"""Return element-wise remainder of polynomial division."""
from __future__ import annotations
from typing import Any, Optional
import numpy
import numpy.typing
from ...baseclass import ndpoly, PolyLike
from ...dispatch import implements_function
from .divmod import poly_divmod
[docs]@implements_function(numpy.remainder)
def poly_remainder(
x1: PolyLike,
x2: PolyLike,
out: Optional[ndpoly] = None,
where: numpy.typing.ArrayLike = True,
**kwargs: Any,
) -> ndpoly:
"""
Return element-wise remainder of polynomial division.
Args:
x1:
Dividend array.
x2:
Divisor array. If ``x1.shape != x2.shape``, they must be
broadcastable to a common shape (which becomes the shape of the
output).
out:
A location into which the result is stored. If provided, it must
have a shape that the inputs broadcast to. If not provided or
`None`, a freshly-allocated array is returned. A tuple (possible
only as a keyword argument) must have length equal to the number of
outputs.
where:
This condition is broadcast over the input. At locations where the
condition is True, the `out` array will be set to the ufunc result.
Elsewhere, the `out` array will retain its original value. Note
that if an uninitialized `out` array is created via the default
``out=None``, locations within it where the condition is False will
remain uninitialized.
kwargs:
Keyword args passed to numpy.ufunc.
Return:
The element-wise remainder of the quotient ``floor_divide(x1, x2)``.
This is a scalar if both `x1` and `x2` are scalars.
Note:
Unlike numbers, this returns the polynomial division and polynomial
remainder. This means that this function is _not_ backwards compatible
with ``numpy.remainder`` for constants. For example:
``numpoly.remainder(11, 2) == 1`` while
``numpoly.poly_remainder(11, 2) == 0``.
Example:
>>> q0, q1 = numpoly.variable(2)
>>> denominator = [q0*q1**2+2*q0**3*q1**2, -2+q0*q1**2]
>>> numerator = -2+q0*q1**2
>>> numpoly.poly_remainder(denominator, numerator)
polynomial([4.0*q0**2+2.0, 0.0])
"""
dividend, remainder = poly_divmod(x1, x2, out=out, where=where, **kwargs)
return remainder