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math_solve

Solves algebraic equations, differential equations, and systems of equations symbolically with optional variable specification.

Instructions

求解方程或方程组。

equation: 方程,支持三种写法: (1) 'x^2 - 4 = 0'(显式等式) (2) 'x^2 - 4'(隐式 = 0) (3) 方程组: 'x + y = 10, 2*x - y = 5' 配合 variables='x,y' (4) 微分方程: 'Derivative(f(x),x) + f(x)' 配合 function='f' variables: 待求解变量,默认 'x'。方程组用逗号分隔: 'x,y,z'。 equation_type: 'auto'(自动检测)、'algebraic'、'differential'、'system'。 function: 微分方程中的未知函数名,默认自动从表达式中提取(如 f(x) → f)。

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
equationYes
variablesNox
equation_typeNoauto
functionNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior2/5

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

No annotations exist, so description must disclose behavior. It focuses on input formats but omits output behavior, limitations, or error handling—critical for an AI agent.

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?

Front-loaded purpose and well-structured with bullet points, but slightly verbose; could be more concise without losing clarity.

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?

Covers input comprehensively; output is handled by the existing output schema per rules. Lacks mention of constraints or edge cases.

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

Parameters5/5

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

With 0% schema description coverage, the description fully compensates by explaining each parameter with examples and defaults, adding significant meaning.

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

Purpose5/5

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

The description clearly states it solves equations and systems, with a specific verb 'solve' and resource. Sibling tools like math_calculus and math_eval are distinct, so purpose is well-defined.

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

Usage Guidelines4/5

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

Provides examples of different equation types and how to set parameters, but no explicit comparison to siblings or when-not-to-use.

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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