FA-6126 / Polynomial arithmetic / Open access
Polynomial degree trailing zeroes · case 01
Storage length is mistaken for the highest nonzero degree.
ROOT CAUSE
Storage length is mistaken for the highest nonzero degree.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return max((i for i,c in enumerate(coeff) if c),default=-1)
Unsuccessful approach: The lowest nonzero degree is selected instead.
Case contract
Integer coefficients in ascending power order and integer evaluation bounds; missing high-degree coefficients are zero. Rational outputs are reduced Fraction strings; the zero-polynomial degree is -1. Polynomial degree trailing zeroes. Exact operational definition: max((i for i,c in enumerate(coeff) if c),default=-1)
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Polynomial arithmetic results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return len(coeff)-1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 0, 0],)', solve(*([1, 2, 0, 0],)), 1)
check('fixture 2: ([0, 0],)', solve(*([0, 0],)), -1)
check('fixture 3: ([],)', solve(*([],)), -1)
check('fixture 4: ([0, 0, 3],)', solve(*([0, 0, 3],)), 2)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 0, 0],) | 3 | 1 | Failed |
| fixture 2: ([0, 0],) | 1 | -1 | Failed |
| fixture 3: ([],) | -1 | -1 | Passed |
| fixture 4: ([0, 0, 3],) | 2 | 2 | Passed |
SHA-256 / fdef1b221457bf2a700ee2e444683b15c550c0e459212fc5f841bcbbc4ca69bd
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return next((i for i,c in enumerate(coeff) if c),-1)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 0, 0],)', solve(*([1, 2, 0, 0],)), 1)
check('fixture 2: ([0, 0],)', solve(*([0, 0],)), -1)
check('fixture 3: ([],)', solve(*([],)), -1)
check('fixture 4: ([0, 0, 3],)', solve(*([0, 0, 3],)), 2)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 0, 0],) | 0 | 1 | Failed |
| fixture 2: ([0, 0],) | -1 | -1 | Passed |
| fixture 3: ([],) | -1 | -1 | Passed |
| fixture 4: ([0, 0, 3],) | 2 | 2 | Passed |
SHA-256 / e41c0b1cf3c94da911b074af494f6695214a96c6cae2d2f1055816773d2e0df9
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(coeff):
return max((i for i,c in enumerate(coeff) if c),default=-1)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 0, 0],)', solve(*([1, 2, 0, 0],)), 1)
check('fixture 2: ([0, 0],)', solve(*([0, 0],)), -1)
check('fixture 3: ([],)', solve(*([],)), -1)
check('fixture 4: ([0, 0, 3],)', solve(*([0, 0, 3],)), 2)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: ([1, 2, 0, 0],) | 1 | 1 | Passed |
| fixture 2: ([0, 0],) | -1 | -1 | Passed |
| fixture 3: ([],) | -1 | -1 | Passed |
| fixture 4: ([0, 0, 3],) | 2 | 2 | Passed |
SHA-256 / ffecc320ffd2e70740b97ebeb270acf3e974e38fb9b340c0692271ab923a6e40
Verification & scope
This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:37:57.852766+00:00.
Case digest / e8785acdf5467ede7fd995bb07b7a450c9627c05f749f89d0f66167d764af664