numpy.polynomial.chebyshev.chebdiv

numpy.polynomial.chebyshev.chebdiv(c1, c2)

Divide one Chebyshev series by another.

Returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2.

Parameters:

c1, c2 : array_like

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

Returns:

[quo, rem] : ndarrays

Of Chebyshev series coefficients representing the quotient and remainder.

See also

chebadd, chebsub, chemulx, chebmul, chebpow

Notes

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

Examples

>>> from numpy.polynomial import chebyshev as C
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> C.chebdiv(c1,c2) # quotient "intuitive," remainder not
(array([3.]), array([-8., -4.]))
>>> c2 = (0,1,2,3)
>>> C.chebdiv(c2,c1) # neither "intuitive"
(array([0., 2.]), array([-2., -4.]))