Source: https://guthlabs.ai/docs/instruments/polynomial-operations-add-sub-mul-div-synthetic-division/implementation/

instrument implementation / implementation-contract

# Polynomial Operations (add/sub/mul/div/synthetic division) implementation

A source-bound implementation contract for Polynomial Operations (add/sub/mul/div/synthetic division); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## 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**: t2-033

**Effect**: Computation or source lookup only

## Input and validation requirements

The instrument specification does not define coefficient-list ordering, so identical inputs can be interpreted as different polynomials. It also does not explicitly state the required behavior for a zero divisor; such an input must be rejected as undefined.

## 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": {
    "operation": "add_and_subtract",
    "polynomial_a": [
      3,
      -2,
      5
    ],
    "polynomial_b": [
      -1,
      4,
      0
    ]
  },
  "expected_outputs": {
    "sum": [
      2,
      2,
      5
    ],
    "difference_a_minus_b": [
      4,
      -6,
      5
    ]
  },
  "working": "A=3x^2-2x+5 and B=-x^2+4x+0. Sum: (3+(-1))x^2+(-2+4)x+(5+0)=2x^2+2x+5, so [2,2,5]. Difference: (3-(-1))x^2+(-2-4)x+(5-0)=4x^2-6x+5, so [4,-6,5]."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/polynomial-operations-add-sub-mul-div-synthetic-division/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/polynomial-operations-add-sub-mul-div-synthetic-division/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/polynomial-operations-add-sub-mul-div-synthetic-division/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche2/tranche2-results.json`