numpoly.lead_exponent

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

Find the lead exponents for each polynomial.

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.

Args:

poly:

Polynomial to locate exponents on.

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 with the largest exponents in the polynomials. The shape is poly.shape + (len(poly.names),). The extra dimension is used to indicate the exponent for the different indeterminants.

Example:

>>> q0 = numpoly.variable()
>>> numpoly.lead_exponent([1, q0+1, q0**2+q0+1]).T
array([[0, 1, 2]])
>>> q0, q1 = numpoly.variable(2)
>>> numpoly.lead_exponent(
...     [1, q0, q1, q0*q1, q0**3-1]).T
array([[0, 1, 0, 1, 3],
       [0, 0, 1, 1, 0]])