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sympy_groebner

Compute Groebner bases for polynomial systems to solve algebraic equations, ideal membership, and elimination problems using symbolic mathematics.

Instructions

Groebner basis.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprsYes
variableNox

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 carries full burden for behavioral disclosure. The description says nothing about what the tool does behaviorally - whether it's a computation, transformation, or analysis tool; what it returns; whether it has side effects; performance characteristics; or error conditions. For a mathematical tool with zero annotation coverage, this is completely inadequate.

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 technically concise with just two words, this is under-specification rather than effective conciseness. The description doesn't contain enough information to be useful. Good conciseness balances brevity with completeness - this fails to provide even basic operational understanding.

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 complexity of Groebner basis computation (a non-trivial mathematical operation), zero annotation coverage, 0% schema description coverage, and the presence of many similar mathematical sibling tools, this description is completely inadequate. While an output schema exists, the description doesn't explain what the tool does, when to use it, or how to use it - failing at the most basic level of contextual completeness.

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%, meaning neither parameter (exprs, variable) has any documentation in the schema. The description provides no information about what these parameters mean, their expected formats, or how they're used. For a tool with 2 parameters (one required), this leaves the agent completely in the dark about how to invoke the tool correctly.

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 'Groebner basis.' is a tautology that merely restates the tool name without explaining what it does. It lacks a specific verb and resource, and doesn't distinguish it from sibling tools like sympy_solve or sympy_factor which also perform mathematical operations. A user or AI agent would not understand the tool's function from this description.

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 absolutely no guidance on when to use this tool versus alternatives. With many sibling tools for symbolic mathematics (e.g., sympy_solve, sympy_factor, sympy_simplify), there's no indication of what problems Groebner basis computation addresses or when it's the appropriate choice. This leaves the agent guessing.

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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