Polynomial GCD / Factoring 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

t8-015

Effect

Computation or source lookup only

Input and validation requirements

The zero-zero input exposes an undefined GCD and undefined zero-polynomial factorization that the specification does not state how to reject or represent. The convention probe also exposes an unstated choice between monic rational GCDs and primitive integer-content GCDs.

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": {
    "A": "x^4 - 1",
    "B": "x^3 - x^2 - x + 1",
    "domain": "Q",
    "gcd_normalization": "monic"
  },
  "expected_outputs": {
    "gcd": "x^2 - 1",
    "factorization_A": "(x - 1)(x + 1)(x^2 + 1)",
    "factorization_B": "(x - 1)^2(x + 1)",
    "spot_checks": [
      {
        "at": 2,
        "input_side": 3,
        "answer_side": 3
      },
      {
        "at": 3,
        "input_side": 8,
        "answer_side": 8
      }
    ]
  },
  "reference_data": {
    "input_side_definition": "The common-factor representation evaluates (x^2-1)=(x-1)(x+1); answer_side evaluates the returned gcd x^2-1.",
    "euclidean_check": "A=(x^2-1)(x^2+1), B=(x^2-1)(x-1), so the monic gcd is x^2-1."
  },
  "working": "Factor A: x^4-1=(x^2-1)(x^2+1)=(x-1)(x+1)(x^2+1). Factor B by grouping: x^3-x^2-x+1=x^2(x-1)-1(x-1)=(x^2-1)(x-1)=(x-1)^2(x+1). The common monic factor is x^2-1. At x=2: x^2-1=4-1=3, and (x-1)(x+1)=1*3=3. At x=3: x^2-1=9-1=8, and (x-1)(x+1)=2*4=8."
}

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