TheAlgorithms/Python · error · ValueError

The program cannot work out a fitting polynomial.

Error message

The program cannot work out a fitting polynomial.

What it means

Raised by points_to_polynomial when the coordinates argument is empty or contains elements that are not (x, y) pairs. The function fits a polynomial through points via a Vandermonde-style linear system, so it needs at least one well-formed 2-element pair to build that system. Malformed input makes the system unbuildable, so it fails fast with ValueError.

Source

Thrown at linear_algebra/src/polynom_for_points.py:38

    >>> points_to_polynomial([[1, 1], [2, 2], [3, 3]])
    'f(x)=x^2*0.0+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'
    >>> points_to_polynomial([[1, 3], [2, 6], [3, 11]])
    'f(x)=x^2*1.0+x^1*-0.0+x^0*2.0'
    >>> points_to_polynomial([[1, -3], [2, -6], [3, -11]])
    'f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0'
    >>> points_to_polynomial([[1, 5], [2, 2], [3, 9]])
    'f(x)=x^2*5.0+x^1*-18.0+x^0*18.0'
    >>> 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.
    """
    if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
        raise ValueError("The program cannot work out a fitting polynomial.")

    if len({tuple(pair) for pair in coordinates}) != len(coordinates):
        raise ValueError("The program cannot work out a fitting polynomial.")

    set_x = {x for x, _ in coordinates}
    if len(set_x) == 1:
        return f"x={coordinates[0][0]}"

    if len(set_x) != len(coordinates):
        raise ValueError("The program cannot work out a fitting polynomial.")

    x = len(coordinates)

    # put the x and x to the power values in a matrix
    matrix: list[list[float]] = [
        [
            coordinates[count_of_line][0] ** (x - (count_in_line + 1))
            for count_in_line in range(x)

View on GitHub (pinned to f5988cc097)

Solutions

1. Ensure every element of the input list is exactly a 2-element pair, e.g. [(x0, y0), (x1, y1), ...].
2. Filter or reject malformed rows before calling: coordinates = [p for p in data if len(p) == 2].
3. If the input is empty, either skip the call or supply at least one valid point.

Example fix

# before
points_to_polynomial([[1, 2, 3], [4, 5]])

# after
points_to_polynomial([(1, 2), (4, 5)])

def valid_coordinates(coords):
    return len(coords) > 0 and all(len(p) == 2 for p in coords)

if not valid_coordinates(coordinates):
    raise ValueError("coordinates must be a non-empty list of (x, y) pairs")
poly = points_to_polynomial(coordinates)

def is_valid_point_list(coords: list) -> bool:
    return bool(coords) and all(
        isinstance(p, (list, tuple)) and len(p) == 2 for p in coords
    )

try:
    poly = points_to_polynomial(coordinates)
except ValueError as e:
    logger.error("invalid coordinates input: %s", e)
    raise

When it happens

Trigger: Calling points_to_polynomial([]) with an empty list, or passing pairs of the wrong arity such as [[1, 2, 3]] or [[1]] or [[1, 2], [3]] (any element whose len() != 2).

Common situations: Passing unvalidated data from a CSV/JSON file where rows have extra columns, passing a flat list of numbers instead of pairs, or passing a list of triples from a 3D-point pipeline.

Related errors

• Expected a_coeffs to have {self.order + 1} elements for {sel
• n must not be negative
• Depth cannot be less than 0
• The parameter costs should be a list of three integers
• number_of_years must be > 0

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/66c053dfbf12e4df. Report an issue: GitHub.