numpy.polynomial.legendre.legdiv¶

numpy.polynomial.legendre.
legdiv
(c1, c2)[source]¶ Divide one Legendre series by another.
Returns the quotientwithremainder 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
.Parameters: c1, c2 : array_like
1D arrays of Legendre series coefficients ordered from low to high.
Returns: quo, rem : ndarrays
Of Legendre series coefficients representing the quotient and remainder.
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]))