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math_manipulate

Transform and simplify mathematical expressions with operations like simplify, expand, factor, cancel, and more. Supports trigonometric and radical simplification, partial fractions, and domain computation.

Instructions

表达式变换与化简。

expression: 数学表达式。 operation: simplify — 通用化简 expand — 展开 factor — 因式分解 cancel — 约分有理函数 apart — 部分分式分解 together — 通分 collect — 按变量合并同类项(会用 variable 参数或自动选主变量) trigsimp — 三角化简 radsimp — 根式化简 piecewise_fold — 分段函数折叠 domain — 求定义域 variable: 用于 collect 操作的变量名(可选,不填则自动选第一个自由变量)。

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
expressionYes
operationNosimplify
variableNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior3/5

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

The description adds behavioral details for some operations (e.g., collect uses variable parameter or auto-selects), but lacks comprehensive behavior disclosure such as error handling, restrictions, or side effects. Since no annotations are provided, the description partially compensates but is not fully transparent.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and well-structured: a clear statement of purpose followed by a bullet list of operations with short descriptions. No unnecessary text, and the most important information (purpose) is front-loaded.

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

Completeness4/5

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

Given the tool's complexity, parameter count, and presence of output schema, the description covers the main operations adequately. It does not explain return values or edge cases, but the output schema likely handles that. Some missing context like error behavior or expression format expectations.

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?

Input schema coverage is 0%, but the description clearly explains each parameter: expression is the math expression, operation lists all options with brief descriptions, and variable is for collect with auto-selection note. This adds significant meaning beyond the schema, though explanations could be more detailed.

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?

The description states '表达式变换与化简' (expression transformation and simplification), clearly indicating the tool's purpose. It lists many specific operations, making the scope well-defined. However, it does not explicitly distinguish from sibling tools like math_solve or math_eval, but the operations are distinct enough.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage through the listed operations (e.g., simplify, expand, factor), but does not provide explicit guidance on when to use this tool versus alternatives like math_solve or math_calculus. No when-not-to-use or alternative tool mentions are 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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