numpy.polynomial.hermite.hermdiv

numpy.polynomial.hermite.hermdiv(c1, c2)

Divide one Hermite series by another.

Returns the quotient-with-remainder of two Hermite 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.

Parameters :

c1, c2 : array_like

1-D arrays of Hermite series coefficients ordered from low to high.

Returns :

[quo, rem] : ndarrays

Of Hermite series coefficients representing the quotient and remainder.

See also

hermadd, hermsub, hermmul, hermpow

Notes

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

Examples

>>> from numpy.polynomial.hermite import hermdiv
>>> hermdiv([ 52.,  29.,  52.,   7.,   6.], [0, 1, 2])
(array([ 1.,  2.,  3.]), array([ 0.]))
>>> hermdiv([ 54.,  31.,  52.,   7.,   6.], [0, 1, 2])
(array([ 1.,  2.,  3.]), array([ 2.,  2.]))
>>> hermdiv([ 53.,  30.,  52.,   7.,   6.], [0, 1, 2])
(array([ 1.,  2.,  3.]), array([ 1.,  1.]))