curl --request POST \
  --url https://api.iotools.cloud/v1/tool/descartes-rule-of-signs-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "coefficients": "1,-3,2,5,-1"
}
'

{
  "tool": "descartes-rule-of-signs-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "degree": "4",
    "positiveSignChanges": "3",
    "negativeSignChanges": "1",
    "possiblePositiveRoots": "3, 1",
    "possibleNegativeRoots": "1",
    "rootCombinations": [
      {
        "positive": "3",
        "negative": "1",
        "complex": "0"
      },
      {
        "positive": "1",
        "negative": "1",
        "complex": "2"
      }
    ],
    "steps": "f(x) = x^4 - 3x^3 + 2x^2 + 5x - 1  (degree 4)\nCoefficients of f(x), zeros skipped: 1, -3, 2, 5, -1 → 3 sign changes.\nf(-x) = x^4 + 3x^3 + 2x^2 - 5x - 1\nCoefficients of f(-x), zeros skipped: 1, 3, 2, -5, -1 → 1 sign change.\nPossible positive real roots: 3, 1 (start at 3 sign changes, subtract 2 each step).\nPossible negative real roots: 1 (start at 1 sign changes, subtract 2 each step).\nEvery (positive, negative) pair from those lists whose sum ≤ degree fills the rest with complex-conjugate pairs (degree − positive − negative): 2 valid combinations."
  },
  "credits_used": 5,
  "credits_remaining": null
}