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The Lambert W function `W(z)` is defined as the inverse function
of `w \exp(w)`. In other words, the value of `W(z)` is such that
`z = W(z) \exp(W(z))` for any complex number `z`.

The Lambert W function is a multivalued function with infinitely
many branches `W_k(z)`, indexed by `k \in \mathbb{Z}`. Each branch
gives a different solution `w` of the equation `z = w \exp(w)`.
All branches are supported by :func:`~mpmath.lambertw`:

* ``lambertw(z)`` gives the principal solution (branch 0)(more...)

src/s/y/sympy-0.7.5/sympy/mpmath/tests/test_fp.py   sympy(Download)
def test_fp_lambertw():
    assert ae(fp.lambertw(0.0), 0.0)
    assert ae(fp.lambertw(1.0), 0.567143290409783873)
    assert ae(fp.lambertw(7.5), 1.5662309537823875394)
    assert ae(fp.lambertw(-0.25), -0.35740295618138890307)
    assert ae(fp.lambertw(-10.0), (1.3699809685212708156 + 2.140194527074713196j))

src/s/y/sympy-HEAD/sympy/mpmath/tests/test_fp.py   sympy(Download)
def test_fp_lambertw():
    assert ae(fp.lambertw(0.0), 0.0)
    assert ae(fp.lambertw(1.0), 0.567143290409783873)
    assert ae(fp.lambertw(7.5), 1.5662309537823875394)
    assert ae(fp.lambertw(-0.25), -0.35740295618138890307)
    assert ae(fp.lambertw(-10.0), (1.3699809685212708156 + 2.140194527074713196j))

src/s/y/sympy-polys-HEAD/sympy/mpmath/tests/test_fp.py   sympy-polys(Download)
def test_fp_lambertw():
    assert ae(fp.lambertw(0.0), 0.0)
    assert ae(fp.lambertw(1.0), 0.567143290409783873)
    assert ae(fp.lambertw(7.5), 1.5662309537823875394)
    assert ae(fp.lambertw(-0.25), -0.35740295618138890307)
    assert ae(fp.lambertw(-10.0), (1.3699809685212708156 + 2.140194527074713196j))