness3/5

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

An output schema exists, so return-value explanation is technically unnecessary (though provided). The main completeness gap is the absence of any note about square matrices or error behavior for a computation with no annotations to fall back on.

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

Parameters4/5

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

With 0% schema coverage on the single parameter, the description compensates well by explaining that matrix_key is 'the key of the matrix' and the example clarifies it comes from create_matrix. The key-reference semantics are made clear beyond the bare string type.

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?

States a specific verb and resource: 'Calculates the determinant of a matrix.' An agent can distinguish this from matrix_inverse or matrix_eigenvalues by purpose alone, though the description does not explicitly contrast with those siblings.

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?

The example shows how to call the tool but gives no guidance on when to use it versus alternatives or what conditions must hold (e.g., square matrix). No when/when-not context is provided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.