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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
zain-cs wants to merge 2 commits into
TheAlgorithms:masterfrom
zain-cs:master

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@zain-cs zain-cs commented Jun 19, 2026

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Describe your change:

Fixes #14817

points_to_polynomial crashed with ZeroDivisionError for any input
containing x=0. The Gaussian elimination had no pivoting, so when
matrix[count][count] was zero it divided by zero.

Added partial pivoting before each elimination step — swaps in the row
with the largest absolute value in the current column, preventing
zero-division and improving numerical stability. Updated doctests to
reflect the corrected output.

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes linear_algebra/polynom_for_points: ZeroDivisionError on valid points containing x=0 (Gaussian elimination without pivoting) #14817".

@algorithms-keeper algorithms-keeper Bot added enhancement This PR modified some existing files awaiting reviews This PR is ready to be reviewed labels Jun 19, 2026
@algorithms-keeper algorithms-keeper Bot added tests are failing Do not merge until tests pass and removed tests are failing Do not merge until tests pass labels Jun 19, 2026
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linear_algebra/polynom_for_points: ZeroDivisionError on valid points containing x=0 (Gaussian elimination without pivoting)

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