numpy.polynomial.legendre.legdiv()

Divide one Legendre series by another.

Returns the quotient-with-remainder of two Legendre series c1 / c2. The arguments are sequences of coefficients from lowest order ?term? to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Notes

In general, the (polynomial) division of one Legendre series by another results in quotient and remainder terms that are not in the Legendre polynomial basis set. Thus, to express these results as a Legendre series, it is necessary to ?reproject? the results onto the Legendre basis set, which may produce ?unintuitive? (but correct) results; see Examples section below.

Examples

>>> from numpy.polynomial import legendre as L
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> L.legdiv(c1,c2) # quotient "intuitive," remainder not
(array([ 3.]), array([-8., -4.]))
>>> c2 = (0,1,2,3)
>>> L.legdiv(c2,c1) # neither "intuitive"
(array([-0.07407407,  1.66666667]), array([-1.03703704, -2.51851852]))