numpoly.sortable_proxy

numpoly.sortable_proxy(poly: numpoly.typing.PolyLike, graded: bool = False, reverse: bool = False) → numpy.ndarray

Create a numerical proxy for a polynomial to allow compare.

As polynomials are not inherently sortable, values are sorted using the highest lexicographical ordering. Between the values that have the same highest ordering, the elements are sorted using the coefficients. This also ensures that the method behaves as expected with numpy.ndarray.

Args:

poly:

Polynomial to convert into something sortable.

graded:

Graded sorting, meaning the indices are always sorted by the index sum. E.g. q0**2*q1**2*q2**2 has an exponent sum of 6, and will therefore be consider larger than both q0**3*q1*q2, q0*q1**3*q2 and q0*q1*z**3.

reverse:

Reverses lexicographical sorting meaning that q0*q1**3 is considered bigger than q0**3*q1, instead of the opposite.

Return:

Integer array where a > b is retained for the giving rule of ordering.

Example:

>>> q0, q1 = numpoly.variable(2)
>>> poly = numpoly.polynomial(
...     [q0**2, 2*q0, 3*q1, 4*q0, 5])
>>> numpoly.sortable_proxy(poly)
array([3, 1, 4, 2, 0])
>>> numpoly.sortable_proxy(poly, reverse=True)
array([4, 2, 1, 3, 0])
>>> numpoly.sortable_proxy([8, 4, 10, -100])
array([2, 1, 3, 0])
>>> numpoly.sortable_proxy([[8, 4], [10, -100]])
array([[2, 1],
       [3, 0]])