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sympy_matrix_nullspace

Compute the nullspace of a matrix to find all vectors that satisfy the homogeneous equation Ax = 0, enabling analysis of linear dependencies and solution spaces in symbolic algebra.

Instructions

Nullspace.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
matrixYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior1/5

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

No annotations are provided, so the description must fully disclose behavioral traits. 'Nullspace.' offers no information about the tool's behavior, such as whether it performs read-only computations, requires specific input formats, handles errors, or returns structured results. This leaves the agent with no understanding of how the tool operates beyond its name.

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 'Nullspace.' is extremely concise, it is under-specified rather than efficiently structured. A single word does not provide enough information to be helpful, and it lacks any front-loaded explanation of the tool's purpose or usage. This brevity comes at the cost of clarity and completeness.

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 tool's complexity (matrix operation), lack of annotations, low schema coverage (0%), and presence of an output schema, the description is inadequate. It does not explain what the tool does, how to use it, or what to expect in terms of behavior or results. The output schema may help with return values, but the description fails to provide essential context for effective tool selection and invocation.

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 1 parameter with 0% description coverage, meaning the parameter 'matrix' is undocumented. The description 'Nullspace.' adds no semantic information about this parameter, such as what format the matrix should be in (e.g., string representation, SymPy object) or any constraints. This fails to compensate for the lack of schema documentation.

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?

The description 'Nullspace.' is a tautology that restates the tool name without providing meaningful context. It does not specify what action is performed (e.g., 'compute' or 'find') or what resource is involved (e.g., 'of a matrix'), nor does it distinguish this tool from its many sibling tools in the SymPy family. While 'nullspace' is a mathematical term, the description fails to articulate the tool's function clearly for an AI 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?

The description provides no guidance on when to use this tool versus alternatives. It does not mention any context, prerequisites, or sibling tools (e.g., other matrix operations like sympy_matrix_rank or sympy_matrix_inverse) that might be relevant. Without such information, an AI agent lacks direction on appropriate usage scenarios.

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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