Partial Fraction Decomposition 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

t8-017

Effect

Computation or source lookup only

Input and validation requirements

The zero-denominator vector is an unavoidable undefined-result trap: the instrument must reject an identically zero denominator. The convention probe also exposes a correctness hazard unless polynomial coefficient order is explicitly fixed.

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": {
    "numerator": "2x + 3",
    "denominator": "(x - 1)(x + 2)"
  },
  "expected_outputs": {
    "canonical_exact": "5/(3(x - 1)) + 1/(3(x + 2))",
    "spot_checks": [
      {
        "at": "x = 0.00000000",
        "input_side": -1.5,
        "answer_side": -1.5
      },
      {
        "at": "x = 3.0000000",
        "input_side": 0.9,
        "answer_side": 0.9
      }
    ]
  },
  "reference_data": {
    "method": "Distinct-linear-factor coefficient matching",
    "domain": "real numbers",
    "excluded_points": [
      "x = 1",
      "x = -2"
    ]
  },
  "working": "Assume (2x+3)/((x-1)(x+2)) = A/(x-1) + B/(x+2). Multiply by (x-1)(x+2): 2x+3 = A(x+2)+B(x-1) = (A+B)x + (2A-B). Thus A+B=2 and 2A-B=3. Adding the equations gives 3A=5, so A=5/3. Then B=2-5/3=1/3. At x=0: original = 3/((-1)(2)) = -3/2 = -1.5000000; answer = (5/3)/(-1)+(1/3)/2 = -5/3+1/6 = -3/2 = -1.5000000. At x=3: original = 9/((2)(5)) = 9/10 = 0.90000000; answer = (5/3)/2+(1/3)/5 = 5/6+1/15 = 9/10 = 0.90000000."
}

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