Polynomial Root Finder implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t8-012

Effect

Computation or source lookup only

Input and validation requirements

The degree-3 input with a zero leading coefficient exposes an undefined normalization step: a cubic routine can require division by zero. The instrument must reject it or explicitly trim leading zeros and reinterpret the polynomial; silently proceeding is unsafe.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "coefficient_order": "descending powers",
    "coefficients": [
      1,
      -5,
      6
    ],
    "polynomial": "x^2 - 5x + 6"
  },
  "expected_outputs": {
    "roots": [
      "2",
      "3"
    ],
    "multiplicities": {
      "2": 1,
      "3": 1
    },
    "factored_form": "(x - 2)(x - 3)",
    "rational_root_candidates": [
      "1",
      "2",
      "3",
      "6"
    ],
    "residuals": {
      "p(2)": "0",
      "p(3)": "0"
    },
    "spot_checks": [
      {
        "at": 2,
        "input_side": 0,
        "answer_side": 0
      },
      {
        "at": 3,
        "input_side": 0,
        "answer_side": 0
      }
    ]
  },
  "reference_data": {
    "method": "quadratic factorization and rational-root theorem",
    "canonical_result": "x^2 - 5x + 6 = (x - 2)(x - 3)"
  },
  "working": "p(x)=x^2-5x+6. Candidate 2: p(2)=2^2-5(2)+6=4-10+6=0. Candidate 3: p(3)=3^2-5(3)+6=9-15+6=0. Therefore p(x)=(x-2)(x-3), so the roots are 2 and 3, each with multiplicity 1. The integer candidate set is ±1, ±2, ±3, ±6; the positive candidates that test as roots are 2 and 3."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche8/tranche8-results.json