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Fix ZeroDivisionError in polynom_for_points by adding partial pivoting #14827

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Fix ZeroDivisionError in polynom_for_points by adding partial pivoting #14827

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Fix ZeroDivisionError in polynom_for_points by adding partial pivoting
zain-cs Jun 19, 2026
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[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Jun 19, 2026
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25 changes: 17 additions & 8 deletions linear_algebra/src/polynom_for_points.py
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Original file line number Diff line number Diff line change
Expand Up @@ -12,27 +12,31 @@ def points_to_polynomial(coordinates: list[list[int]]) -> str:
...
ValueError: The program cannot work out a fitting polynomial.
>>> points_to_polynomial([[1, 0], [2, 0], [3, 0]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*0.0'
'f(x)=x^2*0.0+x^1*0.0+x^0*0.0'
>>> points_to_polynomial([[1, 1], [2, 1], [3, 1]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*1.0'
'f(x)=x^2*0.0+x^1*0.0+x^0*1.0'
>>> points_to_polynomial([[1, 3], [2, 3], [3, 3]])
'f(x)=x^2*0.0+x^1*-0.0+x^0*3.0'
'f(x)=x^2*0.0+x^1*0.0+x^0*3.0'
>>> points_to_polynomial([[1, 1], [2, 2], [3, 3]])
'f(x)=x^2*0.0+x^1*1.0+x^0*0.0'
'f(x)=x^2*4.9343245538895844e-17+x^1*1.0+x^0*0.0'
>>> points_to_polynomial([[1, 1], [2, 4], [3, 9]])
'f(x)=x^2*1.0+x^1*-0.0+x^0*0.0'
'f(x)=x^2*1.0+x^1*0.0+x^0*0.0'
>>> points_to_polynomial([[1, 3], [2, 6], [3, 11]])
'f(x)=x^2*1.0+x^1*-0.0+x^0*2.0'
'f(x)=x^2*0.9999999999999996+x^1*9.992007221626407e-16+x^0*1.9999999999999993'
>>> points_to_polynomial([[1, -3], [2, -6], [3, -11]])
'f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0'
'f(x)=x^2*-0.9999999999999996+x^1*-9.992007221626407e-16+x^0*-1.9999999999999993'
>>> points_to_polynomial([[1, 5], [2, 2], [3, 9]])
'f(x)=x^2*5.0+x^1*-18.0+x^0*18.0'
'f(x)=x^2*5.0+x^1*-18.000000000000004+x^0*18.000000000000004'
>>> points_to_polynomial([[1, 1], [1, 2], [1, 3]])
'x=1'
>>> points_to_polynomial([[1, 1], [2, 2], [2, 2]])
Traceback (most recent call last):
...
ValueError: The program cannot work out a fitting polynomial.
>>> points_to_polynomial([[0, 1], [1, 2], [2, 5]])
'f(x)=x^2*1.0+x^1*0.0+x^0*1.0'
>>> points_to_polynomial([[0, 0], [1, 1], [2, 4]])
'f(x)=x^2*1.0+x^1*0.0+x^0*0.0'
"""
if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
raise ValueError("The program cannot work out a fitting polynomial.")
Expand Down Expand Up @@ -62,6 +66,11 @@ def points_to_polynomial(coordinates: list[list[int]]) -> str:
vector: list[float] = [coordinates[count_of_line][1] for count_of_line in range(x)]

for count in range(x):
# Partial pivoting: swap in the row with the largest absolute pivot value
max_row = max(range(count, x), key=lambda r: abs(matrix[r][count]))
matrix[count], matrix[max_row] = matrix[max_row], matrix[count]
vector[count], vector[max_row] = vector[max_row], vector[count]

for number in range(x):
if count == number:
continue
Expand Down