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numpy.polydiv — NumPy v2.3 Manual

numpy.polydiv(u, v)[source]#

Returns the quotient and remainder of polynomial division.

Note

This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.

The input arrays are the coefficients (including any coefficients equal to zero) of the “numerator” (dividend) and “denominator” (divisor) polynomials, respectively.

Parameters:

uarray_like or poly1d

Dividend polynomial’s coefficients.

varray_like or poly1d

Divisor polynomial’s coefficients.

Returns:

qndarray

Coefficients, including those equal to zero, of the quotient.

rndarray

Coefficients, including those equal to zero, of the remainder.

Notes

Both u and v must be 0-d or 1-d (ndim = 0 or 1), but u.ndim need not equal v.ndim. In other words, all four possible combinations - u.ndim = v.ndim = 0, u.ndim = v.ndim = 1, u.ndim = 1, v.ndim = 0, and u.ndim = 0, v.ndim = 1 - work.

Examples

\[\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25\]

>>> x = np.array([3.0, 5.0, 2.0])
>>> y = np.array([2.0, 1.0])
>>> np.polydiv(x, y)
(array([1.5 , 1.75]), array([0.25]))

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