`numpy.polynomial.legendre:legdiv`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/legendre.py :532

Signature

def legdiv ( c1 , c2 )

Summary

Divide one Legendre series by another.

Extended Summary

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.

Parameters

c1, c2 : array_like: 1-D 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
c2 = (0,1,2,3)

✓

L.legdiv(c2,c1) # neither "intuitive"

✗

Aliases

numpy.polynomial.Legendre._div
numpy.polynomial.legendre.legdiv