Math & Numbers

Newton-Raphson Root Finder

Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/newton-raphson-root-finder' \
  -H 'Content-Type: application/json' \
  -d '{"fxExpr":"x^2 - 2","dfxExpr":"","x0":1,"tolerance":1e-10,"maxIter":50,"decimalPlaces":10}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/newton-raphson-root-finder

Parameters

Name	Type	Required	Description
fxExpr	text	Yes	The function whose root is sought, in the variable x. Supports + - * / ^, parentheses, and functions like exp, sin, cos, sqrt, ln.
dfxExpr	text	No	Optional analytic derivative; when blank a central difference (h ≈ 1e-7) is used.
x0	number	No	Starting point of the iteration.
tolerance	number	No	Convergence threshold on \|f(x)\| and on the step size.
maxIter	number

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-newton-raphson-root-finder": {
      "name": "newton-raphson-root-finder",
      "description": "Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=newton-raphson-root-finder",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "newton-raphson-root-finder",
    "arguments": {
  "fxExpr": "x^2 - 2",
  "dfxExpr": "",
  "x0": 1,
  "tolerance": 1e-10,
  "maxIter": 50,
  "decimalPlaces": 10
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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