calculator

newton_method

newton_method

Solve equation roots using Newton's method by providing function type, coefficients, and initial guess. This tool calculates numerical approximations for mathematical equations.

Instructions

使用牛顿法求解方程的根

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "function_type": "<function_type>",
      "coefficients": "<coefficients>",
      "initial_guess": "<initial_guess>"
    },
    "name": "newton_method"
  }
}

Input Schema

Name	Required	Description	Default
`function_type`	Yes
`coefficients`	Yes
`initial_guess`	Yes
`tolerance`	No
`max_iterations`	No

Schema Changelog

Changes observed during successful MCP inspections.

First observedv1.0.0Jan 5, 2026

TDQS

C2.8/5.0

Behavior2/5

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

With no annotations provided, the description carries full burden for behavioral disclosure. It mentions the method but doesn't describe key behaviors: convergence properties (may fail for poor initial guesses), iteration limits, tolerance handling, or output format. For a numerical method with 5 parameters, this leaves significant gaps in understanding how the tool behaves.

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 a single, efficient sentence in Chinese that directly states the tool's purpose without unnecessary words. It's appropriately sized and front-loaded with the core functionality.

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 complexity of a numerical root-finding method with 5 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't address convergence behavior, error handling, output format, or parameter semantics, leaving the agent with insufficient context to use the tool effectively.

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

Parameters2/5

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

Schema description coverage is 0%, so the description must compensate but provides no parameter information. It doesn't explain what 'function_type', 'coefficients', 'initial_guess', 'tolerance', or 'max_iterations' mean or how they interact. For a tool with 5 undocumented parameters, this is inadequate.

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 clearly states the tool's purpose as '使用牛顿法求解方程的根' (use Newton's method to find the root of an equation), which specifies the verb (solve) and resource (equation root). It distinguishes from siblings like bisection_method by naming the specific numerical method, but doesn't explicitly differentiate beyond that.

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 description provides no guidance on when to use this tool versus alternatives like bisection_method or other root-finding approaches. There's no mention of prerequisites (e.g., function differentiability), convergence conditions, or typical use cases where Newton's method is preferred.

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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